%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW322+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:57 EDT 2023

% Result   : Theorem 48.29s 47.23s
% Output   : Proof 48.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW322+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.34  % Computer : n014.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu May 18 22:33:12 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 48.29/47.23  
% 48.29/47.23  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 48.29/47.23  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 48.29/47.23  %-----------------------------------------------------
% 48.29/47.23  ncf(matrix, plain, [(52451 ^ _2080615) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q, v_x))), hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P)), v_c0)), v_Q)), v_F)))], !, (31228 ^ _780478) ^ [_1361727, _1361729, _1361731, _1361733] : [-(hAPP(c_Set_Ovimage(_1361727, _1361729, _1361731), hAPP(c_Set_OCollect(_1361729), _1361733)) = hAPP(c_Set_OCollect(_1361727), hAPP(hAPP(c_COMBB(_1361729, tc_HOL_Obool, _1361727), _1361733), _1361731)))], (35573 ^ _780478) ^ [_1450124, _1450126] : [-(c_Fun_Oinj__on(tc_fun(_1450124, _1450126), tc_fun(tc_prod(_1450124, _1450126), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1450124, _1450126), tc_HOL_Obool), tc_fun(tc_prod(_1450124, _1450126), tc_HOL_Obool), tc_fun(_1450124, _1450126)), c_Set_OCollect(tc_prod(_1450124, _1450126))), hAPP(hAPP(c_COMBB(tc_fun(_1450124, tc_fun(_1450126, tc_HOL_Obool)), tc_fun(tc_prod(_1450124, _1450126), tc_HOL_Obool), tc_fun(_1450124, _1450126)), c_Product__Type_Oprod_Oprod__case(_1450124, _1450126, tc_HOL_Obool)), hAPP(c_COMBB(_1450126, tc_fun(_1450126, tc_HOL_Obool), _1450124), hAPP(c_COMBC(_1450126, _1450126, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1450124, _1450126), tc_HOL_Obool))))], (40412 ^ _780478) ^ [_1570152, _1570154] : [-(hAPP(c_Relation_ORange(_1570152, _1570152), c_Transitive__Closure_Otrancl(_1570152, _1570154)) = hAPP(c_Relation_ORange(_1570152, _1570152), _1570154))], (50624 ^ _780478) ^ [_1804561, _1804563, _1804565, _1804567, _1804569] : [c_Fun_Obij__betw(_1804561, _1804563, _1804565, c_Orderings_Otop__class_Otop(tc_fun(_1804561, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804563, tc_HOL_Obool))), 50627 ^ _780478 : [(50634 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1804563, tc_HOL_Obool)), _1804567), hAPP(c_Set_Oimage(_1804561, _1804563, _1804565), _1804569))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1804561, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1804561, _1804563, _1804565), _1804567)), _1804569)))], (50628 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1804561, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1804561, _1804563, _1804565), _1804567)), _1804569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1804563, tc_HOL_Obool)), _1804567), hAPP(c_Set_Oimage(_1804561, _1804563, _1804565), _1804569))))]]], (18187 ^ _780478) ^ [_1120574, _1120576] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120574)), hAPP(c_Nat_OSuc, _1120576)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1120574), _1120576)))], (44203 ^ _780478) ^ [_1665134, _1665136, _1665138] : [-(hAPP(c_List_Orotate(_1665134, _1665136), _1665138) = hAPP(hAPP(c_List_Oappend(_1665134), hAPP(hAPP(c_List_Odrop(_1665134), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1665136, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665134)), _1665138))), _1665138)), hAPP(hAPP(c_List_Otake(_1665134), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1665136, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665134)), _1665138))), _1665138)))], (3836 ^ _780478) ^ [_838003, _838005, _838007, _838009, _838011, _838013] : [-(c_List_OtakeWhile(_838013, _838009, _838005) = c_List_OtakeWhile(_838011, _838007, _838003)), _838013 = _838011, _838009 = _838007, _838005 = _838003], (36367 ^ _780478) ^ [_1472544, _1472546, _1472548, _1472550, _1472552] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1472544, _1472546)), hAPP(hAPP(c_Product__Type_OPair(_1472544, _1472546), _1472550), _1472552)), _1472548)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1472544, _1472546, _1472548), _1472550), _1472552)))], (22129 ^ _780478) ^ [_1191822, _1191824, _1191826, _1191828] : [class_Rings_Olinordered__semidom(_1191822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1191824), _1191826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191822), c_Groups_Ozero__class_Ozero(_1191822)), _1191828)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191822), _1191828), c_Groups_Oone__class_Oone(_1191822))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1191822), hAPP(hAPP(c_Power_Opower__class_Opower(_1191822), _1191828), _1191826)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191822), _1191828), _1191824))))], (40039 ^ _780478) ^ [_1561147, _1561149, _1561151, _1561153, _1561155, _1561157, _1561159] : [c_Finite__Set_Ofolding__image(_1561147, _1561149, _1561151, _1561153, _1561155), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561149), _1561157)), -(hAPP(hAPP(_1561155, _1561159), _1561157) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1561147, _1561149, _1561151), _1561159), _1561153), _1561157))], (44963 ^ _780478) ^ [_1681708, _1681710, _1681712, _1681714] : [class_Groups_Ocomm__monoid__add(_1681708), 44966 ^ _780478 : [(44973 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1681710), _1681712))), -(c_Nitpick_Osetsum_H(_1681710, _1681708, _1681714, _1681712) = c_Groups_Ozero__class_Ozero(_1681708))], (44967 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1681710), _1681712)), -(c_Nitpick_Osetsum_H(_1681710, _1681708, _1681714, _1681712) = hAPP(c_List_Omonoid__add__class_Olistsum(_1681708), hAPP(hAPP(c_List_Omap(_1681710, _1681708), _1681714), c_Hilbert__Choice_OEps(tc_List_Olist(_1681710), hAPP(hAPP(c_COMBS(tc_List_Olist(_1681710), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1681710)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1681710), tc_fun(_1681710, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1681710, tc_HOL_Obool), tc_fun(tc_fun(_1681710, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1681710)), c_fequal), c_List_Oset(_1681710))), _1681712))), c_List_Odistinct(_1681710))))))]]], (24153 ^ _780478) ^ [_1230202, _1230204] : [class_Divides_Osemiring__div(_1230202), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230202), _1230204), c_Groups_Ozero__class_Ozero(_1230202)) = c_Groups_Ozero__class_Ozero(_1230202))], (45534 ^ _780478) ^ [_1694302, _1694304, _1694306, _1694308] : [c_List_Olist__all2(_1694302, _1694304, _1694306, _1694308, c_List_Olist_ONil(_1694304)), -(_1694308 = c_List_Olist_ONil(_1694302))], (18794 ^ _780478) ^ [_1133382, _1133384, _1133386] : [class_Lattices_Olattice(_1133382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133382), _1133384)), -(_1133386 = c_Orderings_Obot__class_Obot(tc_fun(_1133382, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133382, tc_HOL_Obool)), _1133386), _1133384)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1133382), c_Big__Operators_Olattice__class_OInf__fin(_1133382, _1133386)), c_Big__Operators_Olattice__class_OInf__fin(_1133382, _1133384)) = c_Big__Operators_Olattice__class_OInf__fin(_1133382, _1133384))], (45853 ^ _780478) ^ [_1701084, _1701086, _1701088] : [class_Orderings_Olinorder(_1701084), -(c_List_Olinorder__class_Osort__key(_1701086, _1701084, _1701088, c_List_Olist_ONil(_1701086)) = c_List_Olist_ONil(_1701086))], (30711 ^ _780478) ^ [_1350888, _1350890, _1350892] : [class_Rings_Olinordered__idom(_1350888), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350888), c_Groups_Ozero__class_Ozero(_1350888)), _1350890)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350888), hAPP(c_Groups_Oabs__class_Oabs(_1350888), _1350892)), _1350890) = hAPP(c_Groups_Oabs__class_Oabs(_1350888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350888), _1350892), _1350890)))], (8912 ^ _780478) ^ [_934160, _934162, _934164] : [class_Orderings_Olinorder(_934160), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934160), _934162), _934164))), -(_934162 = _934164), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934160), _934164), _934162)))], (44552 ^ _780478) ^ [_1672272, _1672274, _1672276] : [-(_1672272 = c_List_Olist_ONil(_1672274)), -(c_List_Olast(_1672274, hAPP(hAPP(c_List_Olist_OCons(_1672274), _1672276), _1672272)) = c_List_Olast(_1672274, _1672272))], (3668 ^ _780478) ^ [_835403, _835405, _835407, _835409] : [-(c_List_Otranspose(_835409, _835405) = c_List_Otranspose(_835407, _835403)), _835409 = _835407, _835405 = _835403], (33949 ^ _780478) ^ [_1421741] : [class_Rings_Osemiring__1(_1421741), -(c_Int_Oiszero(_1421741, c_Groups_Ozero__class_Ozero(_1421741)))], (19854 ^ _780478) ^ [_1150917, _1150919, _1150921] : [class_Groups_Oordered__comm__monoid__add(_1150917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150917), c_Groups_Ozero__class_Ozero(_1150917)), _1150919)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150917), c_Groups_Ozero__class_Ozero(_1150917)), _1150921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150917), c_Groups_Ozero__class_Ozero(_1150917)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150917), _1150919), _1150921))))], (33272 ^ _780478) ^ [_1409066, _1409068] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1409066)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409066)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409068)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1409066)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409068))))], (18127 ^ _780478) ^ [_1118431, _1118433, _1118435, _1118437] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1118431, tc_fun(_1118433, tc_HOL_Obool)), _1118435), _1118437) = c_Orderings_Otop__class_Otop(tc_fun(_1118433, tc_HOL_Obool)), 18130 ^ _780478 : [(18131 ^ _780478) ^ [_1118547] : [hBOOL(hAPP(hAPP(c_member(_1118431), _1118547), _1118435)), -(hAPP(_1118437, _1118547) = c_Orderings_Otop__class_Otop(tc_fun(_1118433, tc_HOL_Obool)))]]], (38321 ^ _780478) ^ [_1516554] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1516554)))], (6099 ^ _780478) ^ [_877622, _877624, _877626, _877628, _877630] : [hBOOL(hAPP(hAPP(c_member(_877622), _877624), _877626)), -(hBOOL(hAPP(hAPP(c_member(_877628), hAPP(_877630, _877624)), hAPP(c_Set_Oimage(_877622, _877628, _877630), _877626))))], (42011 ^ _780478) ^ [_1612890, _1612892, _1612894, _1612896] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612890), tc_List_Olist(_1612890))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612890), tc_List_Olist(_1612890)), _1612894), _1612896)), c_List_Olistrel(_1612890, _1612892))), -(c_List_Olistrelp(_1612890, hAPP(hAPP(c_COMBC(_1612890, tc_fun(tc_prod(_1612890, _1612890), tc_HOL_Obool), tc_fun(_1612890, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612890, tc_fun(tc_fun(tc_prod(_1612890, _1612890), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1612890, _1612890), tc_HOL_Obool), tc_fun(_1612890, tc_HOL_Obool)), _1612890), c_COMBC(_1612890, tc_fun(tc_prod(_1612890, _1612890), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612890, tc_prod(_1612890, _1612890)), tc_fun(_1612890, tc_fun(tc_fun(tc_prod(_1612890, _1612890), tc_HOL_Obool), tc_HOL_Obool)), _1612890), hAPP(c_COMBB(tc_prod(_1612890, _1612890), tc_fun(tc_fun(tc_prod(_1612890, _1612890), tc_HOL_Obool), tc_HOL_Obool), _1612890), c_member(tc_prod(_1612890, _1612890)))), c_Product__Type_OPair(_1612890, _1612890)))), _1612892), _1612894, _1612896))], (32250 ^ _780478) ^ [_1389640, _1389642, _1389644] : [class_Int_Onumber(_1389640), class_Orderings_Oord(_1389640), 32257 ^ _780478 : [(32264 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389640), hAPP(c_Int_Onumber__class_Onumber__of(_1389640), _1389642)), hAPP(c_Int_Onumber__class_Onumber__of(_1389640), _1389644)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1389640), hAPP(c_Int_Onumber__class_Onumber__of(_1389640), _1389642)), hAPP(c_Int_Onumber__class_Onumber__of(_1389640), _1389644)) = hAPP(c_Int_Onumber__class_Onumber__of(_1389640), _1389642))], (32258 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389640), hAPP(c_Int_Onumber__class_Onumber__of(_1389640), _1389642)), hAPP(c_Int_Onumber__class_Onumber__of(_1389640), _1389644))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1389640), hAPP(c_Int_Onumber__class_Onumber__of(_1389640), _1389642)), hAPP(c_Int_Onumber__class_Onumber__of(_1389640), _1389644)) = hAPP(c_Int_Onumber__class_Onumber__of(_1389640), _1389644))]]], (18387 ^ _780478) ^ [_1124411, _1124413, _1124415, _1124417, _1124419] : [class_Complete__Lattice_Ocomplete__lattice(_1124411), class_Orderings_Olinorder(_1124411), 18394 ^ _780478 : [(18404 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124411), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1124413, _1124411), _1124415), _1124417)), _1124419))), 18405 ^ _780478 : [(18406 ^ _780478) ^ [_1124759] : [hBOOL(hAPP(hAPP(c_member(_1124413), _1124759), _1124415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124411), hAPP(_1124417, _1124759)), _1124419))]]], (18395 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124411), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1124413, _1124411), _1124415), _1124417)), _1124419)), 18399 ^ _780478 : [(18402 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1124411), hAPP(_1124417, 18398 ^ [_1124411, _1124413, _1124415, _1124417, _1124419])), _1124419)))], (18400 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1124413), 18398 ^ [_1124411, _1124413, _1124415, _1124417, _1124419]), _1124415)))]]]]], (52289 ^ _780478) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (7736 ^ _780478) ^ [_911166, _911168, _911170, _911172] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911166, _911168, _911170, _911172, c_Orderings_Obot__class_Obot(tc_fun(_911166, tc_HOL_Obool))), _911172)))], (27419 ^ _780478) ^ [_1287817] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1287817)))], (32122 ^ _780478) ^ [_1387098, _1387100, _1387102, _1387104, _1387106] : [c_Com_Ocom_OLocal(_1387098, _1387100, _1387102) = c_Com_Ocom_OSemi(_1387104, _1387106)], (36250 ^ _780478) ^ [_1469835, _1469837, _1469839, _1469841, _1469843, _1469845] : [hBOOL(hAPP(hAPP(_1469835, _1469837), _1469839)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1469841, tc_fun(_1469843, tc_HOL_Obool))), _1469845), _1469835), _1469837), _1469839)))], (6916 ^ _780478) ^ [_895458, _895460, _895462, _895464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895458, tc_HOL_Obool)), _895460), hAPP(hAPP(c_Set_Oinsert(_895458), _895462), _895464))), 6919 ^ _780478 : [(6926 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895458), _895462), _895460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895458, tc_HOL_Obool)), _895460), _895464)))], (6920 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895458), _895462), _895460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895458, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895458, tc_HOL_Obool)), _895460), hAPP(hAPP(c_Set_Oinsert(_895458), _895462), c_Orderings_Obot__class_Obot(tc_fun(_895458, tc_HOL_Obool))))), _895464)))]]], (49038 ^ _780478) ^ [_1770368, _1770370, _1770372, _1770374, _1770376, _1770378, _1770380] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1770368, tc_fun(_1770370, tc_fun(_1770372, tc_HOL_Obool))), _1770374), _1770376), _1770378), _1770380)), 49042 ^ _780478 : [(49045 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1770376, 49041 ^ [_1770368, _1770370, _1770372, _1770374, _1770376, _1770378, _1770380]), _1770378), _1770380)))], (49043 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770368), 49041 ^ [_1770368, _1770370, _1770372, _1770374, _1770376, _1770378, _1770380]), _1770374)))]]], (39676 ^ _780478) ^ [_1553020, _1553022, _1553024, _1553026, _1553028, _1553030, _1553032] : [hAPP(c_Fun_Ocomp(_1553020, _1553022, _1553024, _1553026), _1553028) = _1553030, -(hAPP(_1553026, hAPP(_1553028, _1553032)) = hAPP(_1553030, _1553032))], (20834 ^ _780478) ^ [_1168609, _1168611] : [class_Groups_Ogroup__add(_1168609), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168609), c_Groups_Ozero__class_Ozero(_1168609)), _1168611) = hAPP(c_Groups_Ouminus__class_Ouminus(_1168609), _1168611))], (7617 ^ _780478) ^ [_908692, _908694] : [_908694 = c_Orderings_Obot__class_Obot(tc_fun(_908692, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908692, tc_HOL_Obool)), _908694), c_Orderings_Obot__class_Obot(tc_fun(_908692, tc_HOL_Obool)))))], (10389 ^ _780478) ^ [_961691, _961693, _961695, _961697] : [class_Orderings_Olinorder(_961691), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961691), hAPP(hAPP(c_Orderings_Oord__class_Omax(_961691), _961693), _961695)), _961697)), 10396 ^ _780478 : [(10399 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961691), _961695), _961697)))], (10397 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961691), _961693), _961697)))]]], (3850 ^ _780478) ^ [_838224, _838226, _838228, _838230, _838232, _838234] : [-(c_List_Olinorder__class_Oinsort__key(_838234, _838230, _838226) = c_List_Olinorder__class_Oinsort__key(_838232, _838228, _838224)), _838234 = _838232, _838230 = _838228, _838226 = _838224], (13110 ^ _780478) ^ [_1012822, _1012824, _1012826] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1012822), _1012824)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012822), _1012826)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012822), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012822, tc_HOL_Obool)), _1012824), _1012826))))], (180 ^ _780478) ^ [_783330, _783332, _783334, _783336, _783338, _783340, _783342, _783344, _783346, _783348, _783350, _783352] : [-(c_Finite__Set_Ofolding__image__simple(_783350, _783346, _783342, _783338, _783334, _783330)), c_Finite__Set_Ofolding__image__simple(_783352, _783348, _783344, _783340, _783336, _783332), _783352 = _783350, _783348 = _783346, _783344 = _783342, _783340 = _783338, _783336 = _783334, _783332 = _783330], (38398 ^ _780478) ^ [_1518220] : [class_Orderings_Owellorder(_1518220), -(c_Wellfounded_Owf(_1518220, hAPP(c_Set_OCollect(tc_prod(_1518220, _1518220)), hAPP(c_Product__Type_Oprod_Oprod__case(_1518220, _1518220, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1518220)))))], (38786 ^ _780478) ^ [_1528976, _1528978, _1528980, _1528982, _1528984] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528976, _1528978), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528976, tc_HOL_Obool)), _1528980), _1528982)), _1528984) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528976, _1528978), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528976, _1528978), _1528980), _1528984)), hAPP(hAPP(c_Product__Type_OSigma(_1528976, _1528978), _1528982), _1528984)))], (31172 ^ _780478) ^ [_1360634, _1360636] : [-(hAPP(c_Set_OCollect(_1360634), hAPP(hAPP(c_COMBC(_1360634, tc_fun(_1360634, tc_HOL_Obool), tc_HOL_Obool), c_member(_1360634)), _1360636)) = _1360636)], (40714 ^ _780478) ^ [_1577607, _1577609, _1577611, _1577613] : [c_Wellfounded_Owf(_1577607, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1577607, _1577607)), hAPP(hAPP(c_Product__Type_OPair(_1577607, _1577607), _1577609), _1577611)), _1577613)), 40717 ^ _780478 : [(40720 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577607, _1577607)), hAPP(hAPP(c_Product__Type_OPair(_1577607, _1577607), _1577611), _1577609)), c_Transitive__Closure_Ortrancl(_1577607, _1577613)))], (40718 ^ _780478) ^ [] : [-(c_Wellfounded_Owf(_1577607, _1577613))]]], (22381 ^ _780478) ^ [_1196689, _1196691, _1196693] : [class_Orderings_Olinorder(_1196689), 22384 ^ _780478 : [(22391 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196689), _1196691), _1196693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196689, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196689), _1196691)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196689), _1196693))))], (22385 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1196689, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196689), _1196691)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196689), _1196693))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196689), _1196691), _1196693)))]]], (4996 ^ _780478) ^ [_856715, _856717] : [_856717 = _856715, -(c_HOL_OEx(_856717) = c_HOL_OEx(_856715))], (30721 ^ _780478) ^ [_1351089, _1351091, _1351093, _1351095] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1351089, tc_fun(_1351091, tc_HOL_Obool)), _1351093), _1351095) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1351091, tc_HOL_Obool), hAPP(c_Set_Oimage(_1351089, tc_fun(_1351091, tc_HOL_Obool), _1351095), _1351093)))], (28484 ^ _780478) ^ [_1307655, _1307657, _1307659, _1307661] : [class_Orderings_Olinorder(_1307655), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307655, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1307655, _1307657, _1307659)), hAPP(c_SetInterval_Oord__class_OatLeast(_1307655), _1307661)) = c_SetInterval_Oord__class_OatLeastAtMost(_1307655, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1307655), _1307657), _1307661), _1307659))], (2912 ^ _780478) ^ [_823607, _823609] : [_823609 = _823607, -(c_Rings_Oinverse__class_Odivide(_823609) = c_Rings_Oinverse__class_Odivide(_823607))], (27988 ^ _780478) ^ [_1298145, _1298147] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1298145, _1298147)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1298147)), _1298145))], (8366 ^ _780478) ^ [_923981, _923983, _923985, _923987, _923989, _923991] : [c_Finite__Set_Ofun__left__comm(_923981, _923983, _923985), hBOOL(hAPP(c_Finite__Set_Ofinite(_923981), _923987)), -(hAPP(hAPP(_923985, _923989), hAPP(hAPP(c_Finite__Set_Ofold(_923981, _923983, _923985), _923991), _923987)) = hAPP(hAPP(c_Finite__Set_Ofold(_923981, _923983, _923985), hAPP(hAPP(_923985, _923989), _923991)), _923987))], (45705 ^ _780478) ^ [_1698252, _1698254, _1698256, _1698258, _1698260] : [c_Finite__Set_Ofun__left__comm(_1698252, _1698254, _1698256), -(hAPP(hAPP(c_Finite__Set_Ofold(_1698252, _1698254, _1698256), _1698258), hAPP(c_List_Oset(_1698252), _1698260)) = hAPP(c_List_Ofoldl(_1698254, _1698252, hAPP(c_COMBC(_1698252, _1698254, _1698254), _1698256), _1698258), c_List_Oremdups(_1698252, _1698260)))], (51921 ^ _780478) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (51953 ^ _780478) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (31833 ^ _780478) ^ [_1381634] : [-(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, _1381634))))))], (50556 ^ _780478) ^ [_1803119, _1803121, _1803123] : [_1803121 = _1803123, -(c_Fun_Obij__betw(_1803119, _1803119, c_Fun_Oid(_1803119), _1803121, _1803123))], (30622 ^ _780478) ^ [_1348835, _1348837, _1348839] : [class_Rings_Olinordered__idom(_1348835), -(hAPP(c_Groups_Oabs__class_Oabs(_1348835), hAPP(hAPP(c_Power_Opower__class_Opower(_1348835), hAPP(c_Groups_Ouminus__class_Ouminus(_1348835), _1348837)), _1348839)) = hAPP(c_Groups_Oabs__class_Oabs(_1348835), hAPP(hAPP(c_Power_Opower__class_Opower(_1348835), _1348837), _1348839)))], (44891 ^ _780478) ^ [_1680050, _1680052, _1680054, _1680056] : [-(hBOOL(hAPP(c_List_Odistinct(_1680050), hAPP(hAPP(c_List_Omap(_1680052, _1680050), _1680054), _1680056)))), hBOOL(hAPP(c_List_Odistinct(_1680052), _1680056)), c_Fun_Oinj__on(_1680052, _1680050, _1680054, hAPP(c_List_Oset(_1680052), _1680056))], (20394 ^ _780478) ^ [_1160787, _1160789, _1160791] : [class_Rings_Olinordered__semiring__strict(_1160787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160787), c_Groups_Ozero__class_Ozero(_1160787)), _1160789)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160787), _1160791), c_Groups_Ozero__class_Ozero(_1160787))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160787), _1160791), _1160789)), c_Groups_Ozero__class_Ozero(_1160787))))], (44694 ^ _780478) ^ [_1675109, _1675111, _1675113, _1675115, _1675117, _1675119] : [-(hAPP(hAPP(c_List_Ozip(_1675109, _1675111), hAPP(hAPP(c_List_Omap(_1675113, _1675109), _1675115), _1675117)), _1675119) = hAPP(hAPP(c_List_Omap(tc_prod(_1675113, _1675111), tc_prod(_1675109, _1675111)), hAPP(c_Product__Type_Oprod_Oprod__case(_1675113, _1675111, tc_prod(_1675109, _1675111)), hAPP(hAPP(c_COMBB(_1675109, tc_fun(_1675111, tc_prod(_1675109, _1675111)), _1675113), c_Product__Type_OPair(_1675109, _1675111)), _1675115))), hAPP(hAPP(c_List_Ozip(_1675113, _1675111), _1675117), _1675119)))], (20044 ^ _780478) ^ [_1154302, _1154304, _1154306, _1154308] : [class_Rings_Oordered__semiring(_1154302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154302), _1154304), _1154306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154302), c_Groups_Ozero__class_Ozero(_1154302)), _1154308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154302), _1154304), _1154308)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154302), _1154306), _1154308))))], (46074 ^ _780478) ^ [_1706647, _1706649, _1706651, _1706653] : [-(hBOOL(hAPP(_1706647, _1706649))), -(hAPP(c_List_Ofilter(_1706651, _1706647), hAPP(hAPP(c_List_Olist_OCons(_1706651), _1706649), _1706653)) = hAPP(c_List_Ofilter(_1706651, _1706647), _1706653))], (2808 ^ _780478) ^ [_822029, _822031, _822033, _822035] : [-(c_Random_Olog(_822035, _822031) = c_Random_Olog(_822033, _822029)), _822035 = _822033, _822031 = _822029], (35457 ^ _780478) ^ [_1448374] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1448374, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27605 ^ _780478) ^ [_1290801, _1290803, _1290805] : [class_Orderings_Olinorder(_1290801), 27608 ^ _780478 : [(27615 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290801), _1290805), _1290803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290801, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290801), _1290803)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290801), _1290805))))], (27609 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290801, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290801), _1290803)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290801), _1290805))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290801), _1290805), _1290803)))]]], (47242 ^ _780478) ^ [_1731065, _1731067, _1731069, _1731071] : [-(hBOOL(hAPP(_1731065, _1731067))), -(c_List_OtakeWhile(_1731069, _1731065, hAPP(hAPP(c_List_Olist_OCons(_1731069), _1731067), _1731071)) = c_List_Olist_ONil(_1731069))], (33424 ^ _780478) ^ [_1411333] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411333) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411333), c_Int_OPls)))], (21215 ^ _780478) ^ [_1174760, _1174762, _1174764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174760)), 21218 ^ _780478 : [(21225 ^ _780478) ^ [] : [_1174762 = _1174764, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174760), _1174762) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174760), _1174764))], (21219 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174760), _1174762) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174760), _1174764), -(_1174762 = _1174764)]]], (45639 ^ _780478) ^ [_1696658, _1696660, _1696662] : [-(c_Enum_Osublists(_1696658, hAPP(hAPP(c_List_Olist_OCons(_1696658), _1696660), _1696662)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1696658)), tc_List_Olist(tc_List_Olist(_1696658))), c_Enum_Osublists(_1696658, _1696662)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1696658)), tc_List_Olist(tc_List_Olist(_1696658)), tc_List_Olist(tc_List_Olist(_1696658))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1696658)), tc_fun(tc_List_Olist(tc_List_Olist(_1696658)), tc_List_Olist(tc_List_Olist(_1696658))), tc_List_Olist(tc_List_Olist(_1696658))), c_List_Oappend(tc_List_Olist(_1696658))), hAPP(c_List_Omap(tc_List_Olist(_1696658), tc_List_Olist(_1696658)), hAPP(c_List_Olist_OCons(_1696658), _1696660)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1696658))))))], (46821 ^ _780478) ^ [_1721948, _1721950] : [class_Orderings_Olinorder(_1721948), 46824 ^ _780478 : [(46825 ^ _780478) ^ [] : [c_List_Olinorder__class_Osorted(_1721948, _1721950), 46828 ^ _780478 : [(46829 ^ _780478) ^ [_1722119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722119), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721948)), _1721950))), 46832 ^ _780478 : [(46833 ^ _780478) ^ [_1722236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1722236), _1722119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1721948), hAPP(hAPP(c_List_Onth(_1721948), _1721950), _1722236)), hAPP(hAPP(c_List_Onth(_1721948), _1721950), _1722119))))]]]]], (46839 ^ _780478) ^ [] : [46841 ^ _780478 : [(46847 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1721948), hAPP(hAPP(c_List_Onth(_1721948), _1721950), 46843 ^ [_1721948, _1721950])), hAPP(hAPP(c_List_Onth(_1721948), _1721950), 46840 ^ [_1721948, _1721950])))], (46845 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46843 ^ [_1721948, _1721950]), 46840 ^ [_1721948, _1721950])))], (46842 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46840 ^ [_1721948, _1721950]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721948)), _1721950))))]], -(c_List_Olinorder__class_Osorted(_1721948, _1721950))]]], (19092 ^ _780478) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52133 ^ _780478) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (15667 ^ _780478) ^ [_1063555, _1063557, _1063559, _1063561] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063555, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063555, tc_HOL_Obool)), _1063557), _1063559)), _1063561) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063555, tc_HOL_Obool)), _1063557), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063555, tc_HOL_Obool)), _1063559), _1063561)))], (41294 ^ _780478) ^ [_1591845, _1591847, _1591849] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591845, _1591845)), _1591847), c_Transitive__Closure_Otrancl(_1591845, _1591849)))), 41295 ^ _780478 : [(41296 ^ _780478) ^ [_1591924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1591924)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591845, _1591845)), _1591847), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591845, _1591845), tc_HOL_Obool), _1591924), _1591849)))]]], (29231 ^ _780478) ^ [_1323108] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323108, _1323108) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7397 ^ _780478) ^ [_904360, _904362, _904364, _904366] : [c_Fun_Oinj__on(_904360, _904362, _904364, _904366), -(hAPP(c_Set_Oimage(_904362, _904360, c_Fun_Othe__inv__into(_904360, _904362, _904366, _904364)), hAPP(c_Set_Oimage(_904360, _904362, _904364), _904366)) = _904366)], (31364 ^ _780478) ^ [_1366032, _1366034, _1366036, _1366038, _1366040, _1366042] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1366032), _1366034)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366036), _1366038)), 31374 ^ _780478 : [(31377 ^ _780478) ^ [] : [hAPP(c_Finite__Set_Ocard(_1366032), hAPP(c_Set_OCollect(_1366032), hAPP(hAPP(c_COMBS(_1366032, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1366032), c_fconj), hAPP(hAPP(c_COMBC(_1366032, tc_fun(_1366032, tc_HOL_Obool), tc_HOL_Obool), c_member(_1366032)), _1366034))), hAPP(hAPP(c_COMBC(_1366032, _1366036, tc_HOL_Obool), _1366040), 31373 ^ [_1366032, _1366034, _1366036, _1366038, _1366040, _1366042])))) = _1366042], (31375 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366036), 31373 ^ [_1366032, _1366034, _1366036, _1366038, _1366040, _1366042]), _1366038)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1366032, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1366036, tc_HOL_Obool), tc_Nat_Onat, _1366032), c_Finite__Set_Ocard(_1366036)), hAPP(hAPP(c_COMBB(tc_fun(_1366036, tc_HOL_Obool), tc_fun(_1366036, tc_HOL_Obool), _1366032), c_Set_OCollect(_1366036)), hAPP(hAPP(c_COMBB(tc_fun(_1366036, tc_HOL_Obool), tc_fun(_1366036, tc_HOL_Obool), _1366032), hAPP(c_COMBS(_1366036, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1366036), c_fconj), hAPP(hAPP(c_COMBC(_1366036, tc_fun(_1366036, tc_HOL_Obool), tc_HOL_Obool), c_member(_1366036)), _1366038)))), _1366040)))), _1366034) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1366042), hAPP(c_Finite__Set_Ocard(_1366036), _1366038)))], (1444 ^ _780478) ^ [_801392, _801394] : [-(class_Orderings_Obot(_801392)), _801394 = _801392, class_Orderings_Obot(_801394)], (14102 ^ _780478) ^ [_1032554] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032554), _1032554)))))], (16236 ^ _780478) ^ [_1075166, _1075168, _1075170, _1075172] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075166, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075166, tc_HOL_Obool)), _1075168), _1075170)), _1075172) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075166, tc_HOL_Obool)), _1075168), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075166, tc_HOL_Obool)), _1075170), _1075172)))], (43967 ^ _780478) ^ [_1660092, _1660094, _1660096, _1660098, _1660100] : [hAPP(hAPP(c_List_Oappend(_1660092), _1660094), _1660096) = hAPP(hAPP(c_List_Oappend(_1660092), _1660098), _1660100), 43970 ^ _780478 : [(43979 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660092)), _1660094)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660092)), _1660098)))), 43982 ^ _780478 : [(43985 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1660092), hAPP(hAPP(c_List_Odrop(_1660092), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660092)), _1660098)), _1660094)), _1660096) = _1660100)], (43983 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1660092), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660092)), _1660098)), _1660094) = _1660098)]]], (43971 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660092)), _1660094)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660092)), _1660098))), 43974 ^ _780478 : [(43977 ^ _780478) ^ [] : [-(_1660096 = hAPP(hAPP(c_List_Oappend(_1660092), hAPP(hAPP(c_List_Odrop(_1660092), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660092)), _1660094)), _1660098)), _1660100))], (43975 ^ _780478) ^ [] : [-(_1660094 = hAPP(hAPP(c_List_Otake(_1660092), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660092)), _1660094)), _1660098))]]]]], (7980 ^ _780478) ^ [_916149, _916151, _916153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916149, tc_HOL_Obool)), _916151), hAPP(hAPP(c_Set_Oinsert(_916149), _916153), c_Orderings_Obot__class_Obot(tc_fun(_916149, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_916149, _916153, _916151) = _916153)], (29273 ^ _780478) ^ [_1323993, _1323995, _1323997, _1323999] : [class_Divides_Osemiring__div(_1323993), -(c_Divides_Odiv__class_Omod(_1323993, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323993), _1323995), _1323997), _1323999) = c_Divides_Odiv__class_Omod(_1323993, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323993), _1323995), c_Divides_Odiv__class_Omod(_1323993, _1323997, _1323999)), _1323999))], (37644 ^ _780478) ^ [_1498959, _1498961, _1498963, _1498965] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1498959), _1498961)), 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)), _1498959), _1498963)), 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)), _1498961), _1498965)), 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)), _1498961), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1498963), _1498965))), c_FunDef_Omin__strict)))], (25029 ^ _780478) ^ [_1245394, _1245396, _1245398, _1245400] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1245394), _1245396)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245398), _1245400)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1245394, _1245398)), c_Sum__Type_OPlus(_1245394, _1245398, _1245396, _1245400))))], (9174 ^ _780478) ^ [_937937, _937939, _937941] : [class_Orderings_Olinorder(_937937), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937937), _937939), _937941))), 9181 ^ _780478 : [(9188 ^ _780478) ^ [] : [_937939 = _937941, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937937), _937939), _937941)))], (9182 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937937), _937939), _937941)), -(_937939 = _937941)]]], (49456 ^ _780478) ^ [_1781106, _1781108] : [c_Equiv__Relations_Oequivp(_1781106, _1781108), 49459 ^ _780478 : [(49464 ^ _780478) ^ [] : [-(c_Predicate_Otransp(_1781106, _1781108))], (49462 ^ _780478) ^ [] : [-(c_Predicate_Osymp(_1781106, _1781108))], (49460 ^ _780478) ^ [] : [-(c_Predicate_Oreflp(_1781106, _1781108))]]], (39537 ^ _780478) ^ [_1548689, _1548691, _1548693, _1548695] : [-(hAPP(c_Set_OCollect(_1548689), hAPP(hAPP(c_COMBB(tc_fun(_1548691, tc_HOL_Obool), tc_HOL_Obool, _1548689), c_HOL_OAll(_1548691)), hAPP(hAPP(c_COMBB(tc_fun(_1548691, tc_HOL_Obool), tc_fun(_1548691, tc_HOL_Obool), _1548689), hAPP(c_COMBS(_1548691, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1548691), c_fimplies), hAPP(hAPP(c_COMBC(_1548691, tc_fun(_1548691, tc_HOL_Obool), tc_HOL_Obool), c_member(_1548691)), _1548693)))), _1548695))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1548691, tc_fun(_1548689, tc_HOL_Obool)), _1548693), hAPP(hAPP(c_COMBB(tc_fun(_1548689, tc_HOL_Obool), tc_fun(_1548689, tc_HOL_Obool), _1548691), c_Set_OCollect(_1548689)), hAPP(c_COMBC(_1548689, _1548691, tc_HOL_Obool), _1548695))))], (10323 ^ _780478) ^ [_960562, _960564, _960566] : [class_Orderings_Olinorder(_960562), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_960562), _960564), _960566) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_960562), _960566), _960564))], (21161 ^ _780478) ^ [_1173783, _1173785, _1173787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173783), _1173785)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173787), _1173785))), 21164 ^ _780478 : [(21167 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173783), _1173787)))], (21165 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173785)))]]], (5574 ^ _780478) ^ [_865850, _865852] : [_865852 = _865850, -(tc_List_Olist(_865852) = tc_List_Olist(_865850))], (16849 ^ _780478) ^ [_1089725, _1089727, _1089729, _1089731, _1089733] : [class_Groups_Ocomm__monoid__mult(_1089725), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089727), _1089729)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089727), _1089731)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1089727, tc_HOL_Obool)), _1089729), _1089731) = c_Orderings_Obot__class_Obot(tc_fun(_1089727, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089727, _1089725), _1089733), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1089727, tc_HOL_Obool)), _1089729), _1089731)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089725), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089727, _1089725), _1089733), _1089729)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089727, _1089725), _1089733), _1089731)))], (43548 ^ _780478) ^ [_1649956, _1649958] : [-(hAPP(hAPP(c_List_Oappend(_1649956), _1649958), c_List_Olist_ONil(_1649956)) = _1649958)], (6178 ^ _780478) ^ [_879313, _879315, _879317, _879319] : [hAPP(c_Set_Oimage(_879313, _879315, _879317), _879319) = c_Orderings_Obot__class_Obot(tc_fun(_879315, tc_HOL_Obool)), -(_879319 = c_Orderings_Obot__class_Obot(tc_fun(_879313, tc_HOL_Obool)))], (16074 ^ _780478) ^ [_1071372, _1071374, _1071376, _1071378, _1071380] : [hBOOL(hAPP(hAPP(c_member(_1071372), _1071374), hAPP(c_Set_Ovimage(_1071372, _1071376, _1071378), _1071380))), -(hBOOL(hAPP(hAPP(c_member(_1071376), hAPP(_1071378, _1071374)), _1071380)))], (17043 ^ _780478) ^ [_1093862, _1093864, _1093866] : [class_Orderings_Olinorder(_1093862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093862), _1093864)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093862), _1093866)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1093862, tc_HOL_Obool)), _1093864), _1093866) = c_Orderings_Obot__class_Obot(tc_fun(_1093862, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093862), c_Big__Operators_Olinorder__class_OMax(_1093862, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1093862, tc_HOL_Obool)), _1093864), _1093866))), c_Big__Operators_Olinorder__class_OMax(_1093862, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1093862, tc_HOL_Obool)), _1093864), _1093866))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093862), c_Big__Operators_Olinorder__class_OMax(_1093862, _1093864)), c_Big__Operators_Olinorder__class_OMax(_1093862, _1093866)))], (33885 ^ _780478) ^ [_1420630, _1420632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420630), _1420632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1420630)), c_Int_OBit1(_1420632))))], (756 ^ _780478) ^ [_791862, _791864, _791866, _791868] : [-(c_Relation_Oantisym(_791866, _791862)), c_Relation_Oantisym(_791868, _791864), _791868 = _791866, _791864 = _791862], (39374 ^ _780478) ^ [_1545377, _1545379, _1545381] : [c_Wellfounded_Oacyclic(_1545377, _1545379), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1545377, _1545377), tc_HOL_Obool)), _1545381), _1545379)), -(c_Wellfounded_Oacyclic(_1545377, _1545381))], (30356 ^ _780478) ^ [_1343661, _1343663, _1343665] : [class_Fields_Olinordered__field__inverse__zero(_1343661), -(hAPP(c_Groups_Oabs__class_Oabs(_1343661), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1343661), _1343663), _1343665)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1343661), hAPP(c_Groups_Oabs__class_Oabs(_1343661), _1343663)), hAPP(c_Groups_Oabs__class_Oabs(_1343661), _1343665)))], (21730 ^ _780478) ^ [_1184002, _1184004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1184002), _1184004))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1184002), _1184004)))], (39652 ^ _780478) ^ [_1552506, _1552508, _1552510, _1552512, _1552514, _1552516, _1552518, _1552520] : [hAPP(c_Fun_Ocomp(_1552506, _1552508, _1552510, _1552512), _1552514) = hAPP(c_Fun_Ocomp(_1552516, _1552508, _1552510, _1552518), _1552520), 39655 ^ _780478 : [(39656 ^ _780478) ^ [_1552621] : [-(hAPP(_1552512, hAPP(_1552514, _1552621)) = hAPP(_1552518, hAPP(_1552520, _1552621)))]]], (35133 ^ _780478) ^ [_1442660, _1442662, _1442664] : [class_Rings_Olinordered__idom(_1442660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442660), c_Groups_Ozero__class_Ozero(_1442660)), hAPP(hAPP(c_Power_Opower__class_Opower(_1442660), _1442662), 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)))), _1442664))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1442660), c_Groups_Ozero__class_Ozero(_1442660)), _1442662)))], (21809 ^ _780478) ^ [_1185399, _1185401, _1185403] : [hBOOL(hAPP(_1185399, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1185401), _1185403))), 21812 ^ _780478 : [(21819 ^ _780478) ^ [_1185584] : [_1185401 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1185403), _1185584), -(hBOOL(hAPP(_1185399, _1185584)))], (21813 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185401), _1185403)), -(hBOOL(hAPP(_1185399, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (47077 ^ _780478) ^ [_1727568, _1727570, _1727572] : [-(hAPP(c_List_Orev(_1727568), hAPP(hAPP(c_List_Olist_OCons(_1727568), _1727570), _1727572)) = hAPP(hAPP(c_List_Oappend(_1727568), hAPP(c_List_Orev(_1727568), _1727572)), hAPP(hAPP(c_List_Olist_OCons(_1727568), _1727570), c_List_Olist_ONil(_1727568))))], (42740 ^ _780478) ^ [_1632449, _1632451, _1632453, _1632455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632449), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632451)), _1632453))), -(hBOOL(hAPP(hAPP(c_member(_1632451), _1632455), hAPP(c_List_Oset(_1632451), hAPP(hAPP(c_List_Olist__update(_1632451, _1632453), _1632449), _1632455)))))], (30855 ^ _780478) ^ [_1353549, _1353551] : [-(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), _1353549)), _1353551))))], (39033 ^ _780478) ^ [_1537055] : [-(hAPP(c_Set_Oimage(_1537055, _1537055, c_Fun_Oid(_1537055)), c_Orderings_Otop__class_Otop(tc_fun(_1537055, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1537055, tc_HOL_Obool)))], (47765 ^ _780478) ^ [_1742677, _1742679, _1742681, _1742683, _1742685] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742677)), _1742679) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742681)), _1742683), 47771 ^ _780478 : [(47774 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1742685, hAPP(hAPP(c_List_Onth(_1742677), _1742679), 47770 ^ [_1742677, _1742679, _1742681, _1742683, _1742685])), hAPP(hAPP(c_List_Onth(_1742681), _1742683), 47770 ^ [_1742677, _1742679, _1742681, _1742683, _1742685])))], (47772 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47770 ^ [_1742677, _1742679, _1742681, _1742683, _1742685]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742677)), _1742679))))]], -(c_List_Olist__all2(_1742677, _1742681, _1742685, _1742679, _1742683))], (42197 ^ _780478) ^ [_1618033, _1618035, _1618037] : [-(hAPP(hAPP(c_List_Onth(_1618033), hAPP(hAPP(c_List_Olist_OCons(_1618033), _1618035), _1618037)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1618035)], (7611 ^ _780478) ^ [_908579, _908581] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908579, tc_HOL_Obool)), _908581), c_Orderings_Obot__class_Obot(tc_fun(_908579, tc_HOL_Obool)))), -(_908581 = c_Orderings_Obot__class_Obot(tc_fun(_908579, tc_HOL_Obool)))], (30823 ^ _780478) ^ [_1353046] : [_1353046 = 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), _1353046)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (19378 ^ _780478) ^ [_1143374, _1143376] : [class_Groups_Olinordered__ab__group__add(_1143374), 19381 ^ _780478 : [(19388 ^ _780478) ^ [] : [_1143376 = c_Groups_Ozero__class_Ozero(_1143374), -(_1143376 = hAPP(c_Groups_Ouminus__class_Ouminus(_1143374), _1143376))], (19382 ^ _780478) ^ [] : [_1143376 = hAPP(c_Groups_Ouminus__class_Ouminus(_1143374), _1143376), -(_1143376 = c_Groups_Ozero__class_Ozero(_1143374))]]], (14591 ^ _780478) ^ [_1041308, _1041310, _1041312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041308), _1041310)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041310), _1041308)), _1041312) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041310), _1041312)), _1041308))], (12820 ^ _780478) ^ [_1007674, _1007676, _1007678] : [class_Lattices_Olattice(_1007674), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007674), _1007676), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007674), _1007676), _1007678))))], (13330 ^ _780478) ^ [_1017681, _1017683, _1017685, _1017687, _1017689] : [c_Fun_Oinj__on(_1017681, _1017683, _1017685, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017681, tc_HOL_Obool)), _1017687), _1017689)), 13333 ^ _780478 : [(13340 ^ _780478) ^ [] : [_1017687 = _1017689, -(hAPP(c_Set_Oimage(_1017681, _1017683, _1017685), _1017687) = hAPP(c_Set_Oimage(_1017681, _1017683, _1017685), _1017689))], (13334 ^ _780478) ^ [] : [hAPP(c_Set_Oimage(_1017681, _1017683, _1017685), _1017687) = hAPP(c_Set_Oimage(_1017681, _1017683, _1017685), _1017689), -(_1017687 = _1017689)]]], (21263 ^ _780478) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27006 ^ _780478) ^ [_1280877, _1280879, _1280881, _1280883] : [class_Fields_Olinordered__field__inverse__zero(_1280877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280877), _1280879), _1280881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280877), _1280883), c_Groups_Ozero__class_Ozero(_1280877))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280877), c_Groups_Ozero__class_Ozero(_1280877)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1280877), _1280879), _1280881))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280877), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280877), _1280883), _1280879)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280877), _1280883), _1280881))))], (38624 ^ _780478) ^ [_1524035, _1524037, _1524039, _1524041, _1524043] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524035, _1524037)), hAPP(hAPP(c_Product__Type_OPair(_1524035, _1524037), _1524039), _1524041)), _1524043)), -(hBOOL(hAPP(hAPP(c_member(_1524035), _1524039), hAPP(c_Relation_ODomain(_1524035, _1524037), _1524043))))], (17247 ^ _780478) ^ [_1098280, _1098282, _1098284, _1098286, _1098288] : [17249 ^ _780478 : [(17252 ^ _780478) ^ [] : [hBOOL(hAPP(_1098288, 17248 ^ [_1098280, _1098282, _1098284, _1098286, _1098288]))], (17250 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098280), 17248 ^ [_1098280, _1098282, _1098284, _1098286, _1098288]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098282, tc_fun(_1098280, tc_HOL_Obool)), _1098284), _1098286))))]], 17253 ^ _780478 : [(17254 ^ _780478) ^ [_1098502] : [hBOOL(hAPP(hAPP(c_member(_1098282), _1098502), _1098284)), 17257 ^ _780478 : [(17258 ^ _780478) ^ [_1098599] : [hBOOL(hAPP(hAPP(c_member(_1098280), _1098599), hAPP(_1098286, _1098502))), -(hBOOL(hAPP(_1098288, _1098599)))]]]]], (39234 ^ _780478) ^ [_1542287, _1542289] : [c_Wellfounded_Owf(_1542287, hAPP(c_Set_OCollect(tc_prod(_1542287, _1542287)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542287, _1542287, tc_HOL_Obool), _1542289))), -(c_Wellfounded_OwfP(_1542287, _1542289))], (19440 ^ _780478) ^ [_1144272, _1144274] : [19441 ^ _780478 : [(19444 ^ _780478) ^ [] : [_1144272 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19442 ^ _780478) ^ [] : [_1144274 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1144272), _1144274) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50325 ^ _780478) ^ [_1798655, _1798657, _1798659, _1798661, _1798663, _1798665] : [c_Fun_Obij__betw(_1798655, _1798657, _1798659, c_Orderings_Otop__class_Otop(tc_fun(_1798655, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1798657, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1798655, _1798657, _1798659), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1798661, tc_fun(_1798655, tc_HOL_Obool)), _1798663), _1798665)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1798661, tc_fun(_1798657, tc_HOL_Obool)), _1798663), hAPP(hAPP(c_COMBB(tc_fun(_1798655, tc_HOL_Obool), tc_fun(_1798657, tc_HOL_Obool), _1798661), c_Set_Oimage(_1798655, _1798657, _1798659)), _1798665)))], (40949 ^ _780478) ^ [_1582829, _1582831, _1582833, _1582835] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582829, _1582829)), hAPP(hAPP(c_Product__Type_OPair(_1582829, _1582829), _1582831), _1582833)), hAPP(c_Relation_Oconverse(_1582829, _1582829), c_Transitive__Closure_Otrancl(_1582829, _1582835)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582829, _1582829)), hAPP(hAPP(c_Product__Type_OPair(_1582829, _1582829), _1582831), _1582833)), c_Transitive__Closure_Otrancl(_1582829, hAPP(c_Relation_Oconverse(_1582829, _1582829), _1582835)))))], (7439 ^ _780478) ^ [_905337, _905339, _905341, _905343, _905345] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_905337, _905339, _905341), _905343), _905345) = c_HOL_OThe(_905339, c_Finite__Set_Ofold__graph(_905337, _905339, _905341, _905343, _905345)))], (50240 ^ _780478) ^ [_1796885] : [-(_1796885 = hAPP(c_Code__Numeral_Oof__nat, 50238 ^ [_1796885]))], (33574 ^ _780478) ^ [_1413738] : [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), _1413738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1413738)))], (34421 ^ _780478) ^ [_1429689, _1429691] : [c_Int_OBit0(_1429689) = c_Int_OBit0(_1429691), -(_1429689 = _1429691)], (15151 ^ _780478) ^ [_1053303, _1053305, _1053307] : [class_Lattices_Olattice(_1053303), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053303), _1053305)), -(_1053305 = c_Orderings_Obot__class_Obot(tc_fun(_1053303, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1053303, hAPP(hAPP(c_Set_Oinsert(_1053303), _1053307), _1053305)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1053303), _1053307), c_Big__Operators_Olattice__class_OSup__fin(_1053303, _1053305)))], (33897 ^ _780478) ^ [_1420853, _1420855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420853), _1420855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1420853)), c_Int_OBit1(_1420855))))], (23309 ^ _780478) ^ [_1214078] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214078)) = _1214078)], (4950 ^ _780478) ^ [_856034, _856036] : [_856036 = _856034, -(c_Relation_OId(_856036) = c_Relation_OId(_856034))], (1764 ^ _780478) ^ [_805392, _805394] : [-(class_Groups_Omonoid__mult(_805392)), _805394 = _805392, class_Groups_Omonoid__mult(_805394)], (29267 ^ _780478) ^ [_1323858, _1323860, _1323862, _1323864] : [class_Divides_Osemiring__div(_1323858), -(c_Divides_Odiv__class_Omod(_1323858, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323858), _1323860), _1323862), _1323864) = c_Divides_Odiv__class_Omod(_1323858, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323858), c_Divides_Odiv__class_Omod(_1323858, _1323860, _1323864)), _1323862), _1323864))], (11387 ^ _780478) ^ [_979940, _979942, _979944, _979946] : [class_Orderings_Olinorder(_979940), hBOOL(hAPP(c_Finite__Set_Ofinite(_979940), _979942)), -(hAPP(hAPP(c_Finite__Set_Ofold(_979940, _979940, c_Orderings_Oord__class_Omax(_979940)), _979944), hAPP(hAPP(c_Set_Oinsert(_979940), _979946), _979942)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_979940), _979946), hAPP(hAPP(c_Finite__Set_Ofold(_979940, _979940, c_Orderings_Oord__class_Omax(_979940)), _979944), _979942)))], (29468 ^ _780478) ^ [_1327627, _1327629] : [29469 ^ _780478 : [(29470 ^ _780478) ^ [_1327676] : [_1327627 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1327629), _1327676)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327627, _1327629) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (52193 ^ _780478) ^ [_1832069] : [-(class_Nat_Osize(tc_Option_Ooption(_1832069)))], (28576 ^ _780478) ^ [_1309551, _1309553, _1309555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309551)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1309553), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1309555)), 28583 ^ _780478 : [(28584 ^ _780478) ^ [_1309759] : [28586 ^ _780478 : [(28592 ^ _780478) ^ [] : [-(_1309759 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28588 ^ [_1309551, _1309553, _1309555, _1309759]), 28585 ^ [_1309551, _1309553, _1309555, _1309759]))], (28590 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28588 ^ [_1309551, _1309553, _1309555, _1309759]), _1309555)))], (28587 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28585 ^ [_1309551, _1309553, _1309555, _1309759]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1309551))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1309759), _1309553)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1309759), _1309551)), _1309553)))]]], (6390 ^ _780478) ^ [_884125, _884127] : [-(c_Set_Othe__elem(_884125, _884127) = c_HOL_OThe(_884125, hAPP(hAPP(c_COMBB(tc_fun(_884125, tc_HOL_Obool), tc_HOL_Obool, _884125), hAPP(c_fequal, _884127)), hAPP(hAPP(c_COMBC(_884125, tc_fun(_884125, tc_HOL_Obool), tc_fun(_884125, tc_HOL_Obool)), c_Set_Oinsert(_884125)), c_Orderings_Obot__class_Obot(tc_fun(_884125, tc_HOL_Obool))))))], (51899 ^ _780478) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (17827 ^ _780478) ^ [_1112767, _1112769] : [_1112767 = _1112769, -(hAPP(c_Nat_OSuc, _1112767) = hAPP(c_Nat_OSuc, _1112769))], (44779 ^ _780478) ^ [_1677524, _1677526, _1677528, _1677530, _1677532] : [class_Rings_Osemiring__0(_1677524), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677524), hAPP(hAPP(c_List_Omap(_1677526, _1677524), hAPP(hAPP(c_COMBC(_1677526, _1677524, _1677524), hAPP(hAPP(c_COMBB(_1677524, tc_fun(_1677524, _1677524), _1677526), c_Groups_Otimes__class_Otimes(_1677524)), _1677528)), _1677530)), _1677532)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1677524), hAPP(c_List_Omonoid__add__class_Olistsum(_1677524), hAPP(hAPP(c_List_Omap(_1677526, _1677524), _1677528), _1677532))), _1677530))], (584 ^ _780478) ^ [_789276, _789278, _789280, _789282, _789284, _789286, _789288, _789290, _789292, _789294] : [-(c_List_Olist__all2(_789292, _789288, _789284, _789280, _789276)), c_List_Olist__all2(_789294, _789290, _789286, _789282, _789278), _789294 = _789292, _789290 = _789288, _789286 = _789284, _789282 = _789280, _789278 = _789276], (41862 ^ _780478) ^ [_1608006, _1608008] : [-(c_List_Olistrel1(_1608006, hAPP(c_Relation_Oconverse(_1608006, _1608006), _1608008)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1608006), tc_List_Olist(_1608006)), c_List_Olistrel1(_1608006, _1608008)))], (20913 ^ _780478) ^ [_1169868, _1169870, _1169872, _1169874] : [class_Rings_Ocomm__semiring__1(_1169868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169870), _1169872)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169870, _1169868), _1169874), _1169872) = c_Groups_Ozero__class_Ozero(_1169868)), 20922 ^ _780478 : [(20923 ^ _780478) ^ [_1170049] : [hBOOL(hAPP(hAPP(c_member(_1169870), _1170049), _1169872)), hAPP(_1169874, _1170049) = c_Groups_Ozero__class_Ozero(_1169868)]]], (18277 ^ _780478) ^ [_1122384, _1122386] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122384), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122384), _1122386)))))], (3224 ^ _780478) ^ [_828413, _828415, _828417, _828419, _828421, _828423, _828425, _828427, _828429, _828431] : [-(c_Fun_Ofun__upd(_828431, _828427, _828423, _828419, _828415) = c_Fun_Ofun__upd(_828429, _828425, _828421, _828417, _828413)), _828431 = _828429, _828427 = _828425, _828423 = _828421, _828419 = _828417, _828415 = _828413], (46969 ^ _780478) ^ [_1725165, _1725167, _1725169] : [_1725169 = hAPP(hAPP(c_List_Olist_OCons(_1725165), _1725167), c_List_Olist_ONil(_1725165)), -(hAPP(hAPP(c_List_Olist_OCons(_1725165), _1725167), c_List_Olist_ONil(_1725165)) = hAPP(c_List_Orev(_1725165), _1725169))], (44009 ^ _780478) ^ [_1661193, _1661195, _1661197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661193), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661195)), _1661197))), -(hAPP(hAPP(c_List_Olist_OCons(_1661195), hAPP(hAPP(c_List_Onth(_1661195), _1661197), _1661193)), hAPP(hAPP(c_List_Odrop(_1661195), hAPP(c_Nat_OSuc, _1661193)), _1661197)) = hAPP(hAPP(c_List_Odrop(_1661195), _1661193), _1661197))], (45669 ^ _780478) ^ [_1697384, _1697386] : [-(c_Enum_On__lists(_1697384, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1697386) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1697384)), c_List_Olist_ONil(_1697384)), c_List_Olist_ONil(tc_List_Olist(_1697384))))], (52119 ^ _780478) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (52353 ^ _780478) ^ [_1833875] : [hBOOL(hAPP(c_fNot, _1833875)), hBOOL(_1833875)], (46925 ^ _780478) ^ [_1724380, _1724382] : [hBOOL(hAPP(c_List_Odistinct(_1724380), hAPP(c_List_Orev(_1724380), _1724382))), -(hBOOL(hAPP(c_List_Odistinct(_1724380), _1724382)))], (610 ^ _780478) ^ [_789721, _789723, _789725, _789727] : [-(c_List_Olinorder__class_Osorted(_789725, _789721)), c_List_Olinorder__class_Osorted(_789727, _789723), _789727 = _789725, _789723 = _789721], (210 ^ _780478) ^ [_783875, _783877] : [-(class_Fields_Ofield(_783875)), _783877 = _783875, class_Fields_Ofield(_783877)], (29518 ^ _780478) ^ [_1328656, _1328658, _1328660, _1328662] : [class_Divides_Osemiring__div(_1328656), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328656), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328656), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1328656), _1328658), _1328660)), _1328660)), c_Divides_Odiv__class_Omod(_1328656, _1328658, _1328660))), _1328662) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328656), _1328658), _1328662))], (18956 ^ _780478) ^ [_1136356, _1136358, _1136360] : [class_Lattices_Olattice(_1136356), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136356), _1136358)), -(hBOOL(hAPP(hAPP(c_member(_1136356), _1136360), _1136358))), -(c_Big__Operators_Olattice__class_OInf__fin(_1136356, hAPP(hAPP(c_Set_Oinsert(_1136356), _1136360), _1136358)) = hAPP(hAPP(c_Finite__Set_Ofold(_1136356, _1136356, c_Lattices_Osemilattice__inf__class_Oinf(_1136356)), _1136360), _1136358))], (28696 ^ _780478) ^ [_1311891, _1311893, _1311895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1311891)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1311893), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1311895)), 28706 ^ _780478 : [(28712 ^ _780478) ^ [] : [-(_1311893 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28708 ^ [_1311891, _1311893, _1311895]), 28705 ^ [_1311891, _1311893, _1311895]))], (28710 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28708 ^ [_1311891, _1311893, _1311895]), _1311895)))], (28707 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28705 ^ [_1311891, _1311893, _1311895]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1311891))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1311893), _1311891) = _1311893)], (18137 ^ _780478) ^ [_1118660, _1118662, _1118664, _1118666] : [18139 ^ _780478 : [(18142 ^ _780478) ^ [] : [hAPP(_1118666, 18138 ^ [_1118660, _1118662, _1118664, _1118666]) = c_Orderings_Otop__class_Otop(tc_fun(_1118662, tc_HOL_Obool))], (18140 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1118660), 18138 ^ [_1118660, _1118662, _1118664, _1118666]), _1118664)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1118660, tc_fun(_1118662, tc_HOL_Obool)), _1118664), _1118666) = c_Orderings_Otop__class_Otop(tc_fun(_1118662, tc_HOL_Obool)))], (33909 ^ _780478) ^ [_1421056, _1421058] : [_1421056 = _1421058, -(c_Int_OBit1(_1421056) = c_Int_OBit1(_1421058))], (21742 ^ _780478) ^ [_1184210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1184210)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1184210), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1184210)], (44195 ^ _780478) ^ [_1665002, _1665004, _1665006] : [-(hAPP(c_List_Otl(_1665002), hAPP(hAPP(c_List_Otake(_1665002), _1665004), _1665006)) = hAPP(hAPP(c_List_Otake(_1665002), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1665004), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1665002), _1665006)))], (17245 ^ _780478) ^ [_1098137, _1098139, _1098141, _1098143, _1098145, _1098147] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098137, tc_fun(_1098139, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098141, tc_fun(_1098137, tc_HOL_Obool)), _1098143), _1098145)), _1098147) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098141, tc_fun(_1098139, tc_HOL_Obool)), _1098143), hAPP(hAPP(c_COMBC(_1098141, tc_fun(_1098137, tc_fun(_1098139, tc_HOL_Obool)), tc_fun(_1098139, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1098137, tc_HOL_Obool), tc_fun(tc_fun(_1098137, tc_fun(_1098139, tc_HOL_Obool)), tc_fun(_1098139, tc_HOL_Obool)), _1098141), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098137, tc_fun(_1098139, tc_HOL_Obool))), _1098145)), _1098147)))], (45739 ^ _780478) ^ [_1698961, _1698963] : [hBOOL(hAPP(c_List_Odistinct(_1698961), _1698963)), -(c_List_Oremdups(_1698961, _1698963) = _1698963)], (27739 ^ _780478) ^ [_1293103, _1293105] : [class_Groups_Oordered__ab__group__add(_1293103), -(hAPP(c_Set_Oimage(_1293103, _1293103, c_Groups_Ouminus__class_Ouminus(_1293103)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1293103), _1293105)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1293103), hAPP(c_Groups_Ouminus__class_Ouminus(_1293103), _1293105)))], (34437 ^ _780478) ^ [_1429956, _1429958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1429956)), c_Int_OBit0(_1429958))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1429956), _1429958)))], (13230 ^ _780478) ^ [_1015418, _1015420, _1015422, _1015424] : [hBOOL(hAPP(hAPP(c_member(_1015418), _1015424), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1015418, tc_HOL_Obool)), _1015420), _1015422))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1015418, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1015418, tc_fun(_1015418, tc_HOL_Obool), tc_HOL_Obool), c_member(_1015418)), _1015420)), hAPP(hAPP(c_COMBC(_1015418, tc_fun(_1015418, tc_HOL_Obool), tc_HOL_Obool), c_member(_1015418)), _1015422)), _1015424)))], (6884 ^ _780478) ^ [_894596, _894598, _894600, _894602, _894604] : [-(c_Fun_Oinj__on(_894596, _894598, _894600, hAPP(hAPP(c_Set_Oinsert(_894596), _894602), _894604))), c_Fun_Oinj__on(_894596, _894598, _894600, _894604), -(hBOOL(hAPP(hAPP(c_member(_894598), hAPP(_894600, _894602)), hAPP(c_Set_Oimage(_894596, _894598, _894600), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894596, tc_HOL_Obool)), _894604), hAPP(hAPP(c_Set_Oinsert(_894596), _894602), c_Orderings_Obot__class_Obot(tc_fun(_894596, tc_HOL_Obool))))))))], (39725 ^ _780478) ^ [_1553935, _1553937, _1553939, _1553941, _1553943, _1553945, _1553947] : [-(hAPP(c_Product__Type_Oapsnd(_1553935, _1553937, _1553939, _1553941), hAPP(c_Product__Type_Oapsnd(_1553943, _1553935, _1553939, _1553945), _1553947)) = hAPP(c_Product__Type_Oapsnd(_1553943, _1553937, _1553939, hAPP(c_Fun_Ocomp(_1553935, _1553937, _1553943, _1553941), _1553945)), _1553947))], (7704 ^ _780478) ^ [_910622, _910624, _910626, _910628] : [c_Hoare__Mirabelle_Ohoare__derivs(_910622, _910624, _910626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_910622), tc_HOL_Obool)), _910624), _910628)), -(c_Hoare__Mirabelle_Ohoare__derivs(_910622, _910628, _910626))], (11335 ^ _780478) ^ [_978846, _978848, _978850] : [class_Groups_Ogroup__add(_978846), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_978846), _978848), hAPP(c_Groups_Ouminus__class_Ouminus(_978846), _978850)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978846), _978848), _978850))], (23321 ^ _780478) ^ [_1214326, _1214328] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214326), _1214328)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214326)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214328)))], (13250 ^ _780478) ^ [_1015935, _1015937, _1015939, _1015941] : [-(hAPP(c_Finite__Set_Ofold__image(_1015935, _1015937, _1015939), _1015941) = c_Finite__Set_Ofold(_1015937, _1015935, hAPP(hAPP(c_COMBB(_1015935, tc_fun(_1015935, _1015935), _1015937), _1015939), _1015941)))], (29942 ^ _780478) ^ [_1336146, _1336148, _1336150] : [class_Rings_Olinordered__idom(_1336146), -(c_Groups_Osgn__class_Osgn(_1336146, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336146), _1336148), _1336150)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336146), c_Groups_Osgn__class_Osgn(_1336146, _1336148)), c_Groups_Osgn__class_Osgn(_1336146, _1336150)))], (43083 ^ _780478) ^ [_1639628, _1639630] : [_1639630 = c_List_Olist_ONil(_1639628), -(hAPP(c_List_Oset(_1639628), _1639630) = c_Orderings_Obot__class_Obot(tc_fun(_1639628, tc_HOL_Obool)))], (38564 ^ _780478) ^ [_1522323, _1522325, _1522327, _1522329] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1522323, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1522325, _1522323), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1522325, _1522323), tc_HOL_Obool)), _1522327), _1522329))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1522323, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1522325, _1522323), _1522327)), hAPP(c_Relation_ORange(_1522325, _1522323), _1522329)))))], (13060 ^ _780478) ^ [_1011907] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1011907) = c_Orderings_Oord__class_Omax(_1011907)), class_Lattices_Osemilattice__sup(_1011907), class_Orderings_Olinorder(_1011907)], (45679 ^ _780478) ^ [_1697617, _1697619, _1697621, _1697623, _1697625] : [45681 ^ _780478 : [(45684 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1697617, _1697619, tc_HOL_Obool), _1697625), 45680 ^ [_1697617, _1697619, _1697621, _1697623, _1697625]))], (45682 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1697617, _1697619)), 45680 ^ [_1697617, _1697619, _1697621, _1697623, _1697625]), hAPP(c_List_Oset(tc_prod(_1697617, _1697619)), hAPP(hAPP(c_List_Ozip(_1697617, _1697619), _1697621), _1697623)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697617)), _1697621) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697619)), _1697623), -(c_List_Olist__all2(_1697617, _1697619, _1697625, _1697621, _1697623))], (37401 ^ _780478) ^ [_1492348] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1492348)], (41430 ^ _780478) ^ [_1595661, _1595663, _1595665, _1595667, _1595669] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595661, _1595661)), hAPP(hAPP(c_Product__Type_OPair(_1595661, _1595661), _1595663), _1595665)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595661, _1595661), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1595667)), _1595669))), 41434 ^ _780478 : [(41437 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595661, _1595661)), hAPP(hAPP(c_Product__Type_OPair(_1595661, _1595661), 41433 ^ [_1595661, _1595663, _1595665, _1595667, _1595669]), _1595665)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595661, _1595661), tc_HOL_Obool), _1595667), _1595669))))], (41435 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595661, _1595661)), hAPP(hAPP(c_Product__Type_OPair(_1595661, _1595661), _1595663), 41433 ^ [_1595661, _1595663, _1595665, _1595667, _1595669])), _1595669)))]]], (41057 ^ _780478) ^ [_1585969, _1585971, _1585973] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585969, _1585969)), hAPP(hAPP(c_Product__Type_OPair(_1585969, _1585969), _1585971), _1585973)), c_Relation_OId(_1585969))), -(_1585971 = _1585973)], (18530 ^ _780478) ^ [_1127762, _1127764, _1127766, _1127768, _1127770] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127762, tc_fun(_1127764, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1127762, tc_HOL_Obool)), _1127766), _1127768)), _1127770) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127764, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127762, tc_fun(_1127764, tc_HOL_Obool)), _1127766), _1127770)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127762, tc_fun(_1127764, tc_HOL_Obool)), _1127768), _1127770)))], (41700 ^ _780478) ^ [_1602393, _1602395, _1602397, _1602399, _1602401] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602393), tc_List_Olist(_1602393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602393), tc_List_Olist(_1602393)), _1602395), _1602397)), hAPP(c_List_Olexn(_1602393, _1602399), _1602401))), 41703 ^ _780478 : [(41706 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602393)), _1602397) = _1602401)], (41704 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602393)), _1602395) = _1602401)]]], (47391 ^ _780478) ^ [_1734072, _1734074, _1734076, _1734078, _1734080] : [-(c_List_OdropWhile(_1734072, _1734074, hAPP(hAPP(c_List_Omap(_1734076, _1734072), _1734078), _1734080)) = hAPP(hAPP(c_List_Omap(_1734076, _1734072), _1734078), c_List_OdropWhile(_1734076, hAPP(c_Fun_Ocomp(_1734072, tc_HOL_Obool, _1734076, _1734074), _1734078), _1734080)))], (29548 ^ _780478) ^ [_1329234, _1329236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1329234), _1329236)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329234, _1329236) = _1329234)], (22413 ^ _780478) ^ [_1197273, _1197275, _1197277] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1197273), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1197275), _1197277)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1197273), _1197275)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1197273), _1197277)))], (37804 ^ _780478) ^ [_1502381, _1502383, _1502385, _1502387] : [c_Wellfounded_Omax__extp(_1502381, hAPP(hAPP(c_COMBC(_1502381, tc_fun(tc_prod(_1502381, _1502381), tc_HOL_Obool), tc_fun(_1502381, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502381, tc_fun(tc_fun(tc_prod(_1502381, _1502381), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1502381, _1502381), tc_HOL_Obool), tc_fun(_1502381, tc_HOL_Obool)), _1502381), c_COMBC(_1502381, tc_fun(tc_prod(_1502381, _1502381), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502381, tc_prod(_1502381, _1502381)), tc_fun(_1502381, tc_fun(tc_fun(tc_prod(_1502381, _1502381), tc_HOL_Obool), tc_HOL_Obool)), _1502381), hAPP(c_COMBB(tc_prod(_1502381, _1502381), tc_fun(tc_fun(tc_prod(_1502381, _1502381), tc_HOL_Obool), tc_HOL_Obool), _1502381), c_member(tc_prod(_1502381, _1502381)))), c_Product__Type_OPair(_1502381, _1502381)))), _1502383), _1502385, _1502387), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1502381, tc_HOL_Obool), tc_fun(_1502381, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1502381, tc_HOL_Obool), tc_fun(_1502381, tc_HOL_Obool)), _1502385), _1502387)), c_Wellfounded_Omax__ext(_1502381, _1502383))))], (51445 ^ _780478) ^ [_1822377, _1822379] : [c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822377, _1822379) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822377), _1822379)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822379), _1822377)))], (47027 ^ _780478) ^ [_1726517, _1726519] : [-(hAPP(c_List_Orev(_1726517), hAPP(c_List_Orev(_1726517), _1726519)) = _1726519)], (6826 ^ _780478) ^ [_893383, _893385, _893387, _893389] : [-(c_Com_Ocom_OWhile(_893383, _893385) = c_Com_Ocom_OWhile(_893387, _893389)), _893383 = _893387, _893385 = _893389], (9576 ^ _780478) ^ [_945132, _945134] : [class_Orderings_Olinorder(_945132), -(c_Big__Operators_Olinorder__class_OMax(_945132, hAPP(hAPP(c_Set_Oinsert(_945132), _945134), c_Orderings_Obot__class_Obot(tc_fun(_945132, tc_HOL_Obool)))) = _945134)], (28997 ^ _780478) ^ [_1317777, _1317779, _1317781, _1317783, _1317785] : [hAPP(c_Set_Oimage(_1317777, _1317779, _1317781), _1317783) = _1317785, -(hAPP(c_Set_Oimage(tc_fun(_1317777, tc_HOL_Obool), tc_fun(_1317779, tc_HOL_Obool), c_Set_Oimage(_1317777, _1317779, _1317781)), hAPP(c_Set_OPow(_1317777), _1317783)) = hAPP(c_Set_OPow(_1317779), _1317785))], (48413 ^ _780478) ^ [_1756382, _1756384, _1756386, _1756388] : [-(c_New__Random__Sequence_Opos__empty(_1756382, _1756384, _1756386, _1756388) = c_New__DSequence_Opos__empty(_1756382))], (6184 ^ _780478) ^ [_879424, _879426, _879428, _879430] : [_879430 = c_Orderings_Obot__class_Obot(tc_fun(_879424, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_879424, _879426, _879428), _879430) = c_Orderings_Obot__class_Obot(tc_fun(_879426, tc_HOL_Obool)))], (31615 ^ _780478) ^ [_1376434, _1376436] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1376434), _1376436)), -(_1376436 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1376434, 31619 ^ [_1376434, _1376436]), 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)), 31618 ^ [_1376434, _1376436]))))], (48194 ^ _780478) ^ [_1752023] : [class_Nat_Osize(_1752023), -(c_FunDef_Ois__measure(_1752023, c_Nat_Osize__class_Osize(_1752023)))], (2182 ^ _780478) ^ [_812334, _812336, _812338, _812340, _812342, _812344, _812346, _812348] : [-(c_Sum__Type_OPlus(_812348, _812344, _812340, _812336) = c_Sum__Type_OPlus(_812346, _812342, _812338, _812334)), _812348 = _812346, _812344 = _812342, _812340 = _812338, _812336 = _812334], (6752 ^ _780478) ^ [_892219, _892221, _892223, _892225, _892227] : [hAPP(_892223, _892225) = _892227, -(c_Fun_Ofun__upd(_892219, _892221, _892223, _892225, _892227) = _892223)], (41285 ^ _780478) ^ [_1591647, _1591649, _1591651] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591647, _1591647)), _1591649), c_Transitive__Closure_Otrancl(_1591647, _1591651))), 41289 ^ _780478 : [(41292 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591647, _1591647)), _1591649), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591647, _1591647), tc_HOL_Obool), 41288 ^ [_1591647, _1591649, _1591651]), _1591651))))], (41290 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41288 ^ [_1591647, _1591649, _1591651])))]]], (31146 ^ _780478) ^ [_1360117, _1360119, _1360121] : [-(hAPP(c_Set_OCollect(_1360117), hAPP(hAPP(c_COMBS(_1360117, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1360117), c_fconj), _1360119)), _1360121)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1360117, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1360117), _1360119)), hAPP(c_Set_OCollect(_1360117), _1360121)))], (41283 ^ _780478) ^ [_1591593, _1591595] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591593, _1591593), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1591595) = c_Fun_Oid(_1591593))], (49220 ^ _780478) ^ [_1774964, _1774966] : [c_Relation_Otrans(_1774964, _1774966), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1774964, _1774964), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1774964, _1774964, _1774964), _1774966), _1774966)), _1774966)))], (13354 ^ _780478) ^ [_1018152, _1018154, _1018156, _1018158] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018152), _1018154)), -(hAPP(c_Set_Oimage(_1018152, _1018156, _1018158), _1018154) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1018156, tc_HOL_Obool), _1018152, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1018156, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1018152, tc_fun(_1018156, tc_HOL_Obool), tc_fun(_1018156, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1018156, tc_fun(tc_fun(_1018156, tc_HOL_Obool), tc_fun(_1018156, tc_HOL_Obool)), _1018152), c_Set_Oinsert(_1018156)), _1018158)), c_Orderings_Obot__class_Obot(tc_fun(_1018156, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1018156, tc_HOL_Obool))), _1018154))], (44755 ^ _780478) ^ [_1676754, _1676756, _1676758, _1676760, _1676762] : [class_Groups_Ocomm__monoid__add(_1676754), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676754), hAPP(hAPP(c_List_Omap(_1676756, _1676754), hAPP(hAPP(c_COMBS(_1676756, _1676754, _1676754), hAPP(hAPP(c_COMBB(_1676754, tc_fun(_1676754, _1676754), _1676756), c_Groups_Oplus__class_Oplus(_1676754)), _1676758)), _1676760)), _1676762)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1676754), hAPP(c_List_Omonoid__add__class_Olistsum(_1676754), hAPP(hAPP(c_List_Omap(_1676756, _1676754), _1676758), _1676762))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676754), hAPP(hAPP(c_List_Omap(_1676756, _1676754), _1676760), _1676762))))], (52313 ^ _780478) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (34619 ^ _780478) ^ [_1433119] : [-(c_Int_Osucc(c_Int_OBit1(_1433119)) = c_Int_OBit0(c_Int_Osucc(_1433119)))], (33314 ^ _780478) ^ [_1409729] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1409729) = _1409729)], (8780 ^ _780478) ^ [_932250, _932252, _932254, _932256] : [class_Orderings_Oorder(_932250), _932252 = _932254, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932250), _932256), _932254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932250), _932256), _932252)))], (7028 ^ _780478) ^ [_897854, _897856] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897854, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_897854, tc_HOL_Obool))), _897856)))], (7802 ^ _780478) ^ [_912614, _912616, _912618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912614, tc_HOL_Obool)), _912616), hAPP(hAPP(c_Set_Oinsert(_912614), _912618), c_Orderings_Obot__class_Obot(tc_fun(_912614, tc_HOL_Obool))))), -(_912616 = c_Orderings_Obot__class_Obot(tc_fun(_912614, tc_HOL_Obool))), -(_912616 = hAPP(hAPP(c_Set_Oinsert(_912614), _912618), c_Orderings_Obot__class_Obot(tc_fun(_912614, tc_HOL_Obool))))], (16326 ^ _780478) ^ [_1077372, _1077374, _1077376, _1077378] : [hBOOL(hAPP(hAPP(c_member(_1077372), _1077374), _1077376)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077372, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1077372), _1077374), _1077378)), _1077376) = hAPP(hAPP(c_Set_Oinsert(_1077372), _1077374), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077372, tc_HOL_Obool)), _1077378), _1077376)))], (5082 ^ _780478) ^ [_858094, _858096, _858098, _858100, _858102, _858104] : [-(c_Product__Type_Oprod_Oprod__case(_858104, _858100, _858096) = c_Product__Type_Oprod_Oprod__case(_858102, _858098, _858094)), _858104 = _858102, _858100 = _858098, _858096 = _858094], (26298 ^ _780478) ^ [_1268001, _1268003, _1268005] : [class_Fields_Olinordered__field__inverse__zero(_1268001), 26301 ^ _780478 : [(26316 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268001), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268001), _1268003), _1268005)), c_Groups_Ozero__class_Ozero(_1268001)))), 26317 ^ _780478 : [(26324 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268001), _1268003), c_Groups_Ozero__class_Ozero(_1268001))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268001), c_Groups_Ozero__class_Ozero(_1268001)), _1268005))], (26318 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268001), c_Groups_Ozero__class_Ozero(_1268001)), _1268003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268001), _1268005), c_Groups_Ozero__class_Ozero(_1268001)))]]], (26302 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268001), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268001), _1268003), _1268005)), c_Groups_Ozero__class_Ozero(_1268001))), 26307 ^ _780478 : [(26310 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268001), _1268005), c_Groups_Ozero__class_Ozero(_1268001))))], (26308 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268001), c_Groups_Ozero__class_Ozero(_1268001)), _1268003)))]], 26311 ^ _780478 : [(26314 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268001), c_Groups_Ozero__class_Ozero(_1268001)), _1268005)))], (26312 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268001), _1268003), c_Groups_Ozero__class_Ozero(_1268001))))]]]]], (27108 ^ _780478) ^ [_1282830, _1282832] : [c_Nat__Transfer_Onat__set(_1282830), c_Nat__Transfer_Onat__set(_1282832), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1282830), _1282832) = 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), _1282830)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1282832))))], (10299 ^ _780478) ^ [_960094, _960096, _960098] : [class_Orderings_Olinorder(_960094), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_960094), _960096), hAPP(hAPP(c_Orderings_Oord__class_Omax(_960094), _960096), _960098)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_960094), _960096), _960098))], (45621 ^ _780478) ^ [_1696261, _1696263, _1696265, _1696267] : [hBOOL(hAPP(c_List_Odistinct(_1696261), _1696263)), hBOOL(hAPP(c_List_Odistinct(_1696265), _1696267)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1696261, _1696265)), c_Enum_Oproduct(_1696261, _1696265, _1696263, _1696267))))], (23427 ^ _780478) ^ [] : [-(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))))], (26966 ^ _780478) ^ [_1280091, _1280093, _1280095, _1280097] : [class_Fields_Ofield(_1280091), -(_1280093 = c_Groups_Ozero__class_Ozero(_1280091)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1280091), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280091), _1280095), _1280093)), _1280097) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280091), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1280091), _1280095), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1280091), _1280093), _1280097))), _1280093))], (51891 ^ _780478) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (34105 ^ _780478) ^ [_1424217, _1424219] : [class_Int_Onumber__ring(_1424217), 34108 ^ _780478 : [(34115 ^ _780478) ^ [] : [c_Int_Oiszero(_1424217, hAPP(c_Int_Onumber__class_Onumber__of(_1424217), 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), _1424219)))), -(c_Groups_Oone__class_Oone(_1424217) = hAPP(c_Int_Onumber__class_Onumber__of(_1424217), _1424219))], (34109 ^ _780478) ^ [] : [c_Groups_Oone__class_Oone(_1424217) = hAPP(c_Int_Onumber__class_Onumber__of(_1424217), _1424219), -(c_Int_Oiszero(_1424217, hAPP(c_Int_Onumber__class_Onumber__of(_1424217), 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), _1424219)))))]]], (44564 ^ _780478) ^ [_1672443, _1672445, _1672447] : [_1672443 = c_List_Olist_ONil(_1672445), -(c_List_Olast(_1672445, hAPP(hAPP(c_List_Oappend(_1672445), _1672447), _1672443)) = c_List_Olast(_1672445, _1672447))], (44919 ^ _780478) ^ [_1680692, _1680694, _1680696] : [c_Fun_Oinj__on(tc_List_Olist(_1680692), tc_List_Olist(_1680694), hAPP(c_List_Omap(_1680692, _1680694), _1680696), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1680692), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1680692, _1680694, _1680696, c_Orderings_Otop__class_Otop(tc_fun(_1680692, tc_HOL_Obool))))], (9508 ^ _780478) ^ [_943506] : [class_Lattices_Oab__semigroup__idem__mult(_943506), -(c_Finite__Set_Ofun__left__comm__idem(_943506, _943506, c_Groups_Otimes__class_Otimes(_943506)))], (42636 ^ _780478) ^ [_1630173, _1630175, _1630177, _1630179, _1630181] : [-(_1630173 = _1630175), -(hAPP(hAPP(c_List_Onth(_1630177), hAPP(hAPP(c_List_Olist__update(_1630177, _1630179), _1630173), _1630181)), _1630175) = hAPP(hAPP(c_List_Onth(_1630177), _1630179), _1630175))], (51573 ^ _780478) ^ [_1824476] : [_1824476 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824476), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (24305 ^ _780478) ^ [_1232542, _1232544] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232542), _1232544) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1232544 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24314 ^ _780478 : [(24317 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232542), _1232544)))], (24315 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232542)))]], 24318 ^ _780478 : [(24321 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232544), _1232542)))], (24319 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232542), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (40750 ^ _780478) ^ [_1578485, _1578487] : [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), _1578485), _1578487)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1578485), _1578487)))], (23203 ^ _780478) ^ [_1212368] : [-(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), _1212368))))], (37449 ^ _780478) ^ [_1494132] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1494132)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1494132)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16142 ^ _780478) ^ [_1072766, _1072768] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072766, tc_HOL_Obool)), _1072768), c_Orderings_Obot__class_Obot(tc_fun(_1072766, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1072766, tc_HOL_Obool)))], (39611 ^ _780478) ^ [_1551504, _1551506, _1551508] : [-(c_Hilbert__Choice_OEps(tc_prod(_1551504, _1551506), hAPP(c_Product__Type_Oprod_Oprod__case(_1551504, _1551506, tc_HOL_Obool), _1551508)) = c_Hilbert__Choice_OEps(tc_prod(_1551504, _1551506), hAPP(hAPP(c_COMBS(tc_prod(_1551504, _1551506), _1551506, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1551504, tc_fun(_1551506, tc_HOL_Obool), tc_prod(_1551504, _1551506)), _1551508), c_Product__Type_Ofst(_1551504, _1551506))), c_Product__Type_Osnd(_1551504, _1551506))))], (6618 ^ _780478) ^ [_889122, _889124, _889126, _889128] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_889122), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889122, tc_HOL_Obool)), _889124), hAPP(hAPP(c_Set_Oinsert(_889122), _889126), _889128)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_889122), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889122, tc_HOL_Obool)), _889124), _889128))))], (29369 ^ _780478) ^ [_1325867, _1325869, _1325871, _1325873] : [class_Divides_Osemiring__div(_1325867), -(c_Divides_Odiv__class_Omod(_1325867, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325867), _1325869), _1325871), _1325873) = c_Divides_Odiv__class_Omod(_1325867, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325867), c_Divides_Odiv__class_Omod(_1325867, _1325869, _1325873)), _1325871), _1325873))], (26650 ^ _780478) ^ [_1274199, _1274201, _1274203, _1274205] : [class_Fields_Olinordered__field__inverse__zero(_1274199), 26653 ^ _780478 : [(26654 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), _1274201), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274199), _1274203), _1274205))), 26657 ^ _780478 : [(26664 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), c_Groups_Ozero__class_Ozero(_1274199)), _1274205))), 26667 ^ _780478 : [(26674 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), _1274205), c_Groups_Ozero__class_Ozero(_1274199)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), _1274201), c_Groups_Ozero__class_Ozero(_1274199))))], (26668 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), _1274205), c_Groups_Ozero__class_Ozero(_1274199))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), _1274203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274199), _1274201), _1274205))))]]], (26658 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), c_Groups_Ozero__class_Ozero(_1274199)), _1274205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274199), _1274201), _1274205)), _1274203)))]]], (26680 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), _1274201), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274199), _1274203), _1274205)))), 26683 ^ _780478 : [(26686 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274199), _1274201), _1274205)), _1274203))], (26684 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), c_Groups_Ozero__class_Ozero(_1274199)), _1274205)))]], 26687 ^ _780478 : [(26690 ^ _780478) ^ [] : [26691 ^ _780478 : [(26694 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), _1274203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1274199), _1274201), _1274205)))], (26692 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), _1274205), c_Groups_Ozero__class_Ozero(_1274199))))]], 26695 ^ _780478 : [(26698 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), _1274201), c_Groups_Ozero__class_Ozero(_1274199)))], (26696 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), _1274205), c_Groups_Ozero__class_Ozero(_1274199)))]]], (26688 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274199), c_Groups_Ozero__class_Ozero(_1274199)), _1274205))]]]]], (51913 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (28128 ^ _780478) ^ [_1300897, _1300899, _1300901, _1300903] : [class_Groups_Ocomm__monoid__add(_1300897), 28131 ^ _780478 : [(28138 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1300899)), _1300901))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300897), _1300903), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1300901, hAPP(c_Nat_OSuc, _1300899))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300897), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300897), _1300903), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1300901, _1300899))), hAPP(_1300903, hAPP(c_Nat_OSuc, _1300899))))], (28132 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1300899)), _1300901)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300897), _1300903), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1300901, hAPP(c_Nat_OSuc, _1300899))) = c_Groups_Ozero__class_Ozero(_1300897))]]], (13134 ^ _780478) ^ [_1013366, _1013368, _1013370] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013366, tc_HOL_Obool)), _1013368), _1013370) = _1013370, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013366, tc_HOL_Obool)), _1013368), _1013370)))], (23731 ^ _780478) ^ [] : [-(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)))], (10281 ^ _780478) ^ [_959701, _959703, _959705, _959707] : [class_Orderings_Olinorder(_959701), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_959701), _959703), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959701), _959705), _959707)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_959701), _959705), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959701), _959703), _959707)))], (10777 ^ _780478) ^ [_968467, _968469, _968471] : [class_Orderings_Olinorder(_968467), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968467), hAPP(hAPP(c_Orderings_Oord__class_Omin(_968467), _968469), _968471)), _968469)))], (45293 ^ _780478) ^ [_1688406, _1688408, _1688410, _1688412] : [-(hBOOL(hAPP(c_List_Olistsp(_1688406, hAPP(hAPP(c_COMBS(_1688406, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1688406), c_fconj), _1688408)), _1688410)), _1688412))), hBOOL(hAPP(c_List_Olistsp(_1688406, _1688408), _1688412)), hBOOL(hAPP(c_List_Olistsp(_1688406, _1688410), _1688412))], (38744 ^ _780478) ^ [_1527572, _1527574, _1527576, _1527578] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1527572, _1527574)), hAPP(hAPP(c_Product__Type_OSigma(_1527572, _1527574), _1527576), hAPP(c_COMBK(tc_fun(_1527574, tc_HOL_Obool), _1527572), _1527578))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1527572), _1527576)), hAPP(c_Finite__Set_Ocard(_1527574), _1527578)))], (18011 ^ _780478) ^ [_1115746, _1115748] : [18012 ^ _780478 : [(18015 ^ _780478) ^ [] : [_1115746 = hAPP(c_Nat_OSuc, _1115748)], (18013 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115746), _1115748))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115746), hAPP(c_Nat_OSuc, _1115748))))], (374 ^ _780478) ^ [_786171, _786173, _786175, _786177] : [-(c_Relation_Oirrefl(_786175, _786171)), c_Relation_Oirrefl(_786177, _786173), _786177 = _786175, _786173 = _786171], (45127 ^ _780478) ^ [_1685061, _1685063] : [-(c_Random_Oselect__weight(_1685061, _1685063) = 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(_1685061, 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, _1685061), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1685061)), _1685063)))), hAPP(hAPP(c_COMBB(_1685061, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1685061, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1685061, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1685061, _1685063))))], (30857 ^ _780478) ^ [_1353585, _1353587, _1353589, _1353591] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1353585, tc_fun(_1353587, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353585, tc_HOL_Obool), _1353589)), _1353591) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1353585, tc_HOL_Obool), tc_fun(_1353587, tc_HOL_Obool)), _1353589), hAPP(hAPP(c_COMBC(tc_fun(_1353585, tc_HOL_Obool), tc_fun(_1353585, tc_fun(_1353587, tc_HOL_Obool)), tc_fun(_1353587, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1353585, tc_fun(_1353587, tc_HOL_Obool))), _1353591)))], (31189 ^ _780478) ^ [_1360913, _1360915] : [hAPP(c_Set_OCollect(_1360913), _1360915) = c_Orderings_Obot__class_Obot(tc_fun(_1360913, tc_HOL_Obool)), 31192 ^ _780478 : [(31193 ^ _780478) ^ [_1360998] : [hBOOL(hAPP(_1360915, _1360998))]]], (12440 ^ _780478) ^ [_1000100, _1000102, _1000104] : [class_Orderings_Olinorder(_1000100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000100), _1000102)), -(_1000102 = c_Orderings_Obot__class_Obot(tc_fun(_1000100, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000100), _1000104)), -(_1000104 = c_Orderings_Obot__class_Obot(tc_fun(_1000100, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1000100, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000100, tc_HOL_Obool)), _1000102), _1000104)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1000100), c_Big__Operators_Olinorder__class_OMax(_1000100, _1000102)), c_Big__Operators_Olinorder__class_OMax(_1000100, _1000104)))], (1254 ^ _780478) ^ [_799017, _799019] : [-(class_Rings_Ocomm__ring(_799017)), _799019 = _799017, class_Rings_Ocomm__ring(_799019)], (43640 ^ _780478) ^ [_1651645, _1651647, _1651649, _1651651, _1651653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1651645), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651647)), _1651649))), -(hAPP(hAPP(c_List_Olist__update(_1651647, hAPP(hAPP(c_List_Oappend(_1651647), _1651649), _1651651)), _1651645), _1651653) = hAPP(hAPP(c_List_Oappend(_1651647), hAPP(hAPP(c_List_Olist__update(_1651647, _1651649), _1651645), _1651653)), _1651651))], (45935 ^ _780478) ^ [_1702727, _1702729] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702727)), c_List_Oconcat(_1702727, _1702729)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1702727), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1702727))), _1702729)))], (31474 ^ _780478) ^ [_1370409] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1370409) = 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), _1370409), c_Int_Onat)))))], (40855 ^ _780478) ^ [_1580517, _1580519] : [-(hAPP(c_Relation_Oconverse(_1580517, _1580517), c_Relation_OId__on(_1580517, _1580519)) = c_Relation_OId__on(_1580517, _1580519))], (28318 ^ _780478) ^ [_1304612] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1304612)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304612))], (34055 ^ _780478) ^ [_1423436] : [class_Int_Onumber__ring(_1423436), -(c_Groups_Oone__class_Oone(_1423436) = hAPP(c_Int_Onumber__class_Onumber__of(_1423436), c_Int_OBit1(c_Int_OPls)))], (9832 ^ _780478) ^ [_950622, _950624, _950626] : [class_Rings_Ocomm__semiring__1(_950622), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950622), _950624), _950626) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950622), _950626), _950624))], (29578 ^ _780478) ^ [_1329717, _1329719] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329717, _1329719) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329717, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1329719)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329717, _1329719)), _1329719))], (2302 ^ _780478) ^ [_814162, _814164] : [_814164 = _814162, -(c_Int_Opred(_814164) = c_Int_Opred(_814162))], (50261 ^ _780478) ^ [_1797250, _1797252] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1797250), _1797252))), -(c_Quickcheck_Obeyond(_1797250, _1797252) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (43742 ^ _780478) ^ [_1654233, _1654235, _1654237, _1654239, _1654241, _1654243, _1654245, _1654247] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654233, _1654233)), hAPP(hAPP(c_Product__Type_OPair(_1654233, _1654233), _1654235), _1654237)), _1654239)), _1654241 = hAPP(hAPP(c_List_Oappend(_1654233), _1654243), hAPP(hAPP(c_List_Olist_OCons(_1654233), _1654235), _1654245)), _1654247 = hAPP(hAPP(c_List_Oappend(_1654233), _1654243), hAPP(hAPP(c_List_Olist_OCons(_1654233), _1654237), _1654245)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654233), tc_List_Olist(_1654233))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654233), tc_List_Olist(_1654233)), _1654241), _1654247)), c_List_Olistrel1(_1654233, _1654239))))], (52023 ^ _780478) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (28322 ^ _780478) ^ [_1304676] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1304676)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1304676)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304676)))], (24823 ^ _780478) ^ [_1241649, _1241651, _1241653] : [class_Orderings_Oorder(_1241649), 24826 ^ _780478 : [(24833 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241649), _1241651), _1241653))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1241649, _1241651, _1241653) = c_Orderings_Obot__class_Obot(tc_fun(_1241649, tc_HOL_Obool)))], (24827 ^ _780478) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1241649, _1241651, _1241653) = c_Orderings_Obot__class_Obot(tc_fun(_1241649, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241649), _1241651), _1241653))]]], (30731 ^ _780478) ^ [_1351424, _1351426, _1351428] : [class_Groups_Oordered__ab__group__add__abs(_1351424), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351424), hAPP(c_Groups_Oabs__class_Oabs(_1351424), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351424), _1351426), _1351428))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351424), hAPP(c_Groups_Oabs__class_Oabs(_1351424), _1351426)), hAPP(c_Groups_Oabs__class_Oabs(_1351424), _1351428)))))], (30548 ^ _780478) ^ [_1347565, _1347567, _1347569] : [class_Groups_Oordered__ab__group__add__abs(_1347565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347565), _1347567), _1347569)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347565), hAPP(c_Groups_Ouminus__class_Ouminus(_1347565), _1347567)), _1347569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347565), hAPP(c_Groups_Oabs__class_Oabs(_1347565), _1347567)), _1347569)))], (35930 ^ _780478) ^ [_1462751, _1462753, _1462755, _1462757, _1462759, _1462761, _1462763] : [c_Equiv__Relations_Oequiv(_1462751, _1462753, _1462755), hBOOL(hAPP(hAPP(c_member(tc_fun(_1462751, tc_HOL_Obool)), _1462757), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462751), _1462753), _1462755))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1462751, tc_HOL_Obool)), _1462759), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462751), _1462753), _1462755))), hBOOL(hAPP(hAPP(c_member(_1462751), _1462761), _1462757)), hBOOL(hAPP(hAPP(c_member(_1462751), _1462763), _1462759)), 35949 ^ _780478 : [(35956 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1462751, _1462751)), hAPP(hAPP(c_Product__Type_OPair(_1462751, _1462751), _1462761), _1462763)), _1462755)), -(_1462757 = _1462759)], (35950 ^ _780478) ^ [] : [_1462757 = _1462759, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1462751, _1462751)), hAPP(hAPP(c_Product__Type_OPair(_1462751, _1462751), _1462761), _1462763)), _1462755)))]]], (35345 ^ _780478) ^ [_1446658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446658), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446658)), c_Int_OMin)))], (34355 ^ _780478) ^ [_1428562, _1428564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1428562)), -(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)))), _1428564))), 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)))), _1428562)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1428564), _1428562))], (12530 ^ _780478) ^ [_1001624] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1001624), c_Orderings_Otop__class_Otop(tc_fun(_1001624, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1001624)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1001624), tc_HOL_Obool)))))], (29363 ^ _780478) ^ [_1325724, _1325726, _1325728, _1325730] : [class_Divides_Osemiring__div(_1325724), -(c_Divides_Odiv__class_Omod(_1325724, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325724), _1325726), _1325728), _1325730) = c_Divides_Odiv__class_Omod(_1325724, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325724), c_Divides_Odiv__class_Omod(_1325724, _1325726, _1325730)), c_Divides_Odiv__class_Omod(_1325724, _1325728, _1325730)), _1325730))], (39147 ^ _780478) ^ [_1539981, _1539983, _1539985] : [-(hAPP(c_Product__Type_Omap__pair(_1539981, _1539981, _1539983, _1539983, c_COMBI(_1539981), c_COMBI(_1539983)), _1539985) = _1539985)], (34095 ^ _780478) ^ [_1424066, _1424068] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1424066), _1424068), hAPP(c_Int_Onumber__class_Onumber__of(_1424066), c_Int_OBit1(c_Int_OPls))) = _1424068), class_Fields_Ofield(_1424066), class_Int_Onumber__ring(_1424066)], (45937 ^ _780478) ^ [_1702780, _1702782] : [-(hAPP(c_List_Oset(_1702780), c_List_Oconcat(_1702780, _1702782)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1702780), tc_fun(_1702780, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1702780)), _1702782)), c_List_Oset(_1702780)))], (27255 ^ _780478) ^ [_1285003, _1285005] : [c_Nat__Transfer_Onat__set(_1285003), c_Nat__Transfer_Onat__set(_1285005), 27262 ^ _780478 : [(27269 ^ _780478) ^ [] : [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), _1285003)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1285005))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1285003), _1285005)))], (27263 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1285003), _1285005)), -(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), _1285003)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1285005))))]]], (24058 ^ _780478) ^ [_1227868, _1227870] : [24066 ^ _780478 : [(24069 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1227870, 24065 ^ [_1227868, _1227870])))], (24067 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24065 ^ [_1227868, _1227870]), _1227868)))]], 24059 ^ _780478 : [(24060 ^ _780478) ^ [_1227936] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1227936), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227868))), hBOOL(hAPP(_1227870, _1227936))]]], (30061 ^ _780478) ^ [_1338251, _1338253] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338251, _1338253) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1338251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1338251), _1338253)), _1338253)))], (37393 ^ _780478) ^ [_1492218, _1492220] : [_1492218 = _1492220, -(c_Code__Numeral_OSuc__code__numeral(_1492218) = c_Code__Numeral_OSuc__code__numeral(_1492220))], (22626 ^ _780478) ^ [_1201891] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201891), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1201891)], (40478 ^ _780478) ^ [_1571765, _1571767, _1571769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571765, _1571765), tc_HOL_Obool)), _1571767), hAPP(hAPP(c_Product__Type_OSigma(_1571765, _1571765), _1571769), hAPP(c_COMBK(tc_fun(_1571765, tc_HOL_Obool), _1571765), _1571769)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571765, _1571765), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1571765, _1571767)), hAPP(hAPP(c_Product__Type_OSigma(_1571765, _1571765), _1571769), hAPP(c_COMBK(tc_fun(_1571765, tc_HOL_Obool), _1571765), _1571769)))))], (6562 ^ _780478) ^ [_887793, _887795] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887793, tc_HOL_Obool)), _887795), _887795) = c_Orderings_Obot__class_Obot(tc_fun(_887793, tc_HOL_Obool)))], (42532 ^ _780478) ^ [_1627892, _1627894, _1627896, _1627898, _1627900, _1627902] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627892, _1627894)), hAPP(hAPP(c_Product__Type_OPair(_1627892, _1627894), _1627896), _1627898)), hAPP(c_List_Oset(tc_prod(_1627892, _1627894)), hAPP(hAPP(c_List_Ozip(_1627892, _1627894), _1627900), _1627902)))), 42535 ^ _780478 : [(42538 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1627894), _1627898), hAPP(c_List_Oset(_1627894), _1627902))))], (42536 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1627892), _1627896), hAPP(c_List_Oset(_1627892), _1627900))))]]], (46270 ^ _780478) ^ [_1711965, _1711967] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711965), _1711967)), -(c_List_Oupt(_1711965, _1711967) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1711965), c_List_Oupt(hAPP(c_Nat_OSuc, _1711965), _1711967)))], (21239 ^ _780478) ^ [_1175142, _1175144] : [-(_1175142 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1175144), _1175142) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175144), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1175144), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1175142), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (49584 ^ _780478) ^ [_1783238, _1783240] : [-(c_Relation_Oantisym(_1783238, c_Relation_OId__on(_1783238, _1783240)))], (50399 ^ _780478) ^ [_1800220, _1800222, _1800224, _1800226, _1800228, _1800230] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1800220, _1800222, _1800224, _1800226), _1800228), _1800230) = hAPP(_1800226, hAPP(hAPP(c_Product__Type_OPair(_1800220, _1800222), _1800228), _1800230)))], (98 ^ _780478) ^ [_782097, _782099, _782101, _782103, _782105, _782107] : [-(c_Finite__Set_Ofolding__one__idem(_782105, _782101, _782097)), c_Finite__Set_Ofolding__one__idem(_782107, _782103, _782099), _782107 = _782105, _782103 = _782101, _782099 = _782097], (26332 ^ _780478) ^ [_1268591, _1268593, _1268595] : [class_Fields_Olinordered__field(_1268591), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268591), c_Groups_Ozero__class_Ozero(_1268591)), _1268593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268591), c_Groups_Ozero__class_Ozero(_1268591)), _1268595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268591), c_Groups_Ozero__class_Ozero(_1268591)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268591), _1268593), _1268595))))], (31598 ^ _780478) ^ [_1375709, _1375711, _1375713, _1375715, _1375717, _1375719] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1375709), _1375711)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375713), _1375715)), 31608 ^ _780478 : [(31611 ^ _780478) ^ [] : [hAPP(c_Finite__Set_Ocard(_1375709), hAPP(c_Set_OCollect(_1375709), hAPP(hAPP(c_COMBS(_1375709, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1375709), c_fconj), hAPP(hAPP(c_COMBC(_1375709, tc_fun(_1375709, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375709)), _1375711))), hAPP(hAPP(c_COMBC(_1375709, _1375713, tc_HOL_Obool), _1375717), 31607 ^ [_1375709, _1375711, _1375713, _1375715, _1375717, _1375719])))) = hAPP(_1375719, 31607 ^ [_1375709, _1375711, _1375713, _1375715, _1375717, _1375719])], (31609 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1375713), 31607 ^ [_1375709, _1375711, _1375713, _1375715, _1375717, _1375719]), _1375715)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1375709, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1375713, tc_HOL_Obool), tc_Nat_Onat, _1375709), c_Finite__Set_Ocard(_1375713)), hAPP(hAPP(c_COMBB(tc_fun(_1375713, tc_HOL_Obool), tc_fun(_1375713, tc_HOL_Obool), _1375709), c_Set_OCollect(_1375713)), hAPP(hAPP(c_COMBB(tc_fun(_1375713, tc_HOL_Obool), tc_fun(_1375713, tc_HOL_Obool), _1375709), hAPP(c_COMBS(_1375713, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1375713), c_fconj), hAPP(hAPP(c_COMBC(_1375713, tc_fun(_1375713, tc_HOL_Obool), tc_HOL_Obool), c_member(_1375713)), _1375715)))), _1375717)))), _1375711) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1375713, tc_Nat_Onat), _1375719), _1375715))], (982 ^ _780478) ^ [_795287, _795289, _795291, _795293, _795295, _795297, _795299, _795301] : [-(c_Equiv__Relations_Ocongruent(_795299, _795295, _795291, _795287)), c_Equiv__Relations_Ocongruent(_795301, _795297, _795293, _795289), _795301 = _795299, _795297 = _795295, _795293 = _795291, _795289 = _795287], (45745 ^ _780478) ^ [_1699054, _1699056] : [-(hAPP(c_List_Oset(_1699054), c_List_Oremdups(_1699054, _1699056)) = hAPP(c_List_Oset(_1699054), _1699056))], (38788 ^ _780478) ^ [_1529059, _1529061, _1529063, _1529065, _1529067, _1529069, _1529071, _1529073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529059, _1529061), tc_HOL_Obool)), _1529063), hAPP(hAPP(c_Product__Type_OSigma(_1529059, _1529061), _1529065), hAPP(c_COMBK(tc_fun(_1529061, tc_HOL_Obool), _1529059), _1529067)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529061, _1529069), tc_HOL_Obool)), _1529071), hAPP(hAPP(c_Product__Type_OSigma(_1529061, _1529069), _1529067), hAPP(c_COMBK(tc_fun(_1529069, tc_HOL_Obool), _1529061), _1529073)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529059, _1529069), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1529059, _1529061, _1529069), _1529063), _1529071)), hAPP(hAPP(c_Product__Type_OSigma(_1529059, _1529069), _1529065), hAPP(c_COMBK(tc_fun(_1529069, tc_HOL_Obool), _1529059), _1529073)))))], (17519 ^ _780478) ^ [_1105935, _1105937, _1105939, _1105941, _1105943] : [class_Complete__Lattice_Ocomplete__lattice(_1105935), class_Orderings_Olinorder(_1105935), 17526 ^ _780478 : [(17536 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105935), _1105937), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105939, _1105935), _1105941), _1105943)))), 17537 ^ _780478 : [(17538 ^ _780478) ^ [_1106283] : [hBOOL(hAPP(hAPP(c_member(_1105939), _1106283), _1105941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105935), _1105937), hAPP(_1105943, _1106283)))]]], (17527 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105935), _1105937), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105939, _1105935), _1105941), _1105943))), 17531 ^ _780478 : [(17534 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105935), _1105937), hAPP(_1105943, 17530 ^ [_1105935, _1105937, _1105939, _1105941, _1105943]))))], (17532 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1105939), 17530 ^ [_1105935, _1105937, _1105939, _1105941, _1105943]), _1105941)))]]]]], (35079 ^ _780478) ^ [_1441490, _1441492, _1441494] : [class_Groups_Omonoid__mult(_1441490), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1441490), _1441492), 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)))), _1441494))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1441490), _1441492), hAPP(hAPP(c_Power_Opower__class_Opower(_1441490), hAPP(hAPP(c_Power_Opower__class_Opower(_1441490), _1441492), _1441494)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (24124 ^ _780478) ^ [_1229493, _1229495, _1229497, _1229499, _1229501, _1229503, _1229505, _1229507] : [c_Fun_Oinj__on(_1229493, _1229495, _1229497, _1229499), 24130 ^ _780478 : [(24133 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1229493, tc_HOL_Obool)), hAPP(_1229505, 24129 ^ [_1229493, _1229495, _1229497, _1229499, _1229501, _1229503, _1229505, _1229507])), _1229499))], (24131 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1229501), 24129 ^ [_1229493, _1229495, _1229497, _1229499, _1229501, _1229503, _1229505, _1229507]), _1229503)))]], hBOOL(hAPP(hAPP(c_member(_1229501), _1229507), _1229503)), -(hAPP(c_Set_Oimage(_1229493, _1229495, _1229497), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1229501, tc_fun(_1229493, tc_HOL_Obool)), _1229503), _1229505)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1229501, tc_fun(_1229495, tc_HOL_Obool)), _1229503), hAPP(hAPP(c_COMBB(tc_fun(_1229493, tc_HOL_Obool), tc_fun(_1229495, tc_HOL_Obool), _1229501), c_Set_Oimage(_1229493, _1229495, _1229497)), _1229505)))], (39027 ^ _780478) ^ [_1536963, _1536965] : [-(c_Product__Type_Oapsnd(_1536963, _1536963, _1536965, c_Fun_Oid(_1536963)) = c_Fun_Oid(tc_prod(_1536965, _1536963)))], (10453 ^ _780478) ^ [_962844, _962846, _962848] : [class_Orderings_Olinorder(_962844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962844), _962846), _962848)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_962844), _962846), _962848) = _962848)], (35061 ^ _780478) ^ [_1441014, _1441016, _1441018] : [class_Rings_Olinordered__idom(_1441014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1441014), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1441014), hAPP(hAPP(c_Power_Opower__class_Opower(_1441014), _1441016), 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(_1441014), _1441018), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1441014)))], (34539 ^ _780478) ^ [_1431724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431724), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1431724)), c_Int_OPls)))], (13404 ^ _780478) ^ [_1019248, _1019250, _1019252, _1019254, _1019256] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1019248), hAPP(c_Set_Oimage(_1019250, _1019248, _1019252), c_Orderings_Otop__class_Otop(tc_fun(_1019250, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1019254), hAPP(c_Set_Oimage(_1019250, _1019254, hAPP(hAPP(c_COMBB(_1019248, _1019254, _1019250), _1019256), _1019252)), c_Orderings_Otop__class_Otop(tc_fun(_1019250, tc_HOL_Obool))))))], (26922 ^ _780478) ^ [_1279310, _1279312, _1279314, _1279316] : [class_Fields_Ofield__inverse__zero(_1279310), -(_1279312 = c_Groups_Ozero__class_Ozero(_1279310)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279310), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279310), _1279314), _1279312)), _1279316) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279310), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279310), _1279314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279310), _1279316), _1279312))), _1279312))], (17887 ^ _780478) ^ [_1113779, _1113781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113779), _1113781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113779), hAPP(c_Nat_OSuc, _1113781))))], (43604 ^ _780478) ^ [_1650961, _1650963, _1650965] : [hAPP(hAPP(c_List_Oappend(_1650961), _1650963), _1650965) = _1650965, -(_1650963 = c_List_Olist_ONil(_1650961))], (24917 ^ _780478) ^ [_1243216, _1243218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1243216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1243218), _1243216))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1243218), _1243216) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243218), _1243216)), _1243216)))], (3640 ^ _780478) ^ [_834929, _834931, _834933, _834935, _834937, _834939, _834941, _834943, _834945, _834947] : [-(c_List_Ofoldr(_834947, _834943, _834939, _834935, _834931) = c_List_Ofoldr(_834945, _834941, _834937, _834933, _834929)), _834947 = _834945, _834943 = _834941, _834939 = _834937, _834935 = _834933, _834931 = _834929], (50763 ^ _780478) ^ [_1807281, _1807283, _1807285, _1807287] : [c_Equiv__Relations_Oequivp(_1807281, _1807283), -(c_Quotient_OBabs(_1807281, _1807285, c_Quotient_ORespects(_1807281, _1807283), _1807287) = _1807287)], (11097 ^ _780478) ^ [_974218, _974220] : [class_Orderings_Olinorder(_974218), hBOOL(hAPP(c_Finite__Set_Ofinite(_974218), _974220)), -(c_Big__Operators_Olinorder__class_OMin(_974218, _974220) = hAPP(c_Finite__Set_Ofold1(_974218, c_Orderings_Oord__class_Omin(_974218)), _974220))], (45583 ^ _780478) ^ [_1695446, _1695448, _1695450, _1695452, _1695454, _1695456] : [c_List_Olist__all2(_1695446, _1695448, _1695450, _1695452, _1695454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695456), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695448)), _1695454))), -(hBOOL(hAPP(hAPP(_1695450, hAPP(hAPP(c_List_Onth(_1695446), _1695452), _1695456)), hAPP(hAPP(c_List_Onth(_1695448), _1695454), _1695456))))], (35641 ^ _780478) ^ [_1453118, _1453120, _1453122, _1453124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool)), _1453122), _1453124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1453118, tc_fun(_1453120, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1453118, tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_fun(_1453120, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453120, tc_fun(tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_fun(_1453120, tc_HOL_Obool)), _1453118), c_COMBC(_1453120, tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453120, tc_prod(_1453118, _1453120)), tc_fun(_1453120, tc_fun(tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_HOL_Obool)), _1453118), hAPP(c_COMBB(tc_prod(_1453118, _1453120), tc_fun(tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_HOL_Obool), _1453120), c_member(tc_prod(_1453118, _1453120)))), c_Product__Type_OPair(_1453118, _1453120)))), _1453122)), hAPP(hAPP(c_COMBC(_1453118, tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_fun(_1453120, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453120, tc_fun(tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_fun(_1453120, tc_HOL_Obool)), _1453118), c_COMBC(_1453120, tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1453120, tc_prod(_1453118, _1453120)), tc_fun(_1453120, tc_fun(tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_HOL_Obool)), _1453118), hAPP(c_COMBB(tc_prod(_1453118, _1453120), tc_fun(tc_fun(tc_prod(_1453118, _1453120), tc_HOL_Obool), tc_HOL_Obool), _1453120), c_member(tc_prod(_1453118, _1453120)))), c_Product__Type_OPair(_1453118, _1453120)))), _1453124))))], (51381 ^ _780478) ^ [_1821233, _1821235, _1821237] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821233, _1821235) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1821237), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1821233 = _1821235, _1821235 = _1821237], (6452 ^ _780478) ^ [_885492, _885494, _885496, _885498, _885500, _885502, _885504, _885506] : [c_Finite__Set_Ofolding__image__simple__idem(_885492, _885494, _885496, _885498, _885500, _885502), hBOOL(hAPP(c_Finite__Set_Ofinite(_885494), _885504)), -(hAPP(_885502, hAPP(hAPP(c_Set_Oinsert(_885494), _885506), _885504)) = hAPP(hAPP(_885496, hAPP(_885500, _885506)), hAPP(_885502, _885504)))], (34985 ^ _780478) ^ [_1439559, _1439561, _1439563] : [class_Rings_Ocomm__semiring__1(_1439559), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1439559), _1439561), 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)))), _1439563)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1439559), hAPP(hAPP(c_Power_Opower__class_Opower(_1439559), _1439561), _1439563)), hAPP(hAPP(c_Power_Opower__class_Opower(_1439559), _1439561), _1439563)))], (6166 ^ _780478) ^ [_879072, _879074, _879076] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_879072), hAPP(hAPP(c_Set_Oinsert(_879072), _879074), _879076))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_879072), _879076)))], (40901 ^ _780478) ^ [_1581746, _1581748, _1581750] : [c_Relation_Orefl__on(_1581746, _1581748, hAPP(c_Relation_Oconverse(_1581746, _1581746), _1581750)), -(c_Relation_Orefl__on(_1581746, _1581748, _1581750))], (51975 ^ _780478) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (45405 ^ _780478) ^ [_1691407, _1691409, _1691411, _1691413, _1691415] : [-(c_List_Olist__all2(_1691407, _1691409, _1691411, _1691413, _1691415)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691407)), _1691413) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691409)), _1691415), 45411 ^ _780478 : [(45414 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1691407, _1691409, tc_HOL_Obool), _1691411), 45410 ^ [_1691407, _1691409, _1691411, _1691413, _1691415]))], (45412 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1691407, _1691409)), 45410 ^ [_1691407, _1691409, _1691411, _1691413, _1691415]), hAPP(c_List_Oset(tc_prod(_1691407, _1691409)), hAPP(hAPP(c_List_Ozip(_1691407, _1691409), _1691413), _1691415)))))]]], (13660 ^ _780478) ^ [_1024446, _1024448, _1024450, _1024452, _1024454] : [c_Fun_Oinj__on(_1024446, _1024448, _1024450, _1024452), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024448, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1024446, _1024448, _1024450), _1024452)), _1024454)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024448), _1024454)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1024446), _1024452)), hAPP(c_Finite__Set_Ocard(_1024448), _1024454))))], (33322 ^ _780478) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (49826 ^ _780478) ^ [_1787810, _1787812] : [c_Relation_Osym(_1787810, hAPP(c_Set_OCollect(tc_prod(_1787810, _1787810)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787810, _1787810, tc_HOL_Obool), _1787812))), -(c_Predicate_Osymp(_1787810, _1787812))], (1084 ^ _780478) ^ [_796892, _796894] : [-(class_Lattices_Obounded__lattice(_796892)), _796894 = _796892, class_Lattices_Obounded__lattice(_796894)], (13861 ^ _780478) ^ [_1028318, _1028320] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028318), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028318), _1028320))))], (39384 ^ _780478) ^ [_1545536, _1545538, _1545540] : [c_Predicate_Oreflp(_1545536, _1545538), -(hBOOL(hAPP(hAPP(_1545538, _1545540), _1545540)))], (14466 ^ _780478) ^ [_1038575] : [14468 ^ _780478 : [(14471 ^ _780478) ^ [_1038685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14467 ^ [_1038575, _1038685]), _1038685))], (14469 ^ _780478) ^ [_1038651] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 14467 ^ [_1038575, _1038651]), _1038575)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1038575)))], (47001 ^ _780478) ^ [_1725973, _1725975] : [-(hAPP(c_List_Oset(_1725973), hAPP(c_List_Orev(_1725973), _1725975)) = hAPP(c_List_Oset(_1725973), _1725975))], (45037 ^ _780478) ^ [_1683088, _1683090, _1683092, _1683094] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683088)), _1683090) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683092)), _1683094), -(hAPP(hAPP(c_List_Omap(tc_prod(_1683088, _1683092), _1683088), c_Product__Type_Ofst(_1683088, _1683092)), hAPP(hAPP(c_List_Ozip(_1683088, _1683092), _1683090), _1683094)) = _1683090)], (46975 ^ _780478) ^ [_1725314, _1725316, _1725318] : [hAPP(c_List_Orev(_1725314), _1725316) = hAPP(hAPP(c_List_Olist_OCons(_1725314), _1725318), c_List_Olist_ONil(_1725314)), -(_1725316 = hAPP(hAPP(c_List_Olist_OCons(_1725314), _1725318), c_List_Olist_ONil(_1725314)))], (3574 ^ _780478) ^ [_833872, _833874, _833876, _833878, _833880, _833882, _833884, _833886, _833888, _833890] : [-(c_List_Olinorder__class_Oinsort__insert__key(_833890, _833886, _833882, _833878, _833874) = c_List_Olinorder__class_Oinsort__insert__key(_833888, _833884, _833880, _833876, _833872)), _833890 = _833888, _833886 = _833884, _833882 = _833880, _833878 = _833876, _833874 = _833872], (10521 ^ _780478) ^ [_963999, _964001, _964003] : [class_Orderings_Olinorder(_963999), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963999), _964001), hAPP(hAPP(c_Orderings_Oord__class_Omax(_963999), _964003), _964001))))], (38685 ^ _780478) ^ [_1525581, _1525583, _1525585] : [-(hAPP(c_Relation_ODomain(_1525581, _1525583), hAPP(c_Set_OCollect(tc_prod(_1525581, _1525583)), hAPP(c_Product__Type_Oprod_Oprod__case(_1525581, _1525583, tc_HOL_Obool), _1525585))) = hAPP(c_Set_OCollect(_1525581), hAPP(hAPP(c_COMBB(tc_fun(_1525583, tc_HOL_Obool), tc_HOL_Obool, _1525581), c_HOL_OEx(_1525583)), _1525585)))], (28310 ^ _780478) ^ [_1304501, _1304503] : [c_Nat__Transfer_Ois__nat(_1304501), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1304501, _1304503)))], (2756 ^ _780478) ^ [_821209, _821211, _821213, _821215] : [-(c_Com_Ocom_OWhile(_821215, _821211) = c_Com_Ocom_OWhile(_821213, _821209)), _821215 = _821213, _821211 = _821209], (34759 ^ _780478) ^ [_1435803, _1435805] : [class_Rings_Ocomm__semiring__1(_1435803), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435803), _1435805), _1435805) = hAPP(hAPP(c_Power_Opower__class_Opower(_1435803), _1435805), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (46931 ^ _780478) ^ [_1724479, _1724481] : [hBOOL(hAPP(c_List_Odistinct(_1724479), _1724481)), -(hBOOL(hAPP(c_List_Odistinct(_1724479), hAPP(c_List_Orev(_1724479), _1724481))))], (15379 ^ _780478) ^ [_1057466, _1057468, _1057470] : [class_Groups_Omonoid__mult(_1057466), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057466), hAPP(hAPP(c_Power_Opower__class_Opower(_1057466), _1057468), _1057470)), _1057468) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057466), _1057468), hAPP(hAPP(c_Power_Opower__class_Opower(_1057466), _1057468), _1057470)))], (14096 ^ _780478) ^ [_1032431, _1032433, _1032435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032431), _1032433)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032431), _1032435)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032433), _1032435))))], (18552 ^ _780478) ^ [_1128446, _1128448, _1128450] : [class_Complete__Lattice_Ocomplete__lattice(_1128446), hBOOL(hAPP(hAPP(c_member(_1128446), _1128448), _1128450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128446), c_Complete__Lattice_OInf__class_OInf(_1128446, _1128450)), _1128448)))], (9596 ^ _780478) ^ [_945479, _945481, _945483] : [class_Orderings_Olinorder(_945479), hBOOL(hAPP(c_Finite__Set_Ofinite(_945479), _945481)), hBOOL(hAPP(hAPP(c_member(_945479), _945483), _945481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945479), c_Big__Operators_Olinorder__class_OMin(_945479, _945481)), _945483)))], (28466 ^ _780478) ^ [_1307226, _1307228, _1307230, _1307232] : [class_Orderings_Olinorder(_1307226), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307226, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1307226), _1307228)), c_SetInterval_Oord__class_OatLeastAtMost(_1307226, _1307230, _1307232)) = c_SetInterval_Oord__class_OatLeastAtMost(_1307226, _1307230, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1307226), _1307228), _1307232)))], (3966 ^ _780478) ^ [_840264, _840266, _840268, _840270, _840272, _840274, _840276, _840278] : [-(c_New__DSequence_Opos__decr__bind(_840278, _840274, _840270, _840266) = c_New__DSequence_Opos__decr__bind(_840276, _840272, _840268, _840264)), _840278 = _840276, _840274 = _840272, _840270 = _840268, _840266 = _840264], (46052 ^ _780478) ^ [_1706213, _1706215, _1706217, _1706219, _1706221, _1706223] : [class_Orderings_Olinorder(_1706213), -(hBOOL(hAPP(_1706215, _1706217))), -(hAPP(c_List_Ofilter(_1706219, _1706215), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1706219, _1706213, _1706221), _1706217), _1706223)) = hAPP(c_List_Ofilter(_1706219, _1706215), _1706223))], (14209 ^ _780478) ^ [_1034518, _1034520] : [class_Rings_Ocomm__ring__1(_1034518), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1034518), _1034520) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034518), hAPP(c_Groups_Ouminus__class_Ouminus(_1034518), c_Groups_Oone__class_Oone(_1034518))), _1034520))], (41961 ^ _780478) ^ [_1611144, _1611146, _1611148, _1611150, _1611152] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611144), tc_List_Olist(_1611144))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611144), tc_List_Olist(_1611144)), _1611146), _1611148)), c_List_Olistrel(_1611144, c_Transitive__Closure_Ortrancl(_1611144, _1611150)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611144), tc_List_Olist(_1611144))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611144), tc_List_Olist(_1611144)), _1611148), _1611152)), c_List_Olistrel(_1611144, c_Transitive__Closure_Ortrancl(_1611144, _1611150)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611144), tc_List_Olist(_1611144))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611144), tc_List_Olist(_1611144)), _1611146), _1611152)), c_List_Olistrel(_1611144, c_Transitive__Closure_Ortrancl(_1611144, _1611150)))))], (30133 ^ _780478) ^ [_1339641, _1339643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339643)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1339641, _1339643)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1339641), hAPP(c_Int_Onat, _1339643)))], (36974 ^ _780478) ^ [_1483655, _1483657, _1483659] : [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), _1483655), _1483657))), -(hBOOL(hAPP(hAPP(_1483659, _1483655), _1483657))), 36981 ^ _780478 : [(36984 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1483659, 36979 ^ [_1483655, _1483657, _1483659]), 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)))), 36980 ^ [_1483655, _1483657, _1483659])))), -(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), 36979 ^ [_1483655, _1483657, _1483659]), 36980 ^ [_1483655, _1483657, _1483659])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 36980 ^ [_1483655, _1483657, _1483659]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36994 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1483659, 36979 ^ [_1483655, _1483657, _1483659]), 36980 ^ [_1483655, _1483657, _1483659]))], (36982 ^ _780478) ^ [] : [-(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), 36979 ^ [_1483655, _1483657, _1483659]), 36980 ^ [_1483655, _1483657, _1483659]))))]]], (23733 ^ _780478) ^ [_1221747] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221747), hAPP(c_Nat_OSuc, _1221747)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1221747), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (6662 ^ _780478) ^ [_890098, _890100, _890102, _890104, _890106] : [c_Finite__Set_Ofolding__one(_890098, _890100, _890102), hBOOL(hAPP(c_Finite__Set_Ofinite(_890098), _890104)), 6669 ^ _780478 : [(6676 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890098, tc_HOL_Obool)), _890104), hAPP(hAPP(c_Set_Oinsert(_890098), _890106), c_Orderings_Obot__class_Obot(tc_fun(_890098, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_890098, tc_HOL_Obool))), -(hAPP(_890102, hAPP(hAPP(c_Set_Oinsert(_890098), _890106), _890104)) = hAPP(hAPP(_890100, _890106), hAPP(_890102, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890098, tc_HOL_Obool)), _890104), hAPP(hAPP(c_Set_Oinsert(_890098), _890106), c_Orderings_Obot__class_Obot(tc_fun(_890098, tc_HOL_Obool)))))))], (6670 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890098, tc_HOL_Obool)), _890104), hAPP(hAPP(c_Set_Oinsert(_890098), _890106), c_Orderings_Obot__class_Obot(tc_fun(_890098, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_890098, tc_HOL_Obool)), -(hAPP(_890102, hAPP(hAPP(c_Set_Oinsert(_890098), _890106), _890104)) = _890106)]]], (41279 ^ _780478) ^ [_1591467, _1591469, _1591471] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591467, _1591467), hAPP(c_Nat_OSuc, _1591469)), _1591471) = hAPP(c_Fun_Ocomp(_1591467, _1591467, _1591467, _1591471), hAPP(hAPP(c_Nat_Ocompow(_1591467, _1591467), _1591469), _1591471)))], (37688 ^ _780478) ^ [_1499672, _1499674, _1499676, _1499678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1499672), _1499674)), -(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), _1499672), _1499676)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1499674), _1499678))), c_FunDef_Opair__leq)))], (38798 ^ _780478) ^ [_1529418, _1529420, _1529422, _1529424] : [-(hAPP(c_Set_Oimage(tc_prod(_1529418, _1529420), tc_prod(_1529420, _1529418), hAPP(c_Product__Type_Oprod_Oprod__case(_1529418, _1529420, tc_prod(_1529420, _1529418)), hAPP(c_COMBC(_1529420, _1529418, tc_prod(_1529420, _1529418)), c_Product__Type_OPair(_1529420, _1529418)))), hAPP(hAPP(c_Product__Type_OSigma(_1529418, _1529420), _1529422), hAPP(c_COMBK(tc_fun(_1529420, tc_HOL_Obool), _1529418), _1529424))) = hAPP(hAPP(c_Product__Type_OSigma(_1529420, _1529418), _1529424), hAPP(c_COMBK(tc_fun(_1529418, tc_HOL_Obool), _1529420), _1529422)))], (6566 ^ _780478) ^ [_887875, _887877] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887875, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_887875, tc_HOL_Obool))), _887877) = c_Orderings_Obot__class_Obot(tc_fun(_887875, tc_HOL_Obool)))], (39985 ^ _780478) ^ [_1559994, _1559996, _1559998, _1560000, _1560002, _1560004, _1560006, _1560008] : [c_Finite__Set_Ofolding(_1559994, _1559996, _1559998, _1560000), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559994), _1560002)), -(hAPP(c_Fun_Ocomp(_1559996, _1559996, _1560004, hAPP(_1559998, _1560006)), hAPP(c_Fun_Ocomp(_1559996, _1559996, _1560004, hAPP(_1560000, _1560002)), _1560008)) = hAPP(c_Fun_Ocomp(_1559996, _1559996, _1560004, hAPP(_1560000, _1560002)), hAPP(c_Fun_Ocomp(_1559996, _1559996, _1560004, hAPP(_1559998, _1560006)), _1560008)))], (46963 ^ _780478) ^ [_1725040, _1725042, _1725044] : [hAPP(hAPP(c_List_Olist_OCons(_1725040), _1725042), c_List_Olist_ONil(_1725040)) = hAPP(c_List_Orev(_1725040), _1725044), -(_1725044 = hAPP(hAPP(c_List_Olist_OCons(_1725040), _1725042), c_List_Olist_ONil(_1725040)))], (38863 ^ _780478) ^ [_1531316, _1531318, _1531320, _1531322, _1531324, _1531326] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531316, _1531318)), hAPP(hAPP(c_Product__Type_OPair(_1531316, _1531318), _1531320), _1531322)), hAPP(hAPP(c_Product__Type_OSigma(_1531316, _1531318), _1531324), _1531326))), -(hBOOL(hAPP(hAPP(c_member(_1531316), _1531320), _1531324)))], (34503 ^ _780478) ^ [_1431103, _1431105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431103), _1431105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1431103)), c_Int_OBit1(_1431105))))], (43233 ^ _780478) ^ [_1642535, _1642537] : [-(c_List_Oset__Cons(_1642535, _1642537, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1642535)), c_List_Olist_ONil(_1642535)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1642535), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1642535, tc_List_Olist(_1642535), hAPP(hAPP(c_COMBC(_1642535, tc_List_Olist(_1642535), tc_List_Olist(_1642535)), c_List_Olist_OCons(_1642535)), c_List_Olist_ONil(_1642535))), _1642537))], (45448 ^ _780478) ^ [_1692621, _1692623, _1692625, _1692627, _1692629, _1692631, _1692633] : [c_List_Olist__all2(_1692621, _1692623, _1692625, _1692627, _1692629), c_List_Olist__all2(_1692621, _1692623, _1692625, _1692631, _1692633), -(c_List_Olist__all2(_1692621, _1692623, _1692625, hAPP(hAPP(c_List_Oappend(_1692621), _1692627), _1692631), hAPP(hAPP(c_List_Oappend(_1692623), _1692629), _1692633)))], (23807 ^ _780478) ^ [_1223250, _1223252, _1223254, _1223256] : [class_Groups_Ocomm__monoid__add(_1223250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1223252), _1223254)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223250), _1223256), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1223252), _1223254)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1223250), hAPP(_1223256, _1223252)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223250), _1223256), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1223252)), _1223254))))], (38975 ^ _780478) ^ [_1534601, _1534603, _1534605] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1534601), _1534603)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1534601, _1534601), tc_HOL_Obool)), _1534605), hAPP(hAPP(c_Product__Type_OSigma(_1534601, _1534601), _1534603), hAPP(c_COMBK(tc_fun(_1534601, tc_HOL_Obool), _1534601), _1534603)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1534601, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1534601), _1534603), _1534605))))], (44434 ^ _780478) ^ [_1670264, _1670266, _1670268, _1670270, _1670272] : [class_Orderings_Olinorder(_1670264), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1670266, _1670264, _1670268), _1670270), _1670272) = c_List_Olist_ONil(_1670266)], (5190 ^ _780478) ^ [_859784, _859786, _859788, _859790] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_859790, _859786) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_859788, _859784)), _859790 = _859788, _859786 = _859784], (52439 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(t_a), v_x), v_F))], (43053 ^ _780478) ^ [_1639104, _1639106, _1639108] : [-(hAPP(hAPP(c_List_Ozip(_1639104, _1639106), c_List_Olist_ONil(_1639104)), _1639108) = c_List_Olist_ONil(tc_prod(_1639104, _1639106)))], (42670 ^ _780478) ^ [_1630880, _1630882, _1630884, _1630886, _1630888] : [-(hAPP(hAPP(c_List_Olist__update(_1630880, hAPP(hAPP(c_List_Olist_OCons(_1630880), _1630882), _1630884)), _1630886), _1630888) = c_Nat_Onat_Onat__case(tc_List_Olist(_1630880), hAPP(hAPP(c_List_Olist_OCons(_1630880), _1630888), _1630884), hAPP(hAPP(c_COMBB(tc_List_Olist(_1630880), tc_List_Olist(_1630880), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1630880), _1630882)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1630880, tc_List_Olist(_1630880)), c_List_Olist__update(_1630880, _1630884)), _1630888)), _1630886))], (37231 ^ _780478) ^ [_1488803, _1488805, _1488807, _1488809, _1488811, _1488813] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1488803, _1488805), _1488805, _1488807), hAPP(hAPP(c_COMBB(_1488809, tc_fun(_1488805, _1488807), tc_prod(_1488803, _1488805)), _1488811), hAPP(hAPP(c_COMBB(_1488803, _1488809, tc_prod(_1488803, _1488805)), _1488813), c_Product__Type_Ofst(_1488803, _1488805)))), c_Product__Type_Osnd(_1488803, _1488805)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1488803, _1488805, _1488807), hAPP(hAPP(c_COMBB(_1488809, tc_fun(_1488805, _1488807), _1488803), _1488811), _1488813)))], (31642 ^ _780478) ^ [_1377165, _1377167, _1377169] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1377165), _1377167)), c_Fun_Oinj__on(_1377165, tc_fun(tc_fun(_1377165, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1377165, tc_fun(tc_prod(_1377165, _1377165), tc_HOL_Obool), tc_fun(tc_fun(_1377165, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1377165, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1377165, _1377165), tc_HOL_Obool), tc_fun(tc_fun(_1377165, tc_HOL_Obool), tc_HOL_Obool)), _1377165), c_Equiv__Relations_Oquotient(_1377165)), hAPP(hAPP(c_COMBC(_1377165, tc_fun(_1377165, tc_HOL_Obool), tc_fun(_1377165, tc_HOL_Obool)), c_Set_Oinsert(_1377165)), c_Orderings_Obot__class_Obot(tc_fun(_1377165, tc_HOL_Obool))))), _1377169), _1377167), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1377165, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377165), _1377167), _1377169)) = hAPP(c_Finite__Set_Ocard(_1377165), _1377167))], (5302 ^ _780478) ^ [_861498, _861500, _861502, _861504, _861506, _861508, _861510, _861512] : [-(c_Fun_Ocomp(_861512, _861508, _861504, _861500) = c_Fun_Ocomp(_861510, _861506, _861502, _861498)), _861512 = _861510, _861508 = _861506, _861504 = _861502, _861500 = _861498], (35707 ^ _780478) ^ [_1457098, _1457100, _1457102, _1457104, _1457106] : [hBOOL(hAPP(hAPP(c_member(_1457098), _1457100), hAPP(c_Relation_OImage(_1457102, _1457098, _1457104), _1457106))), 35711 ^ _780478 : [(35714 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1457102, _1457098)), hAPP(hAPP(c_Product__Type_OPair(_1457102, _1457098), 35710 ^ [_1457098, _1457100, _1457102, _1457104, _1457106]), _1457100)), _1457104)))], (35712 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457102), 35710 ^ [_1457098, _1457100, _1457102, _1457104, _1457106]), _1457106)))]]], (23725 ^ _780478) ^ [_1221618, _1221620, _1221622, _1221624] : [class_Rings_Osemiring__1(_1221618), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1221618, _1221620, hAPP(c_Nat_OSuc, _1221622), _1221624) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1221618, _1221620, _1221622, hAPP(_1221620, _1221624)))], (9920 ^ _780478) ^ [_952707, _952709, _952711, _952713, _952715] : [class_Groups_Ocomm__monoid__add(_952707), class_Groups_Oordered__cancel__ab__semigroup__add(_952707), hBOOL(hAPP(c_Finite__Set_Ofinite(_952709), _952711)), -(_952711 = c_Orderings_Obot__class_Obot(tc_fun(_952709, tc_HOL_Obool))), 9938 ^ _780478 : [(9941 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952707), hAPP(_952713, 9937 ^ [_952707, _952709, _952711, _952713, _952715])), hAPP(_952715, 9937 ^ [_952707, _952709, _952711, _952713, _952715])))], (9939 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_952709), 9937 ^ [_952707, _952709, _952711, _952713, _952715]), _952711)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_952707), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_952709, _952707), _952713), _952711)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_952709, _952707), _952715), _952711))))], (50534 ^ _780478) ^ [_1802761, _1802763, _1802765, _1802767, _1802769] : [c_Fun_Obij__betw(_1802761, _1802763, _1802765, _1802767, _1802769), 50537 ^ _780478 : [(50544 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802763), _1802769)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1802761), _1802767)))], (50538 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802761), _1802767)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1802763), _1802769)))]]], (35583 ^ _780478) ^ [_1450458, _1450460] : [-(_1450458 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1450458, _1450460) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1450458), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1450460)))], (40907 ^ _780478) ^ [_1581837, _1581839, _1581841] : [c_Relation_Orefl__on(_1581837, _1581839, _1581841), -(c_Relation_Orefl__on(_1581837, _1581839, hAPP(c_Relation_Oconverse(_1581837, _1581837), _1581841)))], (17237 ^ _780478) ^ [_1097910, _1097912, _1097914, _1097916, _1097918] : [-(_1097910 = c_Orderings_Obot__class_Obot(tc_fun(_1097912, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097912, tc_fun(_1097914, tc_HOL_Obool)), _1097910), hAPP(hAPP(c_COMBB(tc_fun(_1097914, tc_HOL_Obool), tc_fun(_1097914, tc_HOL_Obool), _1097912), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1097914, tc_HOL_Obool)), _1097916)), _1097918)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1097914, tc_HOL_Obool)), _1097916), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097912, tc_fun(_1097914, tc_HOL_Obool)), _1097910), _1097918)))], (33750 ^ _780478) ^ [_1417508, _1417510, _1417512, _1417514] : [-(hAPP(c_Nat_Onat_Onat__rec(_1417508, _1417510, _1417512), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417514)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1417508), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417514))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417508, _1417508), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1417508, tc_fun(_1417508, _1417508)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417508, tc_fun(_1417508, _1417508)), tc_Int_Oint), c_If(_1417508)), c_Nat__Numeral_Oneg)), _1417510)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417508, _1417508), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1417508, _1417508), tc_Int_Oint), _1417512), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1417508, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1417508, _1417510, _1417512)), c_Int_Onat)))))], (52151 ^ _780478) ^ [_1831535] : [class_Lazy__Sequence_Osmall__lazy(_1831535), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1831535)))], (15687 ^ _780478) ^ [_1063983, _1063985, _1063987, _1063989] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063983, tc_HOL_Obool)), _1063985), _1063987), _1063989)), -(hBOOL(hAPP(_1063987, _1063989)))], (23120 ^ _780478) ^ [_1210868, _1210870, _1210872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1210868), _1210870)), -(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)), _1210868)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1210872), _1210870)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1210872), _1210868)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1210870), _1210868)))], (27373 ^ _780478) ^ [_1287150, _1287152, _1287154] : [class_Orderings_Olinorder(_1287150), 27376 ^ _780478 : [(27383 ^ _780478) ^ [] : [_1287152 = _1287154, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1287150), _1287152) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1287150), _1287154))], (27377 ^ _780478) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1287150), _1287152) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1287150), _1287154), -(_1287152 = _1287154)]]], (31839 ^ _780478) ^ [_1381769, _1381771, _1381773, _1381775] : [class_Groups_Ocomm__monoid__mult(_1381769), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381771), _1381773)), 31849 ^ _780478 : [(31852 ^ _780478) ^ [] : [hAPP(_1381775, 31848 ^ [_1381769, _1381771, _1381773, _1381775]) = c_Groups_Oone__class_Oone(_1381769)], (31850 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381771), 31848 ^ [_1381769, _1381771, _1381773, _1381775]), _1381773)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1381769, _1381771, c_Groups_Otimes__class_Otimes(_1381769)), _1381775), c_Groups_Oone__class_Oone(_1381769)), _1381773) = c_Groups_Oone__class_Oone(_1381769))], (46038 ^ _780478) ^ [_1705944, _1705946, _1705948] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705944)), hAPP(c_List_Ofilter(_1705944, _1705946), _1705948))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705944)), _1705948))))], (17759 ^ _780478) ^ [_1111211, _1111213, _1111215, _1111217, _1111219, _1111221] : [hBOOL(hAPP(hAPP(c_member(_1111211), _1111213), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1111215, tc_fun(_1111211, tc_HOL_Obool)), _1111217), _1111219))), -(hBOOL(hAPP(hAPP(c_member(_1111211), _1111213), hAPP(_1111219, _1111221)))), hBOOL(hAPP(hAPP(c_member(_1111215), _1111221), _1111217))], (40077 ^ _780478) ^ [_1561909, _1561911, _1561913, _1561915, _1561917, _1561919] : [c_Finite__Set_Ofolding(_1561909, _1561911, _1561913, _1561915), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561909), _1561917)), -(hAPP(_1561915, hAPP(hAPP(c_Set_Oinsert(_1561909), _1561919), _1561917)) = hAPP(c_Fun_Ocomp(_1561911, _1561911, _1561911, hAPP(_1561915, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1561909, tc_HOL_Obool)), _1561917), hAPP(hAPP(c_Set_Oinsert(_1561909), _1561919), c_Orderings_Obot__class_Obot(tc_fun(_1561909, tc_HOL_Obool)))))), hAPP(_1561913, _1561919)))], (240 ^ _780478) ^ [_784250, _784252, _784254, _784256] : [-(c_Int_Oiszero(_784254, _784250)), c_Int_Oiszero(_784256, _784252), _784256 = _784254, _784252 = _784250], (29092 ^ _780478) ^ [_1320246, _1320248, _1320250, _1320252, _1320254] : [class_Groups_Ocomm__monoid__add(_1320246), class_Groups_Ocomm__monoid__mult(_1320246), _1320248 = _1320250, c_Nat__Transfer_Onat__set(_1320250), 29110 ^ _780478 : [(29113 ^ _780478) ^ [] : [hAPP(_1320252, 29109 ^ [_1320246, _1320248, _1320250, _1320252, _1320254]) = hAPP(_1320254, 29109 ^ [_1320246, _1320248, _1320250, _1320252, _1320254])], (29111 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29109 ^ [_1320246, _1320248, _1320250, _1320252, _1320254])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1320246), _1320252), _1320248) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1320246), _1320254), _1320250))], (21257 ^ _780478) ^ [_1175413, _1175415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1175413), _1175415)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1175413), _1175415) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17185 ^ _780478) ^ [_1096714, _1096716, _1096718, _1096720] : [-(hAPP(c_Set_Ovimage(_1096714, _1096716, _1096718), _1096720) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1096716, tc_fun(_1096714, tc_HOL_Obool)), _1096720), hAPP(hAPP(c_COMBB(tc_fun(_1096716, tc_HOL_Obool), tc_fun(_1096714, tc_HOL_Obool), _1096716), c_Set_Ovimage(_1096714, _1096716, _1096718)), hAPP(hAPP(c_COMBC(_1096716, tc_fun(_1096716, tc_HOL_Obool), tc_fun(_1096716, tc_HOL_Obool)), c_Set_Oinsert(_1096716)), c_Orderings_Obot__class_Obot(tc_fun(_1096716, tc_HOL_Obool))))))], (48687 ^ _780478) ^ [_1762496, _1762498, _1762500, _1762502, _1762504] : [-(hAPP(hAPP(c_List_Omap(_1762496, _1762498), _1762500), c_List_Oreplicate(_1762496, _1762502, _1762504)) = c_List_Oreplicate(_1762498, _1762502, hAPP(_1762500, _1762504)))], (8328 ^ _780478) ^ [_923259, _923261, _923263] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_923259, _923261, c_Orderings_Obot__class_Obot(tc_fun(_923259, tc_HOL_Obool))), _923263))], (25992 ^ _780478) ^ [_1262321, _1262323, _1262325, _1262327] : [class_Fields_Olinordered__field__inverse__zero(_1262321), 25995 ^ _780478 : [(25996 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262321), _1262323), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1262321), _1262325), _1262327))), 25999 ^ _780478 : [(26006 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262321), c_Groups_Ozero__class_Ozero(_1262321)), _1262327))), 26009 ^ _780478 : [(26016 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262321), _1262327), c_Groups_Ozero__class_Ozero(_1262321)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262321), _1262323), c_Groups_Ozero__class_Ozero(_1262321))))], (26010 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262321), _1262327), c_Groups_Ozero__class_Ozero(_1262321))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262321), _1262325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262321), _1262323), _1262327))))]]], (26000 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262321), c_Groups_Ozero__class_Ozero(_1262321)), _1262327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262321), _1262323), _1262327)), _1262325)))]]], (26022 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262321), _1262323), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1262321), _1262325), _1262327)))), 26025 ^ _780478 : [(26028 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262321), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262321), _1262323), _1262327)), _1262325))], (26026 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262321), c_Groups_Ozero__class_Ozero(_1262321)), _1262327)))]], 26029 ^ _780478 : [(26032 ^ _780478) ^ [] : [26033 ^ _780478 : [(26036 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262321), _1262325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1262321), _1262323), _1262327)))], (26034 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262321), _1262327), c_Groups_Ozero__class_Ozero(_1262321))))]], 26037 ^ _780478 : [(26040 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262321), _1262323), c_Groups_Ozero__class_Ozero(_1262321)))], (26038 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262321), _1262327), c_Groups_Ozero__class_Ozero(_1262321)))]]], (26030 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1262321), c_Groups_Ozero__class_Ozero(_1262321)), _1262327))]]]]], (40999 ^ _780478) ^ [_1584100, _1584102, _1584104] : [-(hAPP(c_Relation_Oconverse(_1584100, _1584102), _1584104) = hAPP(c_Set_OCollect(tc_prod(_1584102, _1584100)), hAPP(c_Product__Type_Oprod_Oprod__case(_1584102, _1584100, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1584102, tc_fun(tc_prod(_1584100, _1584102), tc_HOL_Obool), tc_fun(_1584100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584100, tc_fun(tc_fun(tc_prod(_1584100, _1584102), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1584100, _1584102), tc_HOL_Obool), tc_fun(_1584100, tc_HOL_Obool)), _1584102), c_COMBC(_1584100, tc_fun(tc_prod(_1584100, _1584102), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584100, tc_prod(_1584100, _1584102)), tc_fun(_1584100, tc_fun(tc_fun(tc_prod(_1584100, _1584102), tc_HOL_Obool), tc_HOL_Obool)), _1584102), hAPP(c_COMBB(tc_prod(_1584100, _1584102), tc_fun(tc_fun(tc_prod(_1584100, _1584102), tc_HOL_Obool), tc_HOL_Obool), _1584100), c_member(tc_prod(_1584100, _1584102)))), hAPP(c_COMBC(_1584100, _1584102, tc_prod(_1584100, _1584102)), c_Product__Type_OPair(_1584100, _1584102))))), _1584104))))], (9886 ^ _780478) ^ [_951943, _951945, _951947, _951949, _951951] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_951943), 9889 ^ _780478 : [(9890 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951943), _951945), _951947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951943), _951949), _951951)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951943), _951945), _951951)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951943), _951949), _951947)), -(_951945 = _951949), -(_951947 = _951951)], (9900 ^ _780478) ^ [] : [9901 ^ _780478 : [(9904 ^ _780478) ^ [] : [_951947 = _951951], (9902 ^ _780478) ^ [] : [_951945 = _951949]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951943), _951945), _951947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951943), _951949), _951951)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_951943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951943), _951945), _951951)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951943), _951949), _951947)))]]], (31742 ^ _780478) ^ [_1380129, _1380131, _1380133, _1380135, _1380137] : [-(hAPP(c_Relation_OImage(_1380129, _1380131, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1380129, _1380131), tc_HOL_Obool)), _1380133), _1380135)), _1380137) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1380131, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1380129, _1380131, _1380133), _1380137)), hAPP(c_Relation_OImage(_1380129, _1380131, _1380135), _1380137)))], (28422 ^ _780478) ^ [_1306427, _1306429] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1306427), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1306429) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1306427, _1306429))], (22721 ^ _780478) ^ [_1203420] : [-(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, _1203420)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24913 ^ _780478) ^ [_1243160, _1243162] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1243160, _1243162)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243162), _1243160))], (44518 ^ _780478) ^ [_1671761, _1671763, _1671765, _1671767] : [-(_1671761 = c_List_Olist_ONil(_1671763)), 44521 ^ _780478 : [(44528 ^ _780478) ^ [] : [-(_1671765 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671763)), _1671761)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1671763, hAPP(hAPP(c_List_Olist__update(_1671763, _1671761), _1671765), _1671767)) = c_List_Olast(_1671763, _1671761))], (44522 ^ _780478) ^ [] : [_1671765 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1671763)), _1671761)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1671763, hAPP(hAPP(c_List_Olist__update(_1671763, _1671761), _1671765), _1671767)) = _1671767)]]], (32812 ^ _780478) ^ [_1400351, _1400353, _1400355, _1400357] : [class_Fields_Olinordered__field__inverse__zero(_1400351), class_Int_Onumber(_1400351), 32819 ^ _780478 : [(32820 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400351), hAPP(c_Int_Onumber__class_Onumber__of(_1400351), _1400353)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1400351), _1400355), _1400357))), 32823 ^ _780478 : [(32830 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1400351), c_Groups_Ozero__class_Ozero(_1400351)), _1400357))), 32833 ^ _780478 : [(32840 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1400351), _1400357), c_Groups_Ozero__class_Ozero(_1400351)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400351), hAPP(c_Int_Onumber__class_Onumber__of(_1400351), _1400353)), c_Groups_Ozero__class_Ozero(_1400351))))], (32834 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1400351), _1400357), c_Groups_Ozero__class_Ozero(_1400351))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400351), _1400355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400351), hAPP(c_Int_Onumber__class_Onumber__of(_1400351), _1400353)), _1400357))))]]], (32824 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1400351), c_Groups_Ozero__class_Ozero(_1400351)), _1400357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400351), hAPP(c_Int_Onumber__class_Onumber__of(_1400351), _1400353)), _1400357)), _1400355)))]]], (32846 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400351), hAPP(c_Int_Onumber__class_Onumber__of(_1400351), _1400353)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1400351), _1400355), _1400357)))), 32849 ^ _780478 : [(32852 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400351), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400351), hAPP(c_Int_Onumber__class_Onumber__of(_1400351), _1400353)), _1400357)), _1400355))], (32850 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1400351), c_Groups_Ozero__class_Ozero(_1400351)), _1400357)))]], 32853 ^ _780478 : [(32856 ^ _780478) ^ [] : [32857 ^ _780478 : [(32860 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400351), _1400355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1400351), hAPP(c_Int_Onumber__class_Onumber__of(_1400351), _1400353)), _1400357)))], (32858 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1400351), _1400357), c_Groups_Ozero__class_Ozero(_1400351))))]], 32861 ^ _780478 : [(32864 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1400351), hAPP(c_Int_Onumber__class_Onumber__of(_1400351), _1400353)), c_Groups_Ozero__class_Ozero(_1400351)))], (32862 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1400351), _1400357), c_Groups_Ozero__class_Ozero(_1400351)))]]], (32854 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1400351), c_Groups_Ozero__class_Ozero(_1400351)), _1400357))]]]]], (39587 ^ _780478) ^ [_1550668, _1550670, _1550672, _1550674, _1550676, _1550678] : [39590 ^ _780478 : [(39593 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1550674), _1550676), hAPP(hAPP(_1550678, 39588 ^ [_1550668, _1550670, _1550672, _1550674, _1550676, _1550678]), 39589 ^ [_1550668, _1550670, _1550672, _1550674, _1550676, _1550678])))], (39591 ^ _780478) ^ [] : [-(_1550668 = hAPP(hAPP(c_Product__Type_OPair(_1550670, _1550672), 39588 ^ [_1550668, _1550670, _1550672, _1550674, _1550676, _1550678]), 39589 ^ [_1550668, _1550670, _1550672, _1550674, _1550676, _1550678]))]], -(hBOOL(hAPP(hAPP(c_member(_1550674), _1550676), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550670, _1550672, tc_fun(_1550674, tc_HOL_Obool)), _1550678), _1550668))))], (33656 ^ _780478) ^ [_1415158, _1415160] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415158) = hAPP(c_Nat_OSuc, _1415160), -(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(_1415158))), 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)), _1415160))))))], (38446 ^ _780478) ^ [_1519440, _1519442, _1519444, _1519446] : [38448 ^ _780478 : [(38451 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1519442, hAPP(_1519444, 38447 ^ [_1519440, _1519442, _1519444, _1519446]))), hAPP(_1519442, 38447 ^ [_1519440, _1519442, _1519444, _1519446])))], (38449 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1519440, 38447 ^ [_1519440, _1519442, _1519444, _1519446])))]], -(c_Wellfounded_Owf(_1519446, hAPP(c_Set_OCollect(tc_prod(_1519446, _1519446)), hAPP(c_Product__Type_Oprod_Oprod__case(_1519446, _1519446, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1519446, tc_HOL_Obool), tc_fun(_1519446, tc_HOL_Obool), _1519446), hAPP(c_COMBS(_1519446, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1519446), c_fconj), _1519440))), hAPP(hAPP(c_COMBC(_1519446, tc_fun(_1519446, _1519446), tc_fun(_1519446, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1519446, tc_HOL_Obool), tc_fun(tc_fun(_1519446, _1519446), tc_fun(_1519446, tc_HOL_Obool)), _1519446), c_COMBB(_1519446, tc_HOL_Obool, _1519446)), c_fequal)), _1519444))))))], (47623 ^ _780478) ^ [_1739240, _1739242, _1739244] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1739240, _1739240)), hAPP(hAPP(c_Product__Type_OPair(_1739240, _1739240), _1739242), _1739244)), c_List_Omeasures(_1739240, c_List_Olist_ONil(tc_fun(_1739240, tc_Nat_Onat)))))], (4114 ^ _780478) ^ [_842690, _842692, _842694, _842696] : [-(c_Lazy__Sequence_Ohb__single(_842696, _842692) = c_Lazy__Sequence_Ohb__single(_842694, _842690)), _842696 = _842694, _842692 = _842690], (20016 ^ _780478) ^ [_1153792, _1153794, _1153796] : [class_Rings_Oordered__cancel__semiring(_1153792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153792), _1153794), c_Groups_Ozero__class_Ozero(_1153792))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153792), c_Groups_Ozero__class_Ozero(_1153792)), _1153796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153792), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153792), _1153794), _1153796)), c_Groups_Ozero__class_Ozero(_1153792))))], (25547 ^ _780478) ^ [_1254790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254790), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1254790) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46103 ^ _780478) ^ [_1707155, _1707157, _1707159, _1707161] : [-(hBOOL(hAPP(_1707155, _1707157))), -(hAPP(c_List_OremoveAll(_1707159, _1707157), hAPP(c_List_Ofilter(_1707159, _1707155), _1707161)) = hAPP(c_List_Ofilter(_1707159, _1707155), _1707161))], (27197 ^ _780478) ^ [_1284163, _1284165] : [c_Nat__Transfer_Onat__set(_1284163), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1284165), _1284163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1284165)))], (37213 ^ _780478) ^ [_1488426, _1488428, _1488430, _1488432] : [hAPP(c_Product__Type_Ofst(_1488426, _1488428), _1488430) = hAPP(c_Product__Type_Ofst(_1488426, _1488428), _1488432), hAPP(c_Product__Type_Osnd(_1488426, _1488428), _1488430) = hAPP(c_Product__Type_Osnd(_1488426, _1488428), _1488432), -(_1488430 = _1488432)], (4020 ^ _780478) ^ [_841167, _841169] : [_841169 = _841167, -(c_New__DSequence_Opos__empty(_841169) = c_New__DSequence_Opos__empty(_841167))], (48411 ^ _780478) ^ [_1756350, _1756352] : [-(hAPP(c_New__DSequence_Opos__empty(_1756350), _1756352) = c_Lazy__Sequence_Oempty(_1756350))], (42983 ^ _780478) ^ [_1637971] : [-(hBOOL(hAPP(c_List_Odistinct(_1637971), c_List_Olist_ONil(_1637971))))], (18381 ^ _780478) ^ [_1124306, _1124308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1124306)), _1124308)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124306), _1124308)))], (28430 ^ _780478) ^ [_1306558, _1306560, _1306562] : [class_Groups_Ocomm__monoid__add(_1306558), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1306558), _1306560), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1306562))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1306558), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1306558), _1306560), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1306562))), hAPP(_1306560, hAPP(c_Nat_OSuc, _1306562))))], (43457 ^ _780478) ^ [_1647876, _1647878, _1647880, _1647882] : [_1647878 = _1647882, -(hAPP(hAPP(c_List_Oappend(_1647876), _1647878), _1647880) = hAPP(hAPP(c_List_Oappend(_1647876), _1647882), _1647880))], (48707 ^ _780478) ^ [_1762885, _1762887, _1762889] : [-(hAPP(hAPP(c_List_Oappend(_1762885), c_List_Oreplicate(_1762885, _1762887, _1762889)), hAPP(hAPP(c_List_Olist_OCons(_1762885), _1762889), c_List_Olist_ONil(_1762885))) = hAPP(hAPP(c_List_Olist_OCons(_1762885), _1762889), c_List_Oreplicate(_1762885, _1762887, _1762889)))], (22505 ^ _780478) ^ [_1199530, _1199532, _1199534] : [-(hAPP(c_Finite__Set_Ocard(_1199530), _1199532) = hAPP(c_Nat_OSuc, _1199534)), 22506 ^ _780478 : [(22507 ^ _780478) ^ [_1199630, _1199632] : [_1199532 = hAPP(hAPP(c_Set_Oinsert(_1199530), _1199632), _1199630), -(hBOOL(hAPP(hAPP(c_member(_1199530), _1199632), _1199630))), hAPP(c_Finite__Set_Ocard(_1199530), _1199630) = _1199534, 22518 ^ _780478 : [(22521 ^ _780478) ^ [] : [_1199630 = c_Orderings_Obot__class_Obot(tc_fun(_1199530, tc_HOL_Obool))], (22519 ^ _780478) ^ [] : [-(_1199534 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (46176 ^ _780478) ^ [_1709495, _1709497] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1709495)), c_List_Otranspose__rel(_1709495)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1709495)), c_List_Olist_ONil(_1709495)), _1709497))), -(c_List_Otranspose(_1709495, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1709495)), c_List_Olist_ONil(_1709495)), _1709497)) = c_List_Otranspose(_1709495, _1709497))], (31441 ^ _780478) ^ [_1369331, _1369333, _1369335, _1369337] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369331), hAPP(c_Set_OCollect(_1369331), _1369333))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1369335), hAPP(c_Set_OCollect(_1369335), hAPP(hAPP(c_COMBB(tc_fun(_1369331, tc_HOL_Obool), tc_HOL_Obool, _1369335), c_HOL_OEx(_1369331)), hAPP(hAPP(c_COMBC(_1369335, tc_fun(_1369331, tc_HOL_Obool), tc_fun(_1369331, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1369331, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1369331, tc_HOL_Obool), tc_fun(_1369331, tc_HOL_Obool)), _1369335), c_COMBS(_1369331, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1369331, tc_HOL_Obool), tc_fun(_1369331, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1369335), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1369331), c_fconj)), hAPP(hAPP(c_COMBC(_1369335, tc_fun(_1369331, _1369335), tc_fun(_1369331, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1369335, tc_HOL_Obool), tc_fun(tc_fun(_1369331, _1369335), tc_fun(_1369331, tc_HOL_Obool)), _1369335), c_COMBB(_1369335, tc_HOL_Obool, _1369331)), c_fequal)), _1369337)))), _1369333))))))], (35313 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (29858 ^ _780478) ^ [_1334803, _1334805] : [class_Rings_Olinordered__idom(_1334803), 29861 ^ _780478 : [(29868 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334803), _1334805), c_Groups_Ozero__class_Ozero(_1334803))), -(c_Groups_Osgn__class_Osgn(_1334803, _1334805) = hAPP(c_Groups_Ouminus__class_Ouminus(_1334803), c_Groups_Oone__class_Oone(_1334803)))], (29862 ^ _780478) ^ [] : [c_Groups_Osgn__class_Osgn(_1334803, _1334805) = hAPP(c_Groups_Ouminus__class_Ouminus(_1334803), c_Groups_Oone__class_Oone(_1334803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334803), _1334805), c_Groups_Ozero__class_Ozero(_1334803))))]]], (7539 ^ _780478) ^ [_907171, _907173, _907175, _907177, _907179] : [c_Fun_Oinj__on(_907171, _907173, _907175, _907177), -(c_Fun_Oinj__on(_907171, _907173, _907175, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907171, tc_HOL_Obool)), _907177), _907179)))], (29331 ^ _780478) ^ [_1325020, _1325022, _1325024, _1325026, _1325028, _1325030] : [class_Divides_Osemiring__div(_1325020), c_Divides_Odiv__class_Omod(_1325020, _1325022, _1325024) = c_Divides_Odiv__class_Omod(_1325020, _1325026, _1325024), c_Divides_Odiv__class_Omod(_1325020, _1325028, _1325024) = c_Divides_Odiv__class_Omod(_1325020, _1325030, _1325024), -(c_Divides_Odiv__class_Omod(_1325020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325020), _1325022), _1325028), _1325024) = c_Divides_Odiv__class_Omod(_1325020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325020), _1325026), _1325030), _1325024))], (26880 ^ _780478) ^ [_1278526, _1278528, _1278530, _1278532] : [class_Fields_Olinordered__field(_1278526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278526), _1278528), _1278530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278526), _1278532), c_Groups_Ozero__class_Ozero(_1278526))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278526), c_Groups_Ozero__class_Ozero(_1278526)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278526), _1278528), _1278530))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278526), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278526), _1278532), _1278528)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278526), _1278532), _1278530))))], (42672 ^ _780478) ^ [_1630977, _1630979, _1630981, _1630983] : [-(hAPP(hAPP(c_List_Olist__update(_1630977, hAPP(hAPP(c_List_Olist_OCons(_1630977), _1630979), _1630981)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1630983) = hAPP(hAPP(c_List_Olist_OCons(_1630977), _1630983), _1630981))], (50287 ^ _780478) ^ [_1797772, _1797774, _1797776, _1797778, _1797780] : [c_Fun_Obij__betw(_1797772, _1797774, _1797776, _1797778, _1797780), -(c_Fun_Obij__betw(_1797774, _1797772, c_Hilbert__Choice_Oinv__into(_1797772, _1797774, _1797778, _1797776), _1797780, _1797778))], (31774 ^ _780478) ^ [_1380794, _1380796, _1380798] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1380794, _1380796) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1380798, _1380796), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1380798), _1380794)), -(_1380794 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1380798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1380796), 31781 ^ [_1380794, _1380796, _1380798])))], (40979 ^ _780478) ^ [_1583766, _1583768, _1583770] : [hAPP(hAPP(c_Relation_Orel__comp(_1583766, _1583766, _1583766), hAPP(c_Relation_Oconverse(_1583766, _1583766), _1583768)), _1583768) = _1583768, hAPP(c_Relation_ODomain(_1583766, _1583766), _1583768) = _1583770, -(c_Equiv__Relations_Oequiv(_1583766, _1583770, _1583768))], (51897 ^ _780478) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (38050 ^ _780478) ^ [_1510464, _1510466, _1510468, _1510470, _1510472, _1510474, _1510476] : [c_Typedef_Otype__definition(_1510464, _1510466, _1510468, _1510470, _1510472), hBOOL(hAPP(hAPP(c_member(_1510466), _1510474), _1510472)), hBOOL(hAPP(hAPP(c_member(_1510466), _1510476), _1510472)), 38061 ^ _780478 : [(38068 ^ _780478) ^ [] : [_1510474 = _1510476, -(hAPP(_1510470, _1510474) = hAPP(_1510470, _1510476))], (38062 ^ _780478) ^ [] : [hAPP(_1510470, _1510474) = hAPP(_1510470, _1510476), -(_1510474 = _1510476)]]], (39789 ^ _780478) ^ [_1555300, _1555302, _1555304, _1555306, _1555308, _1555310, _1555312, _1555314, _1555316, _1555318, _1555320] : [-(hAPP(c_Product__Type_Omap__pair(_1555300, _1555302, _1555304, _1555306, _1555308, _1555310), hAPP(c_Product__Type_Omap__pair(_1555312, _1555300, _1555314, _1555304, _1555316, _1555318), _1555320)) = hAPP(c_Product__Type_Omap__pair(_1555312, _1555302, _1555314, _1555306, hAPP(c_Fun_Ocomp(_1555300, _1555302, _1555312, _1555308), _1555316), hAPP(c_Fun_Ocomp(_1555304, _1555306, _1555314, _1555310), _1555318)), _1555320))], (316 ^ _780478) ^ [_785272, _785274, _785276, _785278] : [-(c_Wellfounded_OwfP(_785276, _785272)), c_Wellfounded_OwfP(_785278, _785274), _785278 = _785276, _785274 = _785272], (21794 ^ _780478) ^ [_1185088, _1185090, _1185092] : [-(hBOOL(hAPP(_1185088, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1185090), _1185092)))), 21797 ^ _780478 : [(21800 ^ _780478) ^ [] : [hBOOL(hAPP(_1185088, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21798 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185090), _1185092)))]], 21802 ^ _780478 : [(21805 ^ _780478) ^ [] : [hBOOL(hAPP(_1185088, 21801 ^ [_1185088, _1185090, _1185092]))], (21803 ^ _780478) ^ [] : [-(_1185090 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1185092), 21801 ^ [_1185088, _1185090, _1185092]))]]], (31472 ^ _780478) ^ [_1370368] : [-(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)))), _1370368)) = 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), _1370368), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (40347 ^ _780478) ^ [_1568665, _1568667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1568665), _1568667)), -(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), _1568665), _1568667)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (5200 ^ _780478) ^ [_859933, _859935, _859937, _859939] : [-(c_Quotient_ORespects(_859939, _859935) = c_Quotient_ORespects(_859937, _859933)), _859939 = _859937, _859935 = _859933], (16140 ^ _780478) ^ [_1072720, _1072722] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072720, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1072720, tc_HOL_Obool))), _1072722) = c_Orderings_Obot__class_Obot(tc_fun(_1072720, tc_HOL_Obool)))], (52327 ^ _780478) ^ [_1833428, _1833430] : [-(hAPP(c_COMBI(_1833428), _1833430) = _1833430)], (46068 ^ _780478) ^ [_1706512, _1706514, _1706516, _1706518] : [hBOOL(hAPP(_1706512, _1706514)), -(hAPP(c_List_Ofilter(_1706516, _1706512), hAPP(hAPP(c_List_Olist_OCons(_1706516), _1706514), _1706518)) = hAPP(hAPP(c_List_Olist_OCons(_1706516), _1706514), hAPP(c_List_Ofilter(_1706516, _1706512), _1706518)))], (2478 ^ _780478) ^ [_816852, _816854, _816856, _816858] : [-(c_Divides_Odivmod__nat__rel(_816858, _816854) = c_Divides_Odivmod__nat__rel(_816856, _816852)), _816858 = _816856, _816854 = _816852], (52409 ^ _780478) ^ [_1834567, _1834569] : [-(hBOOL(_1834567)), -(hBOOL(hAPP(hAPP(c_fimplies, _1834567), _1834569)))], (1344 ^ _780478) ^ [_800142, _800144] : [-(class_Orderings_Owellorder(_800142)), _800144 = _800142, class_Orderings_Owellorder(_800144)], (34391 ^ _780478) ^ [_1429121] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1429121)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1429121)))], (36320 ^ _780478) ^ [_1471271, _1471273, _1471275] : [hBOOL(hAPP(_1471271, 36321 ^ [_1471271, _1471273, _1471275])), 36324 ^ _780478 : [(36325 ^ _780478) ^ [_1471382, _1471384] : [-(hBOOL(hAPP(_1471271, hAPP(hAPP(c_Product__Type_OPair(_1471273, _1471275), _1471384), _1471382))))]]], (34593 ^ _780478) ^ [_1432737] : [-(c_Int_Opred(c_Int_OBit1(_1432737)) = c_Int_OBit0(_1432737))], (8426 ^ _780478) ^ [_925140, _925142, _925144, _925146, _925148] : [class_Groups_Ocomm__monoid__add(_925140), hBOOL(hAPP(c_Finite__Set_Ofinite(_925142), _925144)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_925142, _925140), _925146), hAPP(hAPP(c_Set_Oinsert(_925142), _925148), _925144)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925140), hAPP(_925146, _925148)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_925142, _925140), _925146), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925142, tc_HOL_Obool)), _925144), hAPP(hAPP(c_Set_Oinsert(_925142), _925148), c_Orderings_Obot__class_Obot(tc_fun(_925142, tc_HOL_Obool)))))))], (30835 ^ _780478) ^ [_1353266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1353266), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1353266) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1353266))], (46230 ^ _780478) ^ [_1711272, _1711274] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1711272, _1711274)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1711272), _1711274))], (5761 ^ _780478) ^ [_871577, _871579, _871581, _871583, _871585, _871587, _871589] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871577), _871579), _871581), _871583) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871577), _871585), _871587), _871589), 5764 ^ _780478 : [(5769 ^ _780478) ^ [] : [-(_871583 = _871589)], (5767 ^ _780478) ^ [] : [-(_871581 = _871587)], (5765 ^ _780478) ^ [] : [-(_871579 = _871585)]]], (5146 ^ _780478) ^ [_859092, _859094, _859096, _859098, _859100, _859102, _859104, _859106] : [-(c_Hilbert__Choice_Oinv__into(_859106, _859102, _859098, _859094) = c_Hilbert__Choice_Oinv__into(_859104, _859100, _859096, _859092)), _859106 = _859104, _859102 = _859100, _859098 = _859096, _859094 = _859092], (20882 ^ _780478) ^ [_1169335, _1169337, _1169339, _1169341] : [class_Rings_Ocomm__semiring__1(_1169335), class_Rings_Ono__zero__divisors(_1169335), hBOOL(hAPP(c_Finite__Set_Ofinite(_1169337), _1169339)), 20893 ^ _780478 : [(20903 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169337, _1169335), _1169341), _1169339) = c_Groups_Ozero__class_Ozero(_1169335)), 20904 ^ _780478 : [(20905 ^ _780478) ^ [_1169713] : [hBOOL(hAPP(hAPP(c_member(_1169337), _1169713), _1169339)), hAPP(_1169341, _1169713) = c_Groups_Ozero__class_Ozero(_1169335)]]], (20894 ^ _780478) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1169337, _1169335), _1169341), _1169339) = c_Groups_Ozero__class_Ozero(_1169335), 20898 ^ _780478 : [(20901 ^ _780478) ^ [] : [-(hAPP(_1169341, 20897 ^ [_1169335, _1169337, _1169339, _1169341]) = c_Groups_Ozero__class_Ozero(_1169335))], (20899 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1169337), 20897 ^ [_1169335, _1169337, _1169339, _1169341]), _1169339)))]]]]], (19988 ^ _780478) ^ [_1153282, _1153284, _1153286] : [class_Rings_Oordered__cancel__semiring(_1153282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153282), c_Groups_Ozero__class_Ozero(_1153282)), _1153284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153282), _1153286), c_Groups_Ozero__class_Ozero(_1153282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153282), _1153284), _1153286)), c_Groups_Ozero__class_Ozero(_1153282))))], (37285 ^ _780478) ^ [_1489922, _1489924, _1489926, _1489928, _1489930] : [-(c_Product__Type_Oprod_Oprod__size(_1489922, _1489924, _1489926, _1489928, _1489930) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1489926, hAPP(c_Product__Type_Ofst(_1489922, _1489924), _1489930))), hAPP(_1489928, hAPP(c_Product__Type_Osnd(_1489922, _1489924), _1489930)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34577 ^ _780478) ^ [_1432433, _1432435] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1432433)), c_Int_OBit0(_1432435)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1432433), _1432435)))], (40989 ^ _780478) ^ [_1583945, _1583947] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583945, _1583945)), _1583947)), c_Wellfounded_Oacyclic(_1583945, _1583947), -(c_Wellfounded_Owf(_1583945, hAPP(c_Relation_Oconverse(_1583945, _1583945), _1583947)))], (3354 ^ _780478) ^ [_830476, _830478, _830480, _830482] : [-(c_Product__Type_OSigma(_830482, _830478) = c_Product__Type_OSigma(_830480, _830476)), _830482 = _830480, _830478 = _830476], (31740 ^ _780478) ^ [_1380055, _1380057, _1380059, _1380061, _1380063] : [-(hAPP(c_Relation_OImage(_1380055, _1380057, _1380059), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1380055, tc_HOL_Obool)), _1380061), _1380063)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1380057, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1380055, _1380057, _1380059), _1380061)), hAPP(c_Relation_OImage(_1380055, _1380057, _1380059), _1380063)))], (17739 ^ _780478) ^ [_1110793, _1110795, _1110797, _1110799, _1110801, _1110803] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1110793, tc_fun(_1110795, tc_HOL_Obool)), _1110797), _1110799), _1110801)), -(hBOOL(hAPP(hAPP(_1110799, _1110803), _1110801))), hBOOL(hAPP(hAPP(c_member(_1110793), _1110803), _1110797))], (41936 ^ _780478) ^ [_1610414, _1610416, _1610418, _1610420] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1610414), tc_List_Olist(_1610414), c_List_Olistrel(_1610414, _1610416)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1610414)), hAPP(hAPP(c_List_Olist_OCons(_1610414), _1610418), _1610420)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1610414), tc_HOL_Obool)))) = c_List_Oset__Cons(_1610414, hAPP(c_Relation_OImage(_1610414, _1610414, _1610416), hAPP(hAPP(c_Set_Oinsert(_1610414), _1610418), c_Orderings_Obot__class_Obot(tc_fun(_1610414, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1610414), tc_List_Olist(_1610414), c_List_Olistrel(_1610414, _1610416)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1610414)), _1610420), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1610414), tc_HOL_Obool))))))], (16901 ^ _780478) ^ [_1090941, _1090943, _1090945, _1090947, _1090949] : [-(c_Fun_Oinj__on(_1090941, _1090943, _1090945, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1090941, tc_HOL_Obool)), _1090947), _1090949))), c_Fun_Oinj__on(_1090941, _1090943, _1090945, _1090947), c_Fun_Oinj__on(_1090941, _1090943, _1090945, _1090949), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090943, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1090941, _1090943, _1090945), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090941, tc_HOL_Obool)), _1090947), _1090949))), hAPP(c_Set_Oimage(_1090941, _1090943, _1090945), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090941, tc_HOL_Obool)), _1090949), _1090947))) = c_Orderings_Obot__class_Obot(tc_fun(_1090943, tc_HOL_Obool))], (43279 ^ _780478) ^ [_1643570, _1643572, _1643574, _1643576, _1643578] : [-(hAPP(hAPP(c_List_Ozip(_1643570, _1643572), hAPP(hAPP(c_List_Olist_OCons(_1643570), _1643574), _1643576)), _1643578) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1643570, _1643572)), _1643572, c_List_Olist_ONil(tc_prod(_1643570, _1643572)), hAPP(hAPP(c_COMBC(_1643572, tc_fun(tc_List_Olist(_1643572), tc_List_Olist(tc_prod(_1643570, _1643572))), tc_fun(tc_List_Olist(_1643572), tc_List_Olist(tc_prod(_1643570, _1643572)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1643570, _1643572)), tc_List_Olist(tc_prod(_1643570, _1643572))), tc_fun(tc_fun(tc_List_Olist(_1643572), tc_List_Olist(tc_prod(_1643570, _1643572))), tc_fun(tc_List_Olist(_1643572), tc_List_Olist(tc_prod(_1643570, _1643572)))), _1643572), c_COMBB(tc_List_Olist(tc_prod(_1643570, _1643572)), tc_List_Olist(tc_prod(_1643570, _1643572)), tc_List_Olist(_1643572))), hAPP(hAPP(c_COMBB(tc_prod(_1643570, _1643572), tc_fun(tc_List_Olist(tc_prod(_1643570, _1643572)), tc_List_Olist(tc_prod(_1643570, _1643572))), _1643572), c_List_Olist_OCons(tc_prod(_1643570, _1643572))), hAPP(c_Product__Type_OPair(_1643570, _1643572), _1643574)))), hAPP(c_List_Ozip(_1643570, _1643572), _1643576))), _1643578))], (45103 ^ _780478) ^ [_1684496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1684496)), _1684496 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5096 ^ _780478) ^ [_858315, _858317, _858319, _858321, _858323, _858325, _858327, _858329] : [-(c_Fun_Othe__inv__into(_858329, _858325, _858321, _858317) = c_Fun_Othe__inv__into(_858327, _858323, _858319, _858315)), _858329 = _858327, _858325 = _858323, _858321 = _858319, _858317 = _858315], (49236 ^ _780478) ^ [_1775248, _1775250] : [-(c_Relation_Otrans(_1775248, c_Transitive__Closure_Ortrancl(_1775248, _1775250)))], (31232 ^ _780478) ^ [_1361868, _1361870, _1361872] : [-(hAPP(hAPP(c_Set_Oinsert(_1361868), _1361870), _1361872) = hAPP(c_Set_OCollect(_1361868), hAPP(hAPP(c_COMBS(_1361868, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361868), c_fdisj), hAPP(hAPP(c_COMBC(_1361868, _1361868, tc_HOL_Obool), c_fequal), _1361870))), hAPP(hAPP(c_COMBC(_1361868, tc_fun(_1361868, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361868)), _1361872))))], (15031 ^ _780478) ^ [_1050977, _1050979, _1050981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050977), _1050979)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1050977), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1050979), _1050981))))], (23755 ^ _780478) ^ [_1222182, _1222184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1222182), _1222184)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222182)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222184))))], (19868 ^ _780478) ^ [_1151172, _1151174] : [class_Groups_Olinordered__ab__group__add(_1151172), 19871 ^ _780478 : [(19878 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151172), _1151174), c_Groups_Ozero__class_Ozero(_1151172))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151172), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151172), _1151174), _1151174)), c_Groups_Ozero__class_Ozero(_1151172))))], (19872 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151172), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151172), _1151174), _1151174)), c_Groups_Ozero__class_Ozero(_1151172))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151172), _1151174), c_Groups_Ozero__class_Ozero(_1151172))))]]], (14665 ^ _780478) ^ [_1042723, _1042725, _1042727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042723), _1042725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042727), _1042725)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042727), _1042723))))], (34449 ^ _780478) ^ [_1430179, _1430181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430179)), c_Int_OBit0(_1430181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430179), _1430181)))], (3792 ^ _780478) ^ [_837311, _837313, _837315, _837317, _837319, _837321, _837323, _837325] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_837325, _837321, _837317, _837313) = c_New__Random__Sequence_Opos__not__random__dseq(_837323, _837319, _837315, _837311)), _837325 = _837323, _837321 = _837319, _837317 = _837315, _837313 = _837311], (22905 ^ _780478) ^ [_1206858] : [class_Nat_Osemiring__char__0(_1206858), -(c_Fun_Oinj__on(tc_Nat_Onat, _1206858, c_Nat_Osemiring__1__class_Oof__nat(_1206858), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (33324 ^ _780478) ^ [_1409850] : [class_Int_Onumber__ring(_1409850), -(c_Groups_Ozero__class_Ozero(_1409850) = hAPP(c_Int_Onumber__class_Onumber__of(_1409850), c_Int_OPls))], (26136 ^ _780478) ^ [_1264989, _1264991, _1264993, _1264995] : [class_Fields_Olinordered__field(_1264989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264989), c_Groups_Ozero__class_Ozero(_1264989)), _1264991)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264989), _1264993), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264989), _1264995), _1264991))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264989), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264989), _1264993), _1264991)), _1264995)))], (7663 ^ _780478) ^ [_909659, _909661, _909663, _909665, _909667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909659, tc_HOL_Obool)), _909661), hAPP(c_Set_Oimage(_909663, _909659, _909665), _909667))), 7667 ^ _780478 : [(7670 ^ _780478) ^ [] : [-(_909661 = hAPP(c_Set_Oimage(_909663, _909659, _909665), 7666 ^ [_909659, _909661, _909663, _909665, _909667]))], (7668 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909663, tc_HOL_Obool)), 7666 ^ [_909659, _909661, _909663, _909665, _909667]), _909667)))]]], (13282 ^ _780478) ^ [_1016557, _1016559, _1016561, _1016563] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1016557), _1016559)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1016561), hAPP(c_Set_Oimage(_1016557, _1016561, _1016563), _1016559))), hAPP(c_Finite__Set_Ocard(_1016557), _1016559))))], (25445 ^ _780478) ^ [_1252950, _1252952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252950)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252952)), 25452 ^ _780478 : [(25459 ^ _780478) ^ [] : [_1252950 = _1252952, -(hAPP(c_Int_Onat, _1252950) = hAPP(c_Int_Onat, _1252952))], (25453 ^ _780478) ^ [] : [hAPP(c_Int_Onat, _1252950) = hAPP(c_Int_Onat, _1252952), -(_1252950 = _1252952)]]], (34307 ^ _780478) ^ [_1427584] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427584))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427584)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44171 ^ _780478) ^ [_1664434, _1664436, _1664438] : [-(hAPP(hAPP(c_List_Otake(_1664434), _1664436), hAPP(c_List_Otl(_1664434), _1664438)) = hAPP(c_List_Otl(_1664434), hAPP(hAPP(c_List_Otake(_1664434), hAPP(c_Nat_OSuc, _1664436)), _1664438)))], (48429 ^ _780478) ^ [_1756931, _1756933, _1756935, _1756937, _1756939] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1756931), _1756933), _1756935), _1756937), _1756939) = c_New__DSequence_Opos__single(_1756931, _1756933))], (43121 ^ _780478) ^ [_1640321, _1640323, _1640325] : [-(hBOOL(hAPP(hAPP(c_member(_1640321), _1640323), hAPP(c_List_Oset(_1640321), _1640325)))), -(c_List_Oremove1(_1640321, _1640323, _1640325) = _1640325)], (1784 ^ _780478) ^ [_805642, _805644] : [-(class_Rings_Osemiring__1(_805642)), _805644 = _805642, class_Rings_Osemiring__1(_805644)], (14533 ^ _780478) ^ [_1040243, _1040245, _1040247] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040243), _1040245)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040247), _1040245)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040243), _1040247))], (22731 ^ _780478) ^ [_1203620, _1203622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203620), _1203622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203620)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203622))))], (45721 ^ _780478) ^ [_1698661, _1698663] : [hBOOL(hAPP(c_List_Odistinct(_1698661), _1698663)), -(c_List_Oremdups(_1698661, _1698663) = _1698663)], (17789 ^ _780478) ^ [_1111882, _1111884, _1111886, _1111888] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1111886), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1111882, tc_fun(_1111886, tc_HOL_Obool)), _1111884), _1111888)))), 17790 ^ _780478 : [(17791 ^ _780478) ^ [_1111956] : [hBOOL(hAPP(hAPP(c_member(_1111882), _1111956), _1111884)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111886), hAPP(_1111888, _1111956)))]]], (41448 ^ _780478) ^ [_1596285, _1596287, _1596289, _1596291] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596285, _1596285)), hAPP(hAPP(c_Product__Type_OPair(_1596285, _1596285), _1596287), _1596289)), c_Transitive__Closure_Otrancl(_1596285, _1596291))), 41452 ^ _780478 : [(41455 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596285, _1596285)), hAPP(hAPP(c_Product__Type_OPair(_1596285, _1596285), 41451 ^ [_1596285, _1596287, _1596289, _1596291]), _1596289)), _1596291)))], (41453 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596285, _1596285)), hAPP(hAPP(c_Product__Type_OPair(_1596285, _1596285), _1596287), 41451 ^ [_1596285, _1596287, _1596289, _1596291])), c_Transitive__Closure_Ortrancl(_1596285, _1596291))))]]], (15960 ^ _780478) ^ [_1069198, _1069200, _1069202, _1069204] : [class_Lattices_Osemilattice__inf(_1069198), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069198), _1069200), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069198), _1069202), _1069204))), 15967 ^ _780478 : [(15970 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069198), _1069200), _1069204)))], (15968 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069198), _1069200), _1069202)))]]], (42278 ^ _780478) ^ [_1620225, _1620227, _1620229, _1620231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1620225), _1620227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1620229, tc_HOL_Obool)), hAPP(c_List_Oset(_1620229), hAPP(hAPP(c_List_Otake(_1620229), _1620225), _1620231))), hAPP(c_List_Oset(_1620229), hAPP(hAPP(c_List_Otake(_1620229), _1620227), _1620231)))))], (18764 ^ _780478) ^ [_1132848, _1132850, _1132852] : [class_Complete__Lattice_Ocomplete__lattice(_1132848), -(c_Complete__Lattice_OInf__class_OInf(_1132848, hAPP(hAPP(c_Set_Oinsert(_1132848), _1132850), hAPP(hAPP(c_Set_Oinsert(_1132848), _1132852), c_Orderings_Obot__class_Obot(tc_fun(_1132848, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1132848), _1132850), _1132852))], (15888 ^ _780478) ^ [_1067928, _1067930, _1067932, _1067934] : [class_Lattices_Osemilattice__inf(_1067928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067928), _1067930), _1067932)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067928), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067928), _1067934), _1067930)), _1067932)))], (23837 ^ _780478) ^ [_1223782] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1223782) = 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)), _1223782)))], (23471 ^ _780478) ^ [_1216835, _1216837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216835), _1216837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216835), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1216837)))], (29962 ^ _780478) ^ [_1336467, _1336469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336469, _1336467)), _1336467)))], (48011 ^ _780478) ^ [_1748236, _1748238, _1748240] : [c_List_Olist__ex(_1748236, _1748238, _1748240), 48015 ^ _780478 : [(48018 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1748238, hAPP(hAPP(c_List_Onth(_1748236), _1748240), 48014 ^ [_1748236, _1748238, _1748240]))))], (48016 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48014 ^ [_1748236, _1748238, _1748240]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748236)), _1748240))))]]], (16418 ^ _780478) ^ [_1079905, _1079907, _1079909] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079905, tc_HOL_Obool)), _1079907), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079905, tc_HOL_Obool)), _1079909)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079905, tc_HOL_Obool)), _1079907), _1079909))], (45747 ^ _780478) ^ [_1699107, _1699109] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699107)), c_List_Oremdups(_1699107, _1699109)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699107)), _1699109), -(c_List_Oremdups(_1699107, _1699109) = _1699109)], (41989 ^ _780478) ^ [_1611946, _1611948, _1611950, _1611952] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611946), tc_List_Olist(_1611946))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611946), tc_List_Olist(_1611946)), _1611948), _1611950)), c_List_Olistrel(_1611946, _1611952))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611946), tc_List_Olist(_1611946))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611946), tc_List_Olist(_1611946)), _1611948), _1611950)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1611946), c_List_Olistrel1(_1611946, _1611952)))))], (46040 ^ _780478) ^ [_1705996, _1705998, _1706000] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1705996), tc_List_Olist(_1705996)), c_List_Opartition(_1705996, _1705998, _1706000)) = hAPP(c_List_Ofilter(_1705996, _1705998), _1706000))], (51783 ^ _780478) ^ [_1827870, _1827872] : [class_Lattices_Olattice(_1827870), -(class_Lattices_Osemilattice__inf(tc_fun(_1827872, _1827870)))], (18104 ^ _780478) ^ [_1117697, _1117699, _1117701, _1117703, _1117705] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117697, tc_fun(_1117699, tc_HOL_Obool)), _1117701), hAPP(hAPP(c_COMBB(tc_fun(_1117699, tc_HOL_Obool), tc_fun(_1117699, tc_HOL_Obool), _1117697), hAPP(c_Set_Oinsert(_1117699), _1117703)), _1117705)) = hAPP(hAPP(c_Set_Oinsert(_1117699), _1117703), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117697, tc_fun(_1117699, tc_HOL_Obool)), _1117701), _1117705)))], (36660 ^ _780478) ^ [_1477625, _1477627] : [36661 ^ _780478 : [(36664 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1477627), _1477625))], (36662 ^ _780478) ^ [] : [_1477625 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1477627, _1477625) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1477627))], (48601 ^ _780478) ^ [_1761011, _1761013, _1761015, _1761017] : [48602 ^ _780478 : [(48605 ^ _780478) ^ [] : [_1761013 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48603 ^ _780478) ^ [] : [hBOOL(hAPP(_1761017, _1761015))]], 48606 ^ _780478 : [(48607 ^ _780478) ^ [_1761136] : [hBOOL(hAPP(hAPP(c_member(_1761011), _1761136), hAPP(c_List_Oset(_1761011), c_List_Oreplicate(_1761011, _1761013, _1761015)))), -(hBOOL(hAPP(_1761017, _1761136)))]]], (45641 ^ _780478) ^ [_1696792, _1696794] : [hBOOL(hAPP(c_List_Odistinct(_1696792), _1696794)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1696792, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1696792), tc_fun(_1696792, tc_HOL_Obool)), c_List_Oset(_1696792)), c_Enum_Osublists(_1696792, _1696794)))))], (37573 ^ _780478) ^ [_1497456, _1497458, _1497460, _1497462, _1497464] : [c_Equiv__Relations_Oequivp(_1497456, _1497458), hBOOL(hAPP(hAPP(_1497458, _1497460), _1497462)), hBOOL(hAPP(hAPP(_1497458, _1497462), _1497464)), -(hBOOL(hAPP(hAPP(_1497458, _1497460), _1497464)))], (52293 ^ _780478) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (18081 ^ _780478) ^ [_1117051, _1117053, _1117055] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1117051, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1117051, tc_HOL_Obool)), _1117053), _1117055)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1117051, tc_HOL_Obool)), _1117053), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1117051, tc_HOL_Obool), _1117055)))], (7812 ^ _780478) ^ [_912788, _912790, _912792, _912794, _912796] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_912788), _912790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912792, tc_HOL_Obool)), _912794), hAPP(c_Set_Oimage(_912788, _912792, _912796), _912790))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_912792), _912794)))], (24533 ^ _780478) ^ [_1236278, _1236280, _1236282, _1236284] : [class_Divides_Osemiring__div(_1236278), -(_1236280 = c_Groups_Ozero__class_Ozero(_1236278)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236278), _1236282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236278), _1236284), _1236280))), _1236280) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236278), _1236284), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236278), _1236282), _1236280)))], (16414 ^ _780478) ^ [_1079759, _1079761, _1079763] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079759, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079759, tc_HOL_Obool)), _1079761), _1079763)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1079759, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079759, tc_HOL_Obool)), _1079761)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079759, tc_HOL_Obool)), _1079763)))], (8346 ^ _780478) ^ [_923668, _923670, _923672, _923674, _923676] : [class_Groups_Oab__group__add(_923668), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_923668), _923670), _923672) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_923668), _923674), _923676), 8353 ^ _780478 : [(8360 ^ _780478) ^ [] : [_923674 = _923676, -(_923670 = _923672)], (8354 ^ _780478) ^ [] : [_923670 = _923672, -(_923674 = _923676)]]], (1904 ^ _780478) ^ [_807142, _807144] : [-(class_Nat_Osize(_807142)), _807144 = _807142, class_Nat_Osize(_807144)], (17403 ^ _780478) ^ [_1102236, _1102238, _1102240, _1102242, _1102244] : [17405 ^ _780478 : [(17408 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1102236, tc_HOL_Obool)), hAPP(_1102242, 17404 ^ [_1102236, _1102238, _1102240, _1102242, _1102244])), _1102244))], (17406 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1102238), 17404 ^ [_1102236, _1102238, _1102240, _1102242, _1102244]), _1102240)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1102236, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102238, tc_fun(_1102236, tc_HOL_Obool)), _1102240), _1102242)), _1102244)))], (44306 ^ _780478) ^ [_1667319, _1667321, _1667323] : [class_Orderings_Olinorder(_1667319), -(c_Big__Operators_Olinorder__class_OMin(_1667319, hAPP(c_List_Oset(_1667319), hAPP(hAPP(c_List_Olist_OCons(_1667319), _1667321), _1667323))) = hAPP(c_List_Ofoldl(_1667319, _1667319, c_Orderings_Oord__class_Omin(_1667319), _1667321), _1667323))], (33096 ^ _780478) ^ [_1405940] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405940))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405940) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42170 ^ _780478) ^ [_1617377] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1617377)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1617377), tc_HOL_Obool))))], (36894 ^ _780478) ^ [_1482323, _1482325] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1482323, _1482325) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1482323, _1482325)))], (46981 ^ _780478) ^ [_1725439, _1725441, _1725443] : [_1725441 = hAPP(hAPP(c_List_Olist_OCons(_1725439), _1725443), c_List_Olist_ONil(_1725439)), -(hAPP(c_List_Orev(_1725439), _1725441) = hAPP(hAPP(c_List_Olist_OCons(_1725439), _1725443), c_List_Olist_ONil(_1725439)))], (2874 ^ _780478) ^ [_823016, _823018, _823020, _823022] : [-(c_Nitpick_Oint__lcm(_823022, _823018) = c_Nitpick_Oint__lcm(_823020, _823016)), _823022 = _823020, _823018 = _823016], (11131 ^ _780478) ^ [_974981, _974983, _974985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974981, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_974981, tc_HOL_Obool)), _974983)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_974981, tc_HOL_Obool)), _974985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974981, tc_HOL_Obool)), _974985), _974983)))], (22083 ^ _780478) ^ [_1190939, _1190941, _1190943] : [class_Rings_Olinordered__semidom(_1190939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190939), c_Groups_Ozero__class_Ozero(_1190939)), _1190941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190939), _1190941), c_Groups_Oone__class_Oone(_1190939))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1190939), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190939), _1190941), hAPP(hAPP(c_Power_Opower__class_Opower(_1190939), _1190941), _1190943))), hAPP(hAPP(c_Power_Opower__class_Opower(_1190939), _1190941), _1190943))))], (18636 ^ _780478) ^ [_1130253, _1130255, _1130257, _1130259, _1130261] : [-(_1130253 = c_Orderings_Obot__class_Obot(tc_fun(_1130255, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130257, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130255, tc_fun(_1130257, tc_HOL_Obool)), _1130253), _1130259)), _1130261) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130255, tc_fun(_1130257, tc_HOL_Obool)), _1130253), hAPP(hAPP(c_COMBC(_1130255, tc_fun(_1130257, tc_HOL_Obool), tc_fun(_1130257, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1130257, tc_HOL_Obool), tc_fun(tc_fun(_1130257, tc_HOL_Obool), tc_fun(_1130257, tc_HOL_Obool)), _1130255), c_Groups_Ominus__class_Ominus(tc_fun(_1130257, tc_HOL_Obool))), _1130259)), _1130261)))], (45573 ^ _780478) ^ [_1695229, _1695231, _1695233, _1695235, _1695237, _1695239] : [c_List_Olist__all2(_1695229, _1695231, _1695233, _1695235, _1695237), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695239), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695229)), _1695235))), -(hBOOL(hAPP(hAPP(_1695233, hAPP(hAPP(c_List_Onth(_1695229), _1695235), _1695239)), hAPP(hAPP(c_List_Onth(_1695231), _1695237), _1695239))))], (1414 ^ _780478) ^ [_801017, _801019] : [-(class_Lattices_Oboolean__algebra(_801017)), _801019 = _801017, class_Lattices_Oboolean__algebra(_801019)], (34479 ^ _780478) ^ [_1430690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1430690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1430690))))], (19544 ^ _780478) ^ [_1145763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1145763), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1145763 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14939 ^ _780478) ^ [_1048923, _1048925, _1048927, _1048929, _1048931] : [hBOOL(hAPP(hAPP(c_member(_1048923), _1048925), c_SetInterval_Oord_OatLeastAtMost(_1048923, _1048927, _1048929, _1048931))), 14942 ^ _780478 : [(14945 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1048927, _1048925), _1048931)))], (14943 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1048927, _1048929), _1048925)))]]], (38687 ^ _780478) ^ [_1525670, _1525672, _1525674, _1525676] : [hBOOL(hAPP(c_Predicate_ODomainP(_1525670, _1525672, hAPP(hAPP(c_COMBC(_1525670, tc_fun(tc_prod(_1525670, _1525672), tc_HOL_Obool), tc_fun(_1525672, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525672, tc_fun(tc_fun(tc_prod(_1525670, _1525672), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525670, _1525672), tc_HOL_Obool), tc_fun(_1525672, tc_HOL_Obool)), _1525670), c_COMBC(_1525672, tc_fun(tc_prod(_1525670, _1525672), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525672, tc_prod(_1525670, _1525672)), tc_fun(_1525672, tc_fun(tc_fun(tc_prod(_1525670, _1525672), tc_HOL_Obool), tc_HOL_Obool)), _1525670), hAPP(c_COMBB(tc_prod(_1525670, _1525672), tc_fun(tc_fun(tc_prod(_1525670, _1525672), tc_HOL_Obool), tc_HOL_Obool), _1525672), c_member(tc_prod(_1525670, _1525672)))), c_Product__Type_OPair(_1525670, _1525672)))), _1525674)), _1525676)), -(hBOOL(hAPP(hAPP(c_member(_1525670), _1525676), hAPP(c_Relation_ODomain(_1525670, _1525672), _1525674))))], (43149 ^ _780478) ^ [_1640798, _1640800] : [-(c_List_Osublist(_1640798, _1640800, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1640798))], (37923 ^ _780478) ^ [_1505794, _1505796, _1505798] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1505794, hAPP(hAPP(c_COMBC(_1505794, tc_fun(tc_prod(_1505794, _1505794), tc_HOL_Obool), tc_fun(_1505794, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505794, tc_fun(tc_fun(tc_prod(_1505794, _1505794), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1505794, _1505794), tc_HOL_Obool), tc_fun(_1505794, tc_HOL_Obool)), _1505794), c_COMBC(_1505794, tc_fun(tc_prod(_1505794, _1505794), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505794, tc_prod(_1505794, _1505794)), tc_fun(_1505794, tc_fun(tc_fun(tc_prod(_1505794, _1505794), tc_HOL_Obool), tc_HOL_Obool)), _1505794), hAPP(c_COMBB(tc_prod(_1505794, _1505794), tc_fun(tc_fun(tc_prod(_1505794, _1505794), tc_HOL_Obool), tc_HOL_Obool), _1505794), c_member(tc_prod(_1505794, _1505794)))), c_Product__Type_OPair(_1505794, _1505794)))), _1505796)), _1505798)), -(hBOOL(hAPP(hAPP(c_member(_1505794), _1505798), c_Wellfounded_Oacc(_1505794, _1505796))))], (9514 ^ _780478) ^ [_943585, _943587, _943589, _943591, _943593] : [class_Rings_Osemiring__0(_943585), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943585), _943587), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943589, _943585), _943591), _943593)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943589, _943585), hAPP(hAPP(c_COMBB(_943585, _943585, _943589), hAPP(c_Groups_Otimes__class_Otimes(_943585), _943587)), _943591)), _943593))], (43798 ^ _780478) ^ [_1655959, _1655961, _1655963, _1655965] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655959), tc_List_Olist(_1655959))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655959), tc_List_Olist(_1655959)), _1655961), _1655963)), c_List_Olistrel1(_1655959, _1655965))), 43803 ^ _780478 : [(43810 ^ _780478) ^ [] : [-(_1655963 = hAPP(hAPP(c_List_Oappend(_1655959), 43805 ^ [_1655959, _1655961, _1655963, _1655965]), hAPP(hAPP(c_List_Olist_OCons(_1655959), 43802 ^ [_1655959, _1655961, _1655963, _1655965]), 43806 ^ [_1655959, _1655961, _1655963, _1655965])))], (43808 ^ _780478) ^ [] : [-(_1655961 = hAPP(hAPP(c_List_Oappend(_1655959), 43805 ^ [_1655959, _1655961, _1655963, _1655965]), hAPP(hAPP(c_List_Olist_OCons(_1655959), 43801 ^ [_1655959, _1655961, _1655963, _1655965]), 43806 ^ [_1655959, _1655961, _1655963, _1655965])))], (43804 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655959, _1655959)), hAPP(hAPP(c_Product__Type_OPair(_1655959, _1655959), 43801 ^ [_1655959, _1655961, _1655963, _1655965]), 43802 ^ [_1655959, _1655961, _1655963, _1655965])), _1655965)))]]], (52181 ^ _780478) ^ [_1831919] : [class_Finite__Set_Ofinite(_1831919), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1831919)))], (37521 ^ _780478) ^ [_1496494, _1496496, _1496498, _1496500, _1496502] : [-(hAPP(c_Product__Type_Osnd(_1496494, _1496496), hAPP(c_Product__Type_Oapfst(_1496498, _1496494, _1496496, _1496500), _1496502)) = hAPP(c_Product__Type_Osnd(_1496498, _1496496), _1496502))], (32282 ^ _780478) ^ [_1390336, _1390338, _1390340] : [class_Int_Onumber__ring(_1390336), -(hAPP(c_Int_Onumber__class_Onumber__of(_1390336), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1390338), _1390340)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1390336), hAPP(c_Int_Onumber__class_Onumber__of(_1390336), _1390338)), hAPP(c_Int_Onumber__class_Onumber__of(_1390336), _1390340)))], (44243 ^ _780478) ^ [_1666074, _1666076, _1666078, _1666080, _1666082, _1666084] : [-(hAPP(c_List_Ofoldl(_1666074, _1666076, _1666078, _1666080), hAPP(hAPP(c_List_Oappend(_1666076), _1666082), _1666084)) = hAPP(c_List_Ofoldl(_1666074, _1666076, _1666078, hAPP(c_List_Ofoldl(_1666074, _1666076, _1666078, _1666080), _1666082)), _1666084))], (44482 ^ _780478) ^ [_1671100, _1671102, _1671104, _1671106, _1671108] : [class_Orderings_Olinorder(_1671100), hBOOL(hAPP(c_List_Odistinct(_1671102), _1671104)), -(hBOOL(hAPP(c_List_Odistinct(_1671102), c_List_Olinorder__class_Oinsort__insert__key(_1671102, _1671100, _1671106, _1671108, _1671104))))], (7643 ^ _780478) ^ [_909149, _909151, _909153, _909155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909149, tc_HOL_Obool)), _909151), _909153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909149, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_909149), _909155), _909151)), hAPP(hAPP(c_Set_Oinsert(_909149), _909155), _909153))))], (6762 ^ _780478) ^ [_892434, _892436, _892438, _892440, _892442, _892444] : [_892434 = _892436, -(hAPP(c_Fun_Ofun__upd(_892438, _892440, _892442, _892436, _892444), _892434) = _892444)], (29033 ^ _780478) ^ [_1318638, _1318640, _1318642, _1318644] : [-(c_Nat_Onat_Onat__case(_1318638, _1318640, _1318642, hAPP(c_Nat_OSuc, _1318644)) = hAPP(_1318642, _1318644))], (44047 ^ _780478) ^ [_1662226, _1662228, _1662230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662226), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662228)), _1662230))), -(_1662230 = hAPP(hAPP(c_List_Oappend(_1662228), hAPP(hAPP(c_List_Otake(_1662228), _1662226), _1662230)), hAPP(hAPP(c_List_Olist_OCons(_1662228), hAPP(hAPP(c_List_Onth(_1662228), _1662230), _1662226)), hAPP(hAPP(c_List_Odrop(_1662228), hAPP(c_Nat_OSuc, _1662226)), _1662230))))], (36084 ^ _780478) ^ [_1466177, _1466179, _1466181, _1466183] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1466177, _1466179), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1466181), _1466183))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1466177), _1466179), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1466183), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1466181)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1466181)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1466183), 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), _1466179), _1466183))))))], (21624 ^ _780478) ^ [_1182050, _1182052, _1182054] : [class_Rings_Olinordered__idom(_1182050), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182050), c_Groups_Ozero__class_Ozero(_1182050)), _1182052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182050), c_Groups_Ozero__class_Ozero(_1182050)), _1182054)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182050), _1182054), c_Groups_Oone__class_Oone(_1182050))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182050), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182050), _1182052), _1182054)), _1182052)))], (34823 ^ _780478) ^ [_1436935] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1436935), _1436935)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1436935)], (36790 ^ _780478) ^ [_1480255, _1480257] : [-(c_Divides_Odivmod__nat(_1480255, _1480257) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1480255, _1480257)))], (51915 ^ _780478) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (14915 ^ _780478) ^ [_1048430, _1048432, _1048434, _1048436] : [hBOOL(hAPP(hAPP(c_member(_1048430), _1048432), c_SetInterval_Oord_OlessThan(_1048430, _1048434, _1048436))), -(hBOOL(hAPP(hAPP(_1048434, _1048432), _1048436)))], (29049 ^ _780478) ^ [_1319108, _1319110, _1319112, _1319114, _1319116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1319108, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1319110, _1319108, _1319112), _1319114)), _1319116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1319108, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1319110, tc_HOL_Obool), tc_fun(_1319108, tc_HOL_Obool), c_Set_Oimage(_1319110, _1319108, _1319112)), hAPP(c_Set_OPow(_1319110), _1319114))), hAPP(c_Set_OPow(_1319108), _1319116))))], (39713 ^ _780478) ^ [_1553725, _1553727, _1553729, _1553731, _1553733, _1553735] : [-(hAPP(hAPP(c_Fun_Ocomp(_1553725, _1553727, _1553729, _1553731), _1553733), _1553735) = hAPP(_1553731, hAPP(_1553733, _1553735)))], (48153 ^ _780478) ^ [_1751248, _1751250, _1751252] : [c_List_Olist__all(_1751248, _1751250, _1751252), 48156 ^ _780478 : [(48157 ^ _780478) ^ [_1751337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751337), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751248)), _1751252))), -(hBOOL(hAPP(_1751250, hAPP(hAPP(c_List_Onth(_1751248), _1751252), _1751337))))]]], (36792 ^ _780478) ^ [_1480289, _1480291, _1480293, _1480295] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480289, _1480291), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1480293), _1480295))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1480289, _1480291) = _1480295)], (27888 ^ _780478) ^ [_1296249, _1296251, _1296253] : [class_Orderings_Oorder(_1296249), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1296249), _1296251), _1296253)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1296249, _1296253, _1296251) = c_Orderings_Obot__class_Obot(tc_fun(_1296249, tc_HOL_Obool)))], (52415 ^ _780478) ^ [_1834607, _1834609] : [hBOOL(_1834607), -(hBOOL(hAPP(hAPP(c_fimplies, _1834609), _1834607)))], (21894 ^ _780478) ^ [_1186975, _1186977, _1186979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186975)), 21897 ^ _780478 : [(21904 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186977), _1186979)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186975), _1186977)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186975), _1186979))))], (21898 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186975), _1186977)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186975), _1186979))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186977), _1186979)))]]], (20616 ^ _780478) ^ [_1164883] : [class_Rings_Olinordered__semidom(_1164883), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164883), c_Groups_Ozero__class_Ozero(_1164883)), c_Groups_Oone__class_Oone(_1164883))))], (43927 ^ _780478) ^ [_1659108, _1659110, _1659112, _1659114] : [-(hAPP(hAPP(c_List_Odrop(_1659108), _1659110), hAPP(hAPP(c_List_Oappend(_1659108), _1659112), _1659114)) = hAPP(hAPP(c_List_Oappend(_1659108), hAPP(hAPP(c_List_Odrop(_1659108), _1659110), _1659112)), hAPP(hAPP(c_List_Odrop(_1659108), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1659110), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659108)), _1659112))), _1659114)))], (38102 ^ _780478) ^ [_1511352, _1511354, _1511356, _1511358, _1511360, _1511362] : [c_Typedef_Otype__definition(_1511352, _1511354, _1511356, _1511358, _1511360), hBOOL(hAPP(hAPP(c_member(_1511354), _1511362), _1511360)), -(hAPP(_1511356, hAPP(_1511358, _1511362)) = _1511362)], (5416 ^ _780478) ^ [_863335, _863337] : [_863337 = _863335, -(c_Orderings_Oord__class_Oless(_863337) = c_Orderings_Oord__class_Oless(_863335))], (37479 ^ _780478) ^ [] : [-(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))], (41870 ^ _780478) ^ [_1608308, _1608310, _1608312, _1608314, _1608316] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608308), tc_List_Olist(_1608308))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608308), tc_List_Olist(_1608308)), _1608310), _1608312)), c_List_Olistrel1(_1608308, _1608314))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608308), tc_List_Olist(_1608308))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608308), tc_List_Olist(_1608308)), hAPP(hAPP(c_List_Olist_OCons(_1608308), _1608316), _1608310)), hAPP(hAPP(c_List_Olist_OCons(_1608308), _1608316), _1608312))), c_List_Olistrel1(_1608308, _1608314))))], (21125 ^ _780478) ^ [_1173137, _1173139] : [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), _1173137), _1173139))), 21128 ^ _780478 : [(21131 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173139)))], (21129 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173137)))]]], (42906 ^ _780478) ^ [_1636296, _1636298] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1636296), _1636298)), -(c_Nitpick_Ocard_H(_1636296, _1636298) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636296)), c_Hilbert__Choice_OEps(tc_List_Olist(_1636296), hAPP(hAPP(c_COMBS(tc_List_Olist(_1636296), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1636296)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1636296), tc_fun(_1636296, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1636296, tc_HOL_Obool), tc_fun(tc_fun(_1636296, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1636296)), c_fequal), c_List_Oset(_1636296))), _1636298))), c_List_Odistinct(_1636296)))))], (30248 ^ _780478) ^ [_1341611, _1341613, _1341615, _1341617] : [class_Groups_Oordered__ab__group__add__abs(_1341611), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341611), hAPP(c_Groups_Oabs__class_Oabs(_1341611), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341613, _1341611), _1341615), _1341617))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341613, _1341611), hAPP(hAPP(c_COMBB(_1341611, _1341611, _1341613), c_Groups_Oabs__class_Oabs(_1341611)), _1341615)), _1341617))))], (2348 ^ _780478) ^ [_814867, _814869, _814871, _814873] : [-(c_Divides_Odivmod__int__rel(_814873, _814869) = c_Divides_Odivmod__int__rel(_814871, _814867)), _814873 = _814871, _814869 = _814867], (19648 ^ _780478) ^ [_1147284, _1147286, _1147288] : [class_Rings_Olinordered__ring__strict(_1147284), 19651 ^ _780478 : [(19660 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1147284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147284), _1147286), _1147286)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147284), _1147288), _1147288)) = c_Groups_Ozero__class_Ozero(_1147284)), _1147286 = c_Groups_Ozero__class_Ozero(_1147284), _1147288 = c_Groups_Ozero__class_Ozero(_1147284)], (19652 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1147284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147284), _1147286), _1147286)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147284), _1147288), _1147288)) = c_Groups_Ozero__class_Ozero(_1147284), 19655 ^ _780478 : [(19658 ^ _780478) ^ [] : [-(_1147288 = c_Groups_Ozero__class_Ozero(_1147284))], (19656 ^ _780478) ^ [] : [-(_1147286 = c_Groups_Ozero__class_Ozero(_1147284))]]]]], (32312 ^ _780478) ^ [_1391045, _1391047] : [class_Int_Onumber__ring(_1391045), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1391045), hAPP(c_Int_Onumber__class_Onumber__of(_1391045), _1391047)) = hAPP(c_Int_Onumber__class_Onumber__of(_1391045), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1391047)))], (4302 ^ _780478) ^ [_845542, _845544, _845546, _845548, _845550, _845552] : [-(c_List_Oreplicate(_845552, _845548, _845544) = c_List_Oreplicate(_845550, _845546, _845542)), _845552 = _845550, _845548 = _845546, _845544 = _845542], (35635 ^ _780478) ^ [_1452517, _1452519, _1452521, _1452523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452517, tc_fun(_1452519, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1452517, tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_fun(_1452519, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452519, tc_fun(tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_fun(_1452519, tc_HOL_Obool)), _1452517), c_COMBC(_1452519, tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452519, tc_prod(_1452517, _1452519)), tc_fun(_1452519, tc_fun(tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_HOL_Obool)), _1452517), hAPP(c_COMBB(tc_prod(_1452517, _1452519), tc_fun(tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_HOL_Obool), _1452519), c_member(tc_prod(_1452517, _1452519)))), c_Product__Type_OPair(_1452517, _1452519)))), _1452521)), hAPP(hAPP(c_COMBC(_1452517, tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_fun(_1452519, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452519, tc_fun(tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_fun(_1452519, tc_HOL_Obool)), _1452517), c_COMBC(_1452519, tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1452519, tc_prod(_1452517, _1452519)), tc_fun(_1452519, tc_fun(tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_HOL_Obool)), _1452517), hAPP(c_COMBB(tc_prod(_1452517, _1452519), tc_fun(tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool), tc_HOL_Obool), _1452519), c_member(tc_prod(_1452517, _1452519)))), c_Product__Type_OPair(_1452517, _1452519)))), _1452523))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1452517, _1452519), tc_HOL_Obool)), _1452521), _1452523)))], (48541 ^ _780478) ^ [_1759941, _1759943, _1759945] : [-(c_List_Oreplicate(_1759941, hAPP(c_Nat_OSuc, _1759943), _1759945) = hAPP(hAPP(c_List_Olist_OCons(_1759941), _1759945), c_List_Oreplicate(_1759941, _1759943, _1759945)))], (49250 ^ _780478) ^ [_1775440, _1775442] : [-(c_Relation_Otrans(_1775440, c_Relation_OId__on(_1775440, _1775442)))], (47907 ^ _780478) ^ [_1746281, _1746283, _1746285, _1746287] : [class_Orderings_Oorder(_1746281), class_Enum_Oenum(_1746283), 47914 ^ _780478 : [(47921 ^ _780478) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746283), hAPP(hAPP(c_COMBS(_1746283, _1746281, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1746281, tc_fun(_1746281, tc_HOL_Obool), _1746283), c_Orderings_Oord__class_Oless__eq(_1746281)), _1746285)), _1746287))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1746283, _1746281)), _1746285), _1746287)))], (47915 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1746283, _1746281)), _1746285), _1746287)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746283), hAPP(hAPP(c_COMBS(_1746283, _1746281, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1746281, tc_fun(_1746281, tc_HOL_Obool), _1746283), c_Orderings_Oord__class_Oless__eq(_1746281)), _1746285)), _1746287))))]]], (39183 ^ _780478) ^ [_1540925, _1540927, _1540929, _1540931, _1540933, _1540935, _1540937, _1540939] : [c_Fun_Oinj__on(_1540925, _1540927, _1540929, _1540931), c_Fun_Oinj__on(_1540933, _1540935, _1540937, _1540939), -(c_Fun_Oinj__on(tc_prod(_1540925, _1540933), tc_prod(_1540927, _1540935), c_Product__Type_Omap__pair(_1540925, _1540927, _1540933, _1540935, _1540929, _1540937), hAPP(hAPP(c_Product__Type_OSigma(_1540925, _1540933), _1540931), hAPP(c_COMBK(tc_fun(_1540933, tc_HOL_Obool), _1540925), _1540939))))], (50242 ^ _780478) ^ [_1796913] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50238 ^ [_1796913]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (43582 ^ _780478) ^ [_1650566, _1650568, _1650570] : [-(hAPP(hAPP(c_List_Oappend(_1650566), _1650568), _1650570) = c_List_Olist_ONil(_1650566)), _1650568 = c_List_Olist_ONil(_1650566), _1650570 = c_List_Olist_ONil(_1650566)], (46991 ^ _780478) ^ [_1725686, _1725688, _1725690, _1725692] : [-(hAPP(c_List_Orev(_1725686), hAPP(hAPP(c_List_Omap(_1725688, _1725686), _1725690), _1725692)) = hAPP(hAPP(c_List_Omap(_1725688, _1725686), _1725690), hAPP(c_List_Orev(_1725688), _1725692)))], (5268 ^ _780478) ^ [_860979, _860981, _860983, _860985, _860987, _860989] : [-(c_Lazy__Sequence_Oappend(_860989, _860985, _860981) = c_Lazy__Sequence_Oappend(_860987, _860983, _860979)), _860989 = _860987, _860985 = _860983, _860981 = _860979], (25120 ^ _780478) ^ [_1247086, _1247088, _1247090, _1247092] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1247086), _1247088)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1247090), _1247092)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1247086, _1247090)), c_Sum__Type_OPlus(_1247086, _1247090, _1247088, _1247092)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1247086), _1247088)), hAPP(c_Finite__Set_Ocard(_1247090), _1247092)))], (9814 ^ _780478) ^ [_950193, _950195, _950197, _950199] : [class_Rings_Ocomm__semiring__1(_950193), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950193), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950193), _950195), _950197)), _950199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950193), _950195), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950193), _950197), _950199)))], (6976 ^ _780478) ^ [_896879, _896881, _896883, _896885, _896887] : [class_Rings_Oring(_896879), hBOOL(hAPP(c_Finite__Set_Ofinite(_896881), _896883)), hBOOL(hAPP(hAPP(c_member(_896881), _896885), _896883)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896881, _896879), _896887), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896881, tc_HOL_Obool)), _896883), hAPP(hAPP(c_Set_Oinsert(_896881), _896885), c_Orderings_Obot__class_Obot(tc_fun(_896881, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_896879), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896881, _896879), _896887), _896883)), hAPP(_896887, _896885)))], (45488 ^ _780478) ^ [_1693435, _1693437, _1693439, _1693441, _1693443, _1693445, _1693447] : [-(c_List_Olist__all2(_1693435, _1693437, _1693439, hAPP(hAPP(c_List_Olist_OCons(_1693435), _1693441), _1693443), hAPP(hAPP(c_List_Olist_OCons(_1693437), _1693445), _1693447))), hBOOL(hAPP(hAPP(_1693439, _1693441), _1693445)), c_List_Olist__all2(_1693435, _1693437, _1693439, _1693443, _1693447)], (35305 ^ _780478) ^ [_1446028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1446028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1446028))))], (25621 ^ _780478) ^ [_1255974] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255974))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1255974)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27589 ^ _780478) ^ [_1290533, _1290535, _1290537] : [class_Orderings_Oord(_1290533), 27592 ^ _780478 : [(27599 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290533), _1290537), _1290535)), -(hBOOL(hAPP(hAPP(c_member(_1290533), _1290535), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290533), _1290537))))], (27593 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1290533), _1290535), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1290533), _1290537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290533), _1290537), _1290535)))]]], (48844 ^ _780478) ^ [_1765872, _1765874, _1765876, _1765878, _1765880] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1765872, _1765874, _1765876, _1765878, _1765880) = c_Option_Ooption_Ooption__case(_1765872, tc_prod(_1765874, tc_Lazy__Sequence_Olazy__sequence(_1765874)), _1765876, hAPP(c_Product__Type_Oprod_Oprod__case(_1765874, tc_Lazy__Sequence_Olazy__sequence(_1765874), _1765872), _1765878), hAPP(c_Lazy__Sequence_Oyield(_1765874), _1765880)))], (1244 ^ _780478) ^ [_798892, _798894] : [-(class_Divides_Oring__div(_798892)), _798894 = _798892, class_Divides_Oring__div(_798894)], (49029 ^ _780478) ^ [_1770110, _1770112, _1770114, _1770116, _1770118, _1770120, _1770122] : [49031 ^ _780478 : [(49034 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1770114, 49030 ^ [_1770110, _1770112, _1770114, _1770116, _1770118, _1770120, _1770122]), _1770116), _1770118))], (49032 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770110), 49030 ^ [_1770110, _1770112, _1770114, _1770116, _1770118, _1770120, _1770122]), _1770112)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1770110, tc_fun(_1770120, tc_fun(_1770122, tc_HOL_Obool))), _1770112), _1770114), _1770116), _1770118)))], (19030 ^ _780478) ^ [_1137746] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1137746))))], (10999 ^ _780478) ^ [_972383, _972385, _972387] : [class_Groups_Ogroup__add(_972383), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972383), _972385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972383), hAPP(c_Groups_Ouminus__class_Ouminus(_972383), _972385)), _972387)) = _972387)], (42345 ^ _780478) ^ [_1621790, _1621792, _1621794] : [42347 ^ _780478 : [(42350 ^ _780478) ^ [] : [hBOOL(hAPP(_1621794, hAPP(hAPP(c_List_Onth(_1621790), _1621792), 42346 ^ [_1621790, _1621792, _1621794])))], (42348 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42346 ^ [_1621790, _1621792, _1621794]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621790)), _1621792))))]], 42351 ^ _780478 : [(42352 ^ _780478) ^ [_1621992] : [hBOOL(hAPP(hAPP(c_member(_1621790), _1621992), hAPP(c_List_Oset(_1621790), _1621792))), -(hBOOL(hAPP(_1621794, _1621992)))]]], (21612 ^ _780478) ^ [_1181905, _1181907] : [_1181905 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1181905), _1181907) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45657 ^ _780478) ^ [_1697221, _1697223] : [_1697221 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1697223, _1697221, c_List_Olist_ONil(_1697223)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1697223)), c_List_Olist_ONil(_1697223)), c_List_Olist_ONil(tc_List_Olist(_1697223))))], (11935 ^ _780478) ^ [_990211, _990213] : [class_Orderings_Olinorder(_990211), hBOOL(hAPP(c_Finite__Set_Ofinite(_990211), _990213)), -(c_Big__Operators_Olattice_OSup__fin(_990211, c_Orderings_Oord__class_Omax(_990211), _990213) = hAPP(c_Finite__Set_Ofold1(_990211, c_Orderings_Oord__class_Omax(_990211)), _990213))], (27733 ^ _780478) ^ [_1292980, _1292982] : [class_Groups_Oordered__ab__group__add(_1292980), -(hAPP(c_Set_Oimage(_1292980, _1292980, c_Groups_Ouminus__class_Ouminus(_1292980)), hAPP(c_SetInterval_Oord__class_OlessThan(_1292980), _1292982)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1292980), hAPP(c_Groups_Ouminus__class_Ouminus(_1292980), _1292982)))], (1924 ^ _780478) ^ [_807388, _807390, _807392, _807394, _807396, _807398] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_807396, _807392, _807388)), c_Hoare__Mirabelle_Ohoare__derivs(_807398, _807394, _807390), _807398 = _807396, _807394 = _807392, _807390 = _807388], (49732 ^ _780478) ^ [_1786366, _1786368] : [c_Relation_Osym(_1786366, _1786368), -(c_Relation_Osym(tc_List_Olist(_1786366), c_List_Olistrel(_1786366, _1786368)))], (23192 ^ _780478) ^ [_1212191] : [23193 ^ _780478 : [(23194 ^ _780478) ^ [_1212248] : [hBOOL(hAPP(_1212191, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212248)))]], 23196 ^ _780478 : [(23199 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1212191, 23195 ^ [_1212191])))], (23197 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23195 ^ [_1212191])))]]], (48899 ^ _780478) ^ [_1767058, _1767060, _1767062] : [hBOOL(hAPP(hAPP(c_member(_1767058), _1767062), hAPP(c_List_Oset(_1767058), _1767060))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1767058), _1767060), _1767062)))], (37587 ^ _780478) ^ [_1497685, _1497687, _1497689, _1497691, _1497693, _1497695, _1497697] : [-(hAPP(c_Product__Type_Oapsnd(_1497685, _1497687, _1497689, _1497691), hAPP(c_Product__Type_Oapfst(_1497693, _1497689, _1497685, _1497695), _1497697)) = hAPP(c_Product__Type_Oapfst(_1497693, _1497689, _1497687, _1497695), hAPP(c_Product__Type_Oapsnd(_1497685, _1497687, _1497693, _1497691), _1497697)))], (21109 ^ _780478) ^ [_1172858, _1172860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1172860), _1172858)), -(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), _1172858), _1172860))))], (46017 ^ _780478) ^ [_1705476, _1705478, _1705480] : [hAPP(c_List_Ofilter(_1705476, _1705478), _1705480) = _1705480, 46020 ^ _780478 : [(46021 ^ _780478) ^ [_1705567] : [hBOOL(hAPP(hAPP(c_member(_1705476), _1705567), hAPP(c_List_Oset(_1705476), _1705480))), -(hBOOL(hAPP(_1705478, _1705567)))]]], (22737 ^ _780478) ^ [_1203731, _1203733] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203731)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203733)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203731), _1203733)))], (16010 ^ _780478) ^ [_1070086, _1070088, _1070090] : [class_Lattices_Olattice(_1070086), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070086), _1070088), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070086), _1070088), _1070090)) = _1070088)], (5228 ^ _780478) ^ [_860383, _860385, _860387, _860389] : [-(c_Transitive__Closure_Otrancl(_860389, _860385) = c_Transitive__Closure_Otrancl(_860387, _860383)), _860389 = _860387, _860385 = _860383], (41051 ^ _780478) ^ [_1585844, _1585846, _1585848] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1585844, _1585844, _1585846), c_Relation_OId(_1585844)), _1585848) = _1585848)], (33632 ^ _780478) ^ [_1414746, _1414748, _1414750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414746), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414746)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414748)), _1414750)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40666 ^ _780478) ^ [_1576583, _1576585, _1576587, _1576589] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576583, _1576583)), hAPP(hAPP(c_Product__Type_OPair(_1576583, _1576583), _1576585), _1576587)), c_Transitive__Closure_Ortrancl(_1576583, _1576589)))), 40667 ^ _780478 : [(40670 ^ _780478) ^ [] : [-(_1576585 = _1576587), hBOOL(hAPP(hAPP(c_member(tc_prod(_1576583, _1576583)), hAPP(hAPP(c_Product__Type_OPair(_1576583, _1576583), _1576585), _1576587)), c_Transitive__Closure_Otrancl(_1576583, _1576589)))], (40668 ^ _780478) ^ [] : [_1576585 = _1576587]]], (8274 ^ _780478) ^ [_922160, _922162, _922164, _922166] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_922160), 8277 ^ _780478 : [(8284 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922160), _922162), _922166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922160), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922160), _922162), _922164)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922160), _922166), _922164))))], (8278 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922160), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922160), _922162), _922164)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922160), _922166), _922164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_922160), _922162), _922166)))]]], (17807 ^ _780478) ^ [_1112250, _1112252, _1112254, _1112256, _1112258] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112250, tc_fun(_1112252, tc_HOL_Obool)), _1112254), hAPP(hAPP(c_COMBS(_1112250, tc_fun(_1112252, tc_HOL_Obool), tc_fun(_1112252, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1112252, tc_HOL_Obool), tc_fun(tc_fun(_1112252, tc_HOL_Obool), tc_fun(_1112252, tc_HOL_Obool)), _1112250), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112252, tc_HOL_Obool))), _1112256)), _1112258)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112252, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1112252, tc_HOL_Obool), hAPP(c_Set_Oimage(_1112250, tc_fun(_1112252, tc_HOL_Obool), _1112256), _1112254))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1112252, tc_HOL_Obool), hAPP(c_Set_Oimage(_1112250, tc_fun(_1112252, tc_HOL_Obool), _1112258), _1112254))))], (49490 ^ _780478) ^ [_1781590, _1781592] : [c_Equiv__Relations_Oequivp(_1781590, _1781592), 49493 ^ _780478 : [(49498 ^ _780478) ^ [] : [-(c_Predicate_Otransp(_1781590, _1781592))], (49496 ^ _780478) ^ [] : [-(c_Predicate_Osymp(_1781590, _1781592))], (49494 ^ _780478) ^ [] : [-(c_Predicate_Oreflp(_1781590, _1781592))]]], (45211 ^ _780478) ^ [_1686598, _1686600] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1686598), _1686600) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686598)), hAPP(c_Code__Numeral_Onat__of, _1686600))))], (24915 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17452 ^ _780478) ^ [_1104300, _1104302, _1104304, _1104306, _1104308, _1104310] : [hBOOL(hAPP(hAPP(c_member(_1104300), _1104302), _1104304)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104300, tc_fun(_1104306, tc_HOL_Obool)), _1104304), hAPP(hAPP(c_COMBB(tc_fun(_1104306, tc_HOL_Obool), tc_fun(_1104306, tc_HOL_Obool), _1104300), hAPP(c_Set_Oinsert(_1104306), _1104308)), _1104310)) = hAPP(hAPP(c_Set_Oinsert(_1104306), _1104308), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104300, tc_fun(_1104306, tc_HOL_Obool)), _1104304), _1104310)))], (37063 ^ _780478) ^ [_1485507, _1485509, _1485511] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1485507, _1485509), _1485511)), 37066 ^ _780478 : [(37067 ^ _780478) ^ [_1485592] : [hBOOL(hAPP(hAPP(_1485509, _1485592), _1485511)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1485507, _1485509), _1485592)))]]], (34335 ^ _780478) ^ [_1428095, _1428097] : [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), _1428095))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1428097)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1428095))) = 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), _1428097), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428095)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35433 ^ _780478) ^ [_1447994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1447994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1447994)))], (16410 ^ _780478) ^ [_1079661, _1079663] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079661, tc_HOL_Obool)), _1079663), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079661, tc_HOL_Obool)), _1079663)) = c_Orderings_Obot__class_Obot(tc_fun(_1079661, tc_HOL_Obool)))], (11369 ^ _780478) ^ [_979610, _979612, _979614, _979616] : [_979610 = c_Finite__Set_Ofold1(_979612, _979614), -(hAPP(_979610, hAPP(hAPP(c_Set_Oinsert(_979612), _979616), c_Orderings_Obot__class_Obot(tc_fun(_979612, tc_HOL_Obool)))) = _979616)], (16220 ^ _780478) ^ [_1074492, _1074494] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074492, tc_HOL_Obool)), _1074494), c_Orderings_Otop__class_Otop(tc_fun(_1074492, tc_HOL_Obool))) = _1074494)], (50147 ^ _780478) ^ [_1794498, _1794500, _1794502, _1794504, _1794506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794498, tc_HOL_Obool)), _1794500), hAPP(c_Set_Oimage(_1794502, _1794498, _1794504), _1794506))), -(c_Fun_Oinj__on(_1794498, _1794502, c_Hilbert__Choice_Oinv__into(_1794502, _1794498, _1794506, _1794504), _1794500))], (37403 ^ _780478) ^ [_1492400, _1492402, _1492404, _1492406, _1492408, _1492410] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492400, _1492400)), hAPP(hAPP(c_Product__Type_OPair(_1492400, _1492400), _1492402), _1492404)), hAPP(hAPP(c_Relation_Oinv__image(_1492406, _1492400), _1492408), _1492410))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492406, _1492406)), hAPP(hAPP(c_Product__Type_OPair(_1492406, _1492406), hAPP(_1492410, _1492402)), hAPP(_1492410, _1492404))), _1492408)))], (51297 ^ _780478) ^ [_1819786, _1819788, _1819790, _1819792] : [class_Rings_Oidom(_1819786), 51300 ^ _780478 : [(51301 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819786), _1819788), _1819790)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819786), _1819792), _1819790))), -(_1819790 = c_Groups_Ozero__class_Ozero(_1819786)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819786), _1819788), _1819792)))], (51311 ^ _780478) ^ [] : [51312 ^ _780478 : [(51315 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819786), _1819788), _1819792))], (51313 ^ _780478) ^ [] : [_1819790 = c_Groups_Ozero__class_Ozero(_1819786)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819786), _1819788), _1819790)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819786), _1819792), _1819790))))]]], (31395 ^ _780478) ^ [_1367220, _1367222, _1367224] : [class_Orderings_Olinorder(_1367220), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367220), _1367222)), -(_1367222 = c_Orderings_Obot__class_Obot(tc_fun(_1367220, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367220), _1367224), c_Big__Operators_Olattice_OSup__fin(_1367220, c_Orderings_Oord__class_Omax(_1367220), _1367222)) = c_Big__Operators_Olattice_OSup__fin(_1367220, c_Orderings_Oord__class_Omax(_1367220), hAPP(c_Set_OCollect(_1367220), hAPP(hAPP(c_COMBB(tc_fun(_1367220, tc_HOL_Obool), tc_HOL_Obool, _1367220), c_HOL_OEx(_1367220)), hAPP(hAPP(c_COMBC(_1367220, tc_fun(_1367220, tc_HOL_Obool), tc_fun(_1367220, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1367220, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1367220, tc_HOL_Obool), tc_fun(_1367220, tc_HOL_Obool)), _1367220), c_COMBS(_1367220, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1367220, tc_HOL_Obool), tc_fun(_1367220, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1367220), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1367220), c_fconj)), hAPP(hAPP(c_COMBC(_1367220, tc_fun(_1367220, _1367220), tc_fun(_1367220, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1367220, tc_HOL_Obool), tc_fun(tc_fun(_1367220, _1367220), tc_fun(_1367220, tc_HOL_Obool)), _1367220), c_COMBB(_1367220, tc_HOL_Obool, _1367220)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1367220), _1367224))))), hAPP(hAPP(c_COMBC(_1367220, tc_fun(_1367220, tc_HOL_Obool), tc_HOL_Obool), c_member(_1367220)), _1367222))))))], (46328 ^ _780478) ^ [_1712998, _1713000] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712998)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1713000)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712998), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1713000)) = c_List_Olist_ONil(tc_Nat_Onat))], (42624 ^ _780478) ^ [_1629901, _1629903, _1629905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1629901), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629903)), _1629905))), -(c_List_Obutlast(_1629903, hAPP(hAPP(c_List_Otake(_1629903), _1629901), _1629905)) = hAPP(hAPP(c_List_Otake(_1629903), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1629901), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1629905))], (48881 ^ _780478) ^ [_1766689, _1766691, _1766693, _1766695] : [48882 ^ _780478 : [(48885 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1766689), _1766693), _1766695))], (48883 ^ _780478) ^ [] : [_1766691 = _1766695]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1766689), hAPP(hAPP(c_List_Olist_OCons(_1766689), _1766691), _1766693)), _1766695)))], (1864 ^ _780478) ^ [_806642, _806644] : [-(class_Groups_Ozero(_806642)), _806644 = _806642, class_Groups_Ozero(_806644)], (30841 ^ _780478) ^ [_1353357] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1353357), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1353357) = _1353357)], (37307 ^ _780478) ^ [_1490454, _1490456, _1490458] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1490454, _1490456), _1490458)), 37310 ^ _780478 : [(37319 ^ _780478) ^ [] : [-(_1490456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37322 ^ _780478 : [(37331 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490456))), 37334 ^ _780478 : [(37337 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490458)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37335 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1490456), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490458))))]]], (37323 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490456)), 37326 ^ _780478 : [(37329 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490458)), _1490456)))], (37327 ^ _780478) ^ [] : [-(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), _1490458))))]]]]], (37313 ^ _780478) ^ [] : [_1490456 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1490458) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37311 ^ _780478) ^ [] : [-(_1490454 = 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), _1490458)), _1490456)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490458)))]]], (29648 ^ _780478) ^ [_1330913, _1330915, _1330917, _1330919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330913)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330915), _1330917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1330917), 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), _1330915), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330919, _1330913))), _1330917)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26528 ^ _780478) ^ [_1271910, _1271912, _1271914] : [class_Fields_Olinordered__field(_1271910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271910), c_Groups_Ozero__class_Ozero(_1271910)), _1271912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271910), c_Groups_Ozero__class_Ozero(_1271910)), _1271914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271910), c_Groups_Ozero__class_Ozero(_1271910)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271910), _1271912), _1271914))))], (34167 ^ _780478) ^ [] : [-(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)))))], (24755 ^ _780478) ^ [_1240455, _1240457, _1240459, _1240461] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1240455, _1240459)), c_Sum__Type_OPlus(_1240455, _1240459, _1240457, _1240461)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1240455), _1240457)), hAPP(c_Finite__Set_Ocard(_1240459), _1240461))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1240455), _1240457)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1240459), _1240461))], (27481 ^ _780478) ^ [_1288657, _1288659] : [class_Int_Oring__char__0(_1288657), 27484 ^ _780478 : [(27491 ^ _780478) ^ [] : [_1288659 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1288657), _1288659) = c_Groups_Ozero__class_Ozero(_1288657))], (27485 ^ _780478) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1288657), _1288659) = c_Groups_Ozero__class_Ozero(_1288657), -(_1288659 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (33028 ^ _780478) ^ [_1404743] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404743))), -(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), _1404743)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (30326 ^ _780478) ^ [_1343147, _1343149, _1343151] : [class_Groups_Oordered__ab__group__add__abs(_1343147), -(hAPP(c_Groups_Oabs__class_Oabs(_1343147), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1343147), hAPP(c_Groups_Oabs__class_Oabs(_1343147), _1343149)), hAPP(c_Groups_Oabs__class_Oabs(_1343147), _1343151))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1343147), hAPP(c_Groups_Oabs__class_Oabs(_1343147), _1343149)), hAPP(c_Groups_Oabs__class_Oabs(_1343147), _1343151)))], (4362 ^ _780478) ^ [_846538, _846540, _846542, _846544, _846546, _846548, _846550, _846552, _846554, _846556, _846558, _846560] : [-(c_New__Random__Sequence_Opos__union(_846560, _846556, _846552, _846548, _846544, _846540) = c_New__Random__Sequence_Opos__union(_846558, _846554, _846550, _846546, _846542, _846538)), _846560 = _846558, _846556 = _846554, _846552 = _846550, _846548 = _846546, _846544 = _846542, _846540 = _846538], (34319 ^ _780478) ^ [_1427728, _1427730, _1427732] : [class_Int_Onumber__ring(_1427728), 34322 ^ _780478 : [(34329 ^ _780478) ^ [] : [-(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), _1427730)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427728), _1427732), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427730))) = c_Groups_Oone__class_Oone(_1427728))], (34323 ^ _780478) ^ [] : [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), _1427730))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427728), _1427732), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427730))) = hAPP(hAPP(c_HOL_OLet(_1427728, _1427728), hAPP(hAPP(c_Power_Opower__class_Opower(_1427728), _1427732), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427730))), hAPP(hAPP(c_COMBS(_1427728, _1427728, _1427728), hAPP(hAPP(c_COMBB(_1427728, tc_fun(_1427728, _1427728), _1427728), c_Groups_Otimes__class_Otimes(_1427728)), hAPP(c_Groups_Otimes__class_Otimes(_1427728), _1427732))), c_COMBI(_1427728))))]]], (2140 ^ _780478) ^ [_811663, _811665, _811667, _811669, _811671, _811673] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_811673, _811669, _811665) = c_Hoare__Mirabelle_Otriple_Otriple__size(_811671, _811667, _811663)), _811673 = _811671, _811669 = _811667, _811665 = _811663], (18345 ^ _780478) ^ [_1123651, _1123653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123651), _1123653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123651), hAPP(c_Nat_OSuc, _1123653))))], (32078 ^ _780478) ^ [_1386293, _1386295, _1386297] : [class_Int_Onumber(_1386293), 32081 ^ _780478 : [(32088 ^ _780478) ^ [] : [_1386297 = hAPP(c_Int_Onumber__class_Onumber__of(_1386293), _1386295), -(hAPP(c_Int_Onumber__class_Onumber__of(_1386293), _1386295) = _1386297)], (32082 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1386293), _1386295) = _1386297, -(_1386297 = hAPP(c_Int_Onumber__class_Onumber__of(_1386293), _1386295))]]], (30980 ^ _780478) ^ [_1356216, _1356218, _1356220] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1356216, tc_HOL_Obool)), _1356218), _1356220))), 30986 ^ _780478 : [(30990 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1356216, tc_HOL_Obool)), 30988 ^ [_1356216, _1356218, _1356220]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1356216, tc_HOL_Obool)), _1356218), _1356220))))], (30992 ^ _780478) ^ [] : [30985 ^ [_1356216, _1356218, _1356220] = 30988 ^ [_1356216, _1356218, _1356220]], (30994 ^ _780478) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1356216, tc_HOL_Obool)), 30985 ^ [_1356216, _1356218, _1356220]), 30988 ^ [_1356216, _1356218, _1356220]) = c_Orderings_Obot__class_Obot(tc_fun(_1356216, tc_HOL_Obool))], (30987 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1356216, tc_HOL_Obool)), 30985 ^ [_1356216, _1356218, _1356220]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1356216, tc_HOL_Obool)), _1356218), _1356220))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1356216, tc_HOL_Obool)), _1356218), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1356216, tc_HOL_Obool), _1356220)) = c_Orderings_Obot__class_Obot(tc_fun(_1356216, tc_HOL_Obool)))], (15409 ^ _780478) ^ [_1058095, _1058097, _1058099] : [class_Rings_Olinordered__semidom(_1058095), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058095), c_Groups_Oone__class_Oone(_1058095)), _1058097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1058095), c_Groups_Oone__class_Oone(_1058095)), hAPP(hAPP(c_Power_Opower__class_Opower(_1058095), _1058097), _1058099))))], (11435 ^ _780478) ^ [_980856, _980858, _980860] : [-(hAPP(c_Finite__Set_Ofold1(_980856, _980858), _980860) = c_HOL_OThe(_980856, c_Finite__Set_Ofold1Set(_980856, _980858, _980860)))], (14130 ^ _780478) ^ [_1033008, _1033010] : [class_Rings_Ocomm__semiring__1(_1033008), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033008), c_Groups_Oone__class_Oone(_1033008)), _1033010) = _1033010)], (48697 ^ _780478) ^ [_1762711, _1762713, _1762715, _1762717] : [-(hBOOL(hAPP(hAPP(c_member(_1762711), _1762713), hAPP(c_List_Oset(_1762711), c_List_Oreplicate(_1762711, _1762715, _1762717))))), _1762713 = _1762717, -(_1762715 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27535 ^ _780478) ^ [_1289572, _1289574, _1289576] : [class_Rings_Oring__1(_1289572), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289572), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1289574), _1289576)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289572), hAPP(c_Int_Oring__1__class_Oof__int(_1289572), _1289574)), hAPP(c_Int_Oring__1__class_Oof__int(_1289572), _1289576)))], (37171 ^ _780478) ^ [_1487622, _1487624, _1487626, _1487628, _1487630] : [-(hAPP(c_Product__Type_Ofst(_1487622, _1487624), hAPP(c_Product__Type_Oapsnd(_1487626, _1487624, _1487622, _1487628), _1487630)) = hAPP(c_Product__Type_Ofst(_1487622, _1487626), _1487630))], (34569 ^ _780478) ^ [_1432271, _1432273] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1432271)), c_Int_OBit1(_1432273)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1432271), _1432273)))], (14347 ^ _780478) ^ [_1036641, _1036643, _1036645, _1036647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036641), _1036643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036645), _1036647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036641), _1036645)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036643), _1036647))))], (48675 ^ _780478) ^ [_1762316, _1762318, _1762320] : [c_List_Oreplicate(_1762316, _1762318, _1762320) = c_List_Olist_ONil(_1762316), -(_1762318 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13878 ^ _780478) ^ [_1028616, _1028618] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028616), _1028618))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028618), _1028616)))], (37903 ^ _780478) ^ [_1505388, _1505390, _1505392, _1505394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1505388), _1505394)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1505392), _1505390))), -(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), _1505388), _1505390)), 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), _1505392), _1505394)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (8336 ^ _780478) ^ [_923401, _923403, _923405, _923407, _923409] : [class_Groups_Ocomm__monoid__add(_923401), hBOOL(hAPP(c_Finite__Set_Ofinite(_923403), _923405)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_923403, _923401), hAPP(hAPP(c_COMBS(_923403, _923401, _923401), hAPP(hAPP(c_COMBB(_923401, tc_fun(_923401, _923401), _923403), c_Groups_Oplus__class_Oplus(_923401)), _923407)), _923409)), _923405) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_923401), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_923403, _923401), _923407), _923405)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_923403, _923401), _923409), _923405)))], (19550 ^ _780478) ^ [_1145844] : [_1145844 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1145844), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23099 ^ _780478) ^ [_1210377, _1210379] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210377)), _1210379) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1210377), _1210379)))], (11119 ^ _780478) ^ [_974653, _974655, _974657, _974659] : [class_Groups_Oordered__ab__group__add(_974653), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974653), hAPP(hAPP(c_Orderings_Oord__class_Omin(_974653), _974655), _974657)), _974659) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_974653), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974653), _974655), _974659)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974653), _974657), _974659)))], (27771 ^ _780478) ^ [_1293860, _1293862, _1293864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1293860, 27772 ^ [_1293860, _1293862, _1293864])), hAPP(_1293862, 27772 ^ [_1293860, _1293862, _1293864]))), -(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), _1293862), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1293864))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1293860), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1293864))) = 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)), _1293862)), _1293860)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1293864)))], (50501 ^ _780478) ^ [_1802193, _1802195, _1802197, _1802199] : [c_Fun_Obij__betw(_1802193, _1802195, _1802197, _1802199, c_Orderings_Obot__class_Obot(tc_fun(_1802195, tc_HOL_Obool))), -(_1802199 = c_Orderings_Obot__class_Obot(tc_fun(_1802193, tc_HOL_Obool)))], (14891 ^ _780478) ^ [_1047940, _1047942, _1047944, _1047946] : [hBOOL(hAPP(hAPP(c_member(_1047940), _1047942), c_SetInterval_Oord_OatMost(_1047940, _1047944, _1047946))), -(hBOOL(hAPP(hAPP(_1047944, _1047942), _1047946)))], (43181 ^ _780478) ^ [_1641618, _1641620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1641618), _1641620)), -(c_List_Oupto(_1641618, _1641620) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1641618), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1641618), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1641620)))], (44861 ^ _780478) ^ [_1679416, _1679418, _1679420, _1679422, _1679424] : [hAPP(hAPP(c_List_Omap(_1679416, _1679418), _1679420), _1679422) = hAPP(hAPP(c_List_Omap(_1679416, _1679418), _1679420), _1679424), c_Fun_Oinj__on(_1679416, _1679418, _1679420, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1679416, tc_HOL_Obool)), hAPP(c_List_Oset(_1679416), _1679422)), hAPP(c_List_Oset(_1679416), _1679424))), -(_1679422 = _1679424)], (49047 ^ _780478) ^ [_1770594, _1770596] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1770594)), _1770596)), 49051 ^ _780478 : [(49052 ^ _780478) ^ [_1770695] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1770594)), _1770695), _1770596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770594)), _1770695)), 49050 ^ [_1770594, _1770596])))]]], (42526 ^ _780478) ^ [_1627711, _1627713, _1627715, _1627717, _1627719, _1627721] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627711, _1627713)), hAPP(hAPP(c_Product__Type_OPair(_1627711, _1627713), _1627715), _1627717)), hAPP(c_List_Oset(tc_prod(_1627711, _1627713)), hAPP(hAPP(c_List_Ozip(_1627711, _1627713), _1627719), _1627721)))), -(hBOOL(hAPP(hAPP(c_member(_1627713), _1627717), hAPP(c_List_Oset(_1627713), _1627721))))], (42227 ^ _780478) ^ [_1618617, _1618619, _1618621, _1618623] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1618617), tc_List_Olist(_1618617))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1618617), tc_List_Olist(_1618617)), _1618619), _1618621)), c_List_Olexord(_1618617, _1618623))), 42232 ^ _780478 : [(42235 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1618617), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618617)), _1618619)), _1618621) = _1618619)], (42233 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618617)), _1618619)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618617)), _1618621))))]], 42237 ^ _780478 : [(42242 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618617, _1618617)), hAPP(hAPP(c_Product__Type_OPair(_1618617, _1618617), hAPP(hAPP(c_List_Onth(_1618617), _1618619), 42236 ^ [_1618617, _1618619, _1618621, _1618623])), hAPP(hAPP(c_List_Onth(_1618617), _1618621), 42236 ^ [_1618617, _1618619, _1618621, _1618623]))), _1618623)))], (42240 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1618617), 42236 ^ [_1618617, _1618619, _1618621, _1618623]), _1618619) = hAPP(hAPP(c_List_Otake(_1618617), 42236 ^ [_1618617, _1618619, _1618621, _1618623]), _1618621))], (42238 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42236 ^ [_1618617, _1618619, _1618621, _1618623]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618617)), _1618619)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1618617)), _1618621)))))]]], (36686 ^ _780478) ^ [_1477975, _1477977] : [-(_1477975 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1477977, _1477975) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477977), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477975)))], (41971 ^ _780478) ^ [_1611483, _1611485] : [-(c_List_Olistrel(_1611483, c_Transitive__Closure_Ortrancl(_1611483, _1611485)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1611483), c_List_Olistrel1(_1611483, _1611485)))], (11587 ^ _780478) ^ [_983613, _983615, _983617] : [class_Lattices_Oab__semigroup__idem__mult(_983613), -(_983615 = c_Orderings_Obot__class_Obot(tc_fun(_983613, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_983613), _983615)), -(hAPP(c_Finite__Set_Ofold1(_983613, c_Groups_Otimes__class_Otimes(_983613)), hAPP(hAPP(c_Set_Oinsert(_983613), _983617), _983615)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983613), _983617), hAPP(c_Finite__Set_Ofold1(_983613, c_Groups_Otimes__class_Otimes(_983613)), _983615)))], (46196 ^ _780478) ^ [_1710147, _1710149, _1710151, _1710153] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710147)), _1710149))), c_List_Ofoldr(tc_List_Olist(_1710151), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1710151)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1710151))), _1710153, 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(_1710147)), _1710149)), c_List_Ofoldr(tc_List_Olist(_1710151), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1710151)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1710151), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1710151)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1710151)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1710151), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1710151)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1710151), tc_List_Olist(_1710151), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1710151)))), _1710153), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (39480 ^ _780478) ^ [_1547302, _1547304, _1547306] : [-(c_Relation_Orefl__on(_1547302, _1547304, _1547306)), 39484 ^ _780478 : [(39487 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1547302, _1547302, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1547302, tc_fun(_1547302, tc_HOL_Obool), tc_fun(_1547302, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1547302, tc_HOL_Obool), tc_fun(_1547302, tc_HOL_Obool)), _1547302), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1547302)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1547302), c_fconj), hAPP(hAPP(c_COMBC(_1547302, tc_fun(_1547302, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547302)), _1547304)))), hAPP(hAPP(c_COMBC(_1547302, tc_fun(_1547302, tc_HOL_Obool), tc_HOL_Obool), c_member(_1547302)), _1547304))), 39483 ^ [_1547302, _1547304, _1547306]))], (39485 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1547302, _1547302)), 39483 ^ [_1547302, _1547304, _1547306]), _1547306)))]], 39489 ^ _780478 : [(39492 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547302, _1547302)), hAPP(hAPP(c_Product__Type_OPair(_1547302, _1547302), 39488 ^ [_1547302, _1547304, _1547306]), 39488 ^ [_1547302, _1547304, _1547306])), _1547306))], (39490 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1547302), 39488 ^ [_1547302, _1547304, _1547306]), _1547304)))]]], (14090 ^ _780478) ^ [_1032308, _1032310, _1032312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032308), _1032310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032312), _1032308)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032312), _1032310))))], (17867 ^ _780478) ^ [_1113486, _1113488, _1113490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113486), _1113488)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113488), _1113490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113486)), _1113490)))], (7224 ^ _780478) ^ [_900961, _900963, _900965] : [class_Orderings_Oorder(_900961), 7227 ^ _780478 : [(7236 ^ _780478) ^ [] : [-(_900963 = _900965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900961), _900963), _900965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900961), _900965), _900963))], (7228 ^ _780478) ^ [] : [_900963 = _900965, 7231 ^ _780478 : [(7234 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900961), _900965), _900963)))], (7232 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900961), _900963), _900965)))]]]]], (24078 ^ _780478) ^ [_1228435, _1228437, _1228439, _1228441] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228435, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24079 ^ [_1228435, _1228437, _1228439, _1228441])), _1228437) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228435, 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), 24079 ^ [_1228435, _1228437, _1228439, _1228441]), _1228439))), _1228441), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228435, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1228437) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228435, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1228441))], (51487 ^ _780478) ^ [_1823088, _1823090] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823088), _1823090))), -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823088, _1823090))], (51801 ^ _780478) ^ [_1828107, _1828109] : [class_Orderings_Opreorder(_1828107), -(class_Orderings_Opreorder(tc_fun(_1828109, _1828107)))], (40305 ^ _780478) ^ [_1567642, _1567644, _1567646] : [c_Wellfounded_Owf(_1567642, _1567644), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567642, _1567642)), hAPP(hAPP(c_Product__Type_OPair(_1567642, _1567642), hAPP(_1567646, hAPP(c_Nat_OSuc, 40308 ^ [_1567642, _1567644, _1567646]))), hAPP(_1567646, 40308 ^ [_1567642, _1567644, _1567646]))), _1567644))], (46082 ^ _780478) ^ [_1706792, _1706794, _1706796] : [hAPP(c_List_Ofilter(_1706792, _1706794), _1706796) = c_List_Olist_ONil(_1706792), 46085 ^ _780478 : [(46086 ^ _780478) ^ [_1706889] : [hBOOL(hAPP(hAPP(c_member(_1706792), _1706889), hAPP(c_List_Oset(_1706792), _1706796))), hBOOL(hAPP(_1706794, _1706889))]]], (29490 ^ _780478) ^ [_1327978] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327978, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1327978)], (37810 ^ _780478) ^ [_1502766, _1502768, _1502770, _1502772] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1502766, tc_HOL_Obool), tc_fun(_1502766, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1502766, tc_HOL_Obool), tc_fun(_1502766, tc_HOL_Obool)), _1502770), _1502772)), c_Wellfounded_Omax__ext(_1502766, _1502768))), -(c_Wellfounded_Omax__extp(_1502766, hAPP(hAPP(c_COMBC(_1502766, tc_fun(tc_prod(_1502766, _1502766), tc_HOL_Obool), tc_fun(_1502766, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502766, tc_fun(tc_fun(tc_prod(_1502766, _1502766), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1502766, _1502766), tc_HOL_Obool), tc_fun(_1502766, tc_HOL_Obool)), _1502766), c_COMBC(_1502766, tc_fun(tc_prod(_1502766, _1502766), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1502766, tc_prod(_1502766, _1502766)), tc_fun(_1502766, tc_fun(tc_fun(tc_prod(_1502766, _1502766), tc_HOL_Obool), tc_HOL_Obool)), _1502766), hAPP(c_COMBB(tc_prod(_1502766, _1502766), tc_fun(tc_fun(tc_prod(_1502766, _1502766), tc_HOL_Obool), tc_HOL_Obool), _1502766), c_member(tc_prod(_1502766, _1502766)))), c_Product__Type_OPair(_1502766, _1502766)))), _1502768), _1502770, _1502772))], (5887 ^ _780478) ^ [_873957, _873959, _873961] : [_873959 = _873961, -(hBOOL(hAPP(hAPP(c_member(_873957), _873959), hAPP(hAPP(c_Set_Oinsert(_873957), _873961), c_Orderings_Obot__class_Obot(tc_fun(_873957, tc_HOL_Obool))))))], (51875 ^ _780478) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (19488 ^ _780478) ^ [_1145042] : [-(_1145042 = 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)), _1145042)))], (36886 ^ _780478) ^ [_1482166, _1482168, _1482170, _1482172] : [-(hAPP(c_Product__Type_Osnd(_1482166, _1482168), hAPP(hAPP(c_Product__Type_OPair(_1482166, _1482168), _1482170), _1482172)) = _1482172)], (5518 ^ _780478) ^ [_864988, _864990, _864992, _864994, _864996, _864998, _865000, _865002] : [-(c_SetInterval_Oord_OatLeastAtMost(_865002, _864998, _864994, _864990) = c_SetInterval_Oord_OatLeastAtMost(_865000, _864996, _864992, _864988)), _865002 = _865000, _864998 = _864996, _864994 = _864992, _864990 = _864988], (35503 ^ _780478) ^ [_1448979] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1448979)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1448979)))], (19026 ^ _780478) ^ [_1137693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1137693), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (39295 ^ _780478) ^ [_1543367, _1543369, _1543371, _1543373] : [c_Relation_Orefl__on(_1543367, _1543369, _1543371), hBOOL(hAPP(hAPP(c_member(_1543367), _1543373), _1543369)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1543367, _1543367)), hAPP(hAPP(c_Product__Type_OPair(_1543367, _1543367), _1543373), _1543373)), _1543371)))], (24791 ^ _780478) ^ [_1241110, _1241112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1241110), _1241112)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1241110), _1241112) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29249 ^ _780478) ^ [_1323445, _1323447, _1323449, _1323451] : [class_Divides_Osemiring__div(_1323445), -(c_Divides_Odiv__class_Omod(_1323445, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323445), c_Divides_Odiv__class_Omod(_1323445, _1323447, _1323449)), _1323451), _1323449) = c_Divides_Odiv__class_Omod(_1323445, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323445), _1323447), _1323451), _1323449))], (11863 ^ _780478) ^ [_988976, _988978, _988980] : [_988978 = _988980, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_988976, tc_HOL_Obool)), _988978) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_988976, tc_HOL_Obool)), _988980))], (24147 ^ _780478) ^ [_1230090] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230090) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32506 ^ _780478) ^ [_1394344, _1394346, _1394348, _1394350] : [class_Fields_Olinordered__field__inverse__zero(_1394344), class_Int_Onumber(_1394344), 32513 ^ _780478 : [(32514 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1394344), _1394346), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348))), _1394350)), 32517 ^ _780478 : [(32524 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), c_Groups_Ozero__class_Ozero(_1394344)), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348)))), 32527 ^ _780478 : [(32534 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348)), c_Groups_Ozero__class_Ozero(_1394344)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), c_Groups_Ozero__class_Ozero(_1394344)), _1394350)))], (32528 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348)), c_Groups_Ozero__class_Ozero(_1394344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394344), _1394350), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348))), _1394346)))]]], (32518 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), c_Groups_Ozero__class_Ozero(_1394344)), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), _1394346), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394344), _1394350), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348)))))]]], (32540 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1394344), _1394346), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348))), _1394350))), 32543 ^ _780478 : [(32546 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), _1394346), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394344), _1394350), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348))))], (32544 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), c_Groups_Ozero__class_Ozero(_1394344)), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348))))]], 32547 ^ _780478 : [(32550 ^ _780478) ^ [] : [32551 ^ _780478 : [(32554 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394344), _1394350), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348))), _1394346))], (32552 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348)), c_Groups_Ozero__class_Ozero(_1394344))))]], 32555 ^ _780478 : [(32558 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), c_Groups_Ozero__class_Ozero(_1394344)), _1394350))], (32556 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348)), c_Groups_Ozero__class_Ozero(_1394344)))]]], (32548 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394344), c_Groups_Ozero__class_Ozero(_1394344)), hAPP(c_Int_Onumber__class_Onumber__of(_1394344), _1394348)))]]]]], (34635 ^ _780478) ^ [_1433448, _1433450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433448), _1433450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1433448)), c_Int_OBit0(_1433450))))], (9258 ^ _780478) ^ [_939135, _939137, _939139] : [class_Orderings_Oorder(_939135), 9261 ^ _780478 : [(9270 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939135), _939137), _939139))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939135), _939137), _939139)), -(_939137 = _939139)], (9262 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939135), _939137), _939139)), 9265 ^ _780478 : [(9268 ^ _780478) ^ [] : [_939137 = _939139], (9266 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939135), _939137), _939139)))]]]]], (25673 ^ _780478) ^ [_1256796, _1256798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256796)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1256796), _1256798)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1256796)), hAPP(c_Int_Onat, _1256798)))], (51463 ^ _780478) ^ [_1822686, _1822688] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822686), _1822688)), -(c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat, hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822688, _1822686) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (45067 ^ _780478) ^ [_1683763, _1683765, _1683767] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1683763), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1683765), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1683765)), _1683767)))), -(hBOOL(hAPP(hAPP(c_member(_1683765), hAPP(c_Random_Opick(_1683765, _1683767), _1683763)), hAPP(c_List_Oset(_1683765), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1683765), _1683765), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1683765)), _1683767)))))], (42581 ^ _780478) ^ [_1628992, _1628994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628992), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1628994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1628994), _1628992)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1628994))))], (7595 ^ _780478) ^ [_908286, _908288, _908290, _908292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908286, tc_HOL_Obool)), _908288), _908290)), hBOOL(hAPP(hAPP(c_member(_908286), _908292), _908288)), -(hBOOL(hAPP(hAPP(c_member(_908286), _908292), _908290)))], (8002 ^ _780478) ^ [_916686, _916688, _916690, _916692, _916694, _916696, _916698] : [c_Nitpick_Ofold__graph_H(_916686, _916688, _916690, _916692, _916694, hAPP(hAPP(_916690, _916696), _916698)), 8007 ^ _780478 : [(8010 ^ _780478) ^ [] : [-(hAPP(hAPP(_916690, _916696), _916698) = _916692)], (8008 ^ _780478) ^ [] : [-(_916694 = c_Orderings_Obot__class_Obot(tc_fun(_916686, tc_HOL_Obool)))]], 8013 ^ _780478 : [(8018 ^ _780478) ^ [] : [-(c_Nitpick_Ofold__graph_H(_916686, _916688, _916690, _916692, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916686, tc_HOL_Obool)), _916694), hAPP(hAPP(c_Set_Oinsert(_916686), 8011 ^ [_916686, _916688, _916690, _916692, _916694, _916696, _916698]), c_Orderings_Obot__class_Obot(tc_fun(_916686, tc_HOL_Obool)))), 8012 ^ [_916686, _916688, _916690, _916692, _916694, _916696, _916698]))], (8016 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916686), 8011 ^ [_916686, _916688, _916690, _916692, _916694, _916696, _916698]), _916694)))], (8014 ^ _780478) ^ [] : [-(hAPP(hAPP(_916690, _916696), _916698) = hAPP(hAPP(_916690, 8011 ^ [_916686, _916688, _916690, _916692, _916694, _916696, _916698]), 8012 ^ [_916686, _916688, _916690, _916692, _916694, _916696, _916698]))]]], (29057 ^ _780478) ^ [_1319362, _1319364] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1319362), hAPP(c_Nat_OSuc, _1319364)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1319364), 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)), _1319364)), _1319362))], (36341 ^ _780478) ^ [_1471721, _1471723, _1471725, _1471727, _1471729, _1471731, _1471733, _1471735] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471721, _1471723, _1471725), _1471727), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471729, _1471731, tc_prod(_1471721, _1471723)), _1471733), _1471735)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471729, _1471731, _1471725), hAPP(hAPP(c_COMBB(tc_fun(_1471731, tc_prod(_1471721, _1471723)), tc_fun(_1471731, _1471725), _1471729), hAPP(c_COMBB(tc_prod(_1471721, _1471723), _1471725, _1471731), hAPP(c_Product__Type_Oprod_Oprod__case(_1471721, _1471723, _1471725), _1471727))), _1471733)), _1471735))], (30107 ^ _780478) ^ [_1339158, _1339160, _1339162, _1339164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1339158)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1339160), _1339162)), -(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), _1339162), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1339164, _1339158))), _1339160)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1339162), _1339158))))], (49264 ^ _780478) ^ [_1775661, _1775663] : [c_Relation_Otrans(_1775661, _1775663), -(c_Relation_Otrans(tc_List_Olist(_1775661), c_List_Olistrel(_1775661, _1775663)))], (21304 ^ _780478) ^ [_1176160, _1176162] : [_1176160 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1176160), _1176162) = _1176162)], (17570 ^ _780478) ^ [_1107008, _1107010, _1107012, _1107014, _1107016] : [_1107008 = c_Orderings_Obot__class_Obot(tc_fun(_1107010, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1107010, tc_fun(_1107012, tc_HOL_Obool)), _1107008), hAPP(hAPP(c_COMBC(_1107010, tc_fun(_1107012, tc_HOL_Obool), tc_fun(_1107012, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1107012, tc_HOL_Obool), tc_fun(tc_fun(_1107012, tc_HOL_Obool), tc_fun(_1107012, tc_HOL_Obool)), _1107010), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1107012, tc_HOL_Obool))), _1107014)), _1107016)) = c_Orderings_Obot__class_Obot(tc_fun(_1107012, tc_HOL_Obool)))], (46226 ^ _780478) ^ [_1710964, _1710966, _1710968] : [-(c_List_Osublist(_1710964, _1710966, _1710968) = hAPP(hAPP(c_List_Omap(tc_prod(_1710964, tc_Nat_Onat), _1710964), c_Product__Type_Ofst(_1710964, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1710964, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1710964, 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(_1710964, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1710964, tc_Nat_Onat))), _1710968)), hAPP(hAPP(c_List_Ozip(_1710964, tc_Nat_Onat), _1710966), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710964)), _1710966))))))], (47047 ^ _780478) ^ [_1726879, _1726881, _1726883] : [_1726881 = _1726883, -(hAPP(c_List_Orev(_1726879), _1726881) = hAPP(c_List_Orev(_1726879), _1726883))], (34137 ^ _780478) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (13188 ^ _780478) ^ [_1014606, _1014608] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1014606, tc_HOL_Obool)), _1014608), c_Orderings_Otop__class_Otop(tc_fun(_1014606, tc_HOL_Obool)))))], (29566 ^ _780478) ^ [_1329522, _1329524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329522)), -(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, _1329524, _1329522))))], (34679 ^ _780478) ^ [_1434242, _1434244] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1434242)), _1434244) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1434242), _1434244))), _1434244))], (41130 ^ _780478) ^ [_1587646, _1587648] : [-(c_Transitive__Closure_Ortrancl(_1587646, _1587648) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587646, _1587646), tc_HOL_Obool)), c_Relation_OId(_1587646)), hAPP(hAPP(c_Relation_Orel__comp(_1587646, _1587646, _1587646), c_Transitive__Closure_Ortrancl(_1587646, _1587648)), _1587648)))], (28736 ^ _780478) ^ [_1312569, _1312571, _1312573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1312569)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1312571), _1312573)), 28743 ^ _780478 : [(28744 ^ _780478) ^ [_1312765] : [28746 ^ _780478 : [(28752 ^ _780478) ^ [] : [-(_1312765 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28748 ^ [_1312569, _1312571, _1312573, _1312765]), 28745 ^ [_1312569, _1312571, _1312573, _1312765]))], (28750 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28748 ^ [_1312569, _1312571, _1312573, _1312765]), _1312573)))], (28747 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28745 ^ [_1312569, _1312571, _1312573, _1312765]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1312569))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1312765), _1312571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1312765), _1312569)), _1312571)))]]], (29357 ^ _780478) ^ [_1325581, _1325583, _1325585, _1325587] : [class_Divides_Osemiring__div(_1325581), -(c_Divides_Odiv__class_Omod(_1325581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325581), _1325583), _1325585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325581), _1325583), _1325587)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325581), _1325583), c_Divides_Odiv__class_Omod(_1325581, _1325585, _1325587)))], (46147 ^ _780478) ^ [_1708325, _1708327] : [c_List_Otranspose(_1708325, _1708327) = c_List_Olist_ONil(tc_List_Olist(_1708325)), 46150 ^ _780478 : [(46151 ^ _780478) ^ [_1708420] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1708325)), _1708420), hAPP(c_List_Oset(tc_List_Olist(_1708325)), _1708327))), -(_1708420 = c_List_Olist_ONil(_1708325))]]], (33995 ^ _780478) ^ [_1422410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1422410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1422410))))], (51711 ^ _780478) ^ [_1826795, _1826797] : [class_Rings_Ocomm__semiring__1(_1826795), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826795), _1826797), _1826797)))], (34551 ^ _780478) ^ [_1431941, _1431943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431941), _1431943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1431941)), c_Int_OBit0(_1431943))))], (46557 ^ _780478) ^ [_1717147, _1717149, _1717151, _1717153] : [class_Orderings_Olinorder(_1717147), 46560 ^ _780478 : [(46569 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1717147, hAPP(hAPP(c_List_Olist_OCons(_1717147), _1717149), hAPP(hAPP(c_List_Olist_OCons(_1717147), _1717151), _1717153)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1717147), _1717149), _1717151)), c_List_Olinorder__class_Osorted(_1717147, hAPP(hAPP(c_List_Olist_OCons(_1717147), _1717151), _1717153))], (46561 ^ _780478) ^ [] : [c_List_Olinorder__class_Osorted(_1717147, hAPP(hAPP(c_List_Olist_OCons(_1717147), _1717149), hAPP(hAPP(c_List_Olist_OCons(_1717147), _1717151), _1717153))), 46564 ^ _780478 : [(46567 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1717147, hAPP(hAPP(c_List_Olist_OCons(_1717147), _1717151), _1717153)))], (46565 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1717147), _1717149), _1717151)))]]]]], (48064 ^ _780478) ^ [_1749297, _1749299, _1749301] : [c_List_Olist__ex(_1749297, _1749299, _1749301), 48068 ^ _780478 : [(48071 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1749299, 48067 ^ [_1749297, _1749299, _1749301])))], (48069 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1749297), 48067 ^ [_1749297, _1749299, _1749301]), hAPP(c_List_Oset(_1749297), _1749301))))]]], (44462 ^ _780478) ^ [_1670772, _1670774, _1670776, _1670778, _1670780] : [class_Orderings_Olinorder(_1670772), -(hBOOL(hAPP(hAPP(c_member(_1670772), hAPP(_1670774, _1670776)), hAPP(c_Set_Oimage(_1670778, _1670772, _1670774), hAPP(c_List_Oset(_1670778), _1670780))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1670778, _1670772, _1670774, _1670776, _1670780) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1670778, _1670772, _1670774), _1670776), _1670780))], (17476 ^ _780478) ^ [_1104996, _1104998, _1105000, _1105002, _1105004] : [-(_1104996 = c_Orderings_Obot__class_Obot(tc_fun(_1104998, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1105000), _1105002), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104998, tc_fun(_1105000, tc_HOL_Obool)), _1104996), _1105004)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104998, tc_fun(_1105000, tc_HOL_Obool)), _1104996), hAPP(hAPP(c_COMBB(tc_fun(_1105000, tc_HOL_Obool), tc_fun(_1105000, tc_HOL_Obool), _1104998), hAPP(c_Set_Oinsert(_1105000), _1105002)), _1105004)))], (33074 ^ _780478) ^ [_1405547] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405547) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1405547))], (48511 ^ _780478) ^ [_1758684, _1758686, _1758688, _1758690] : [-(c_Predicate_Oconversep(_1758684, _1758686, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1758684, tc_fun(_1758686, tc_HOL_Obool))), _1758688), _1758690)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1758686, tc_fun(_1758684, tc_HOL_Obool))), c_Predicate_Oconversep(_1758684, _1758686, _1758688)), c_Predicate_Oconversep(_1758684, _1758686, _1758690)))], (16260 ^ _780478) ^ [_1075741, _1075743, _1075745, _1075747] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075741, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1075741, tc_fun(_1075741, tc_HOL_Obool), tc_HOL_Obool), c_member(_1075741)), _1075743)), hAPP(hAPP(c_COMBC(_1075741, tc_fun(_1075741, tc_HOL_Obool), tc_HOL_Obool), c_member(_1075741)), _1075745)), _1075747)), -(hBOOL(hAPP(hAPP(c_member(_1075741), _1075747), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075741, tc_HOL_Obool)), _1075743), _1075745))))], (21825 ^ _780478) ^ [_1185683, _1185685, _1185687] : [-(hBOOL(hAPP(_1185683, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1185685), _1185687)))), 21828 ^ _780478 : [(21831 ^ _780478) ^ [] : [hBOOL(hAPP(_1185683, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21829 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185685), _1185687)))]], 21833 ^ _780478 : [(21836 ^ _780478) ^ [] : [hBOOL(hAPP(_1185683, 21832 ^ [_1185683, _1185685, _1185687]))], (21834 ^ _780478) ^ [] : [-(_1185685 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1185687), 21832 ^ [_1185683, _1185685, _1185687]))]]], (39632 ^ _780478) ^ [_1551997, _1551999, _1552001, _1552003] : [c_Finite__Set_Ofun__left__comm__idem(_1551997, _1551999, _1552001), -(hAPP(c_Fun_Ocomp(_1551999, _1551999, _1551999, hAPP(_1552001, _1552003)), hAPP(_1552001, _1552003)) = hAPP(_1552001, _1552003))], (41832 ^ _780478) ^ [_1607137, _1607139, _1607141, _1607143, _1607145, _1607147] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607137, _1607137)), hAPP(hAPP(c_Product__Type_OPair(_1607137, _1607137), _1607139), _1607141)), c_Transitive__Closure_Ortrancl(_1607137, _1607143))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607137), tc_List_Olist(_1607137))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607137), tc_List_Olist(_1607137)), _1607145), _1607147)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1607137), c_List_Olistrel1(_1607137, _1607143)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607137), tc_List_Olist(_1607137))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607137), tc_List_Olist(_1607137)), hAPP(hAPP(c_List_Olist_OCons(_1607137), _1607139), _1607145)), hAPP(hAPP(c_List_Olist_OCons(_1607137), _1607141), _1607147))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1607137), c_List_Olistrel1(_1607137, _1607143)))))], (7758 ^ _780478) ^ [_911733, _911735, _911737, _911739] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_911733), hAPP(c_Set_Oimage(_911735, _911733, _911737), _911739))), c_Fun_Oinj__on(_911735, _911733, _911737, _911739), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_911735), _911739)))], (29047 ^ _780478) ^ [_1319041, _1319043, _1319045] : [-(hAPP(c_Set_OPow(_1319041), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319041, tc_HOL_Obool)), _1319043), _1319045)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1319041, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1319041), _1319043)), hAPP(c_Set_OPow(_1319041), _1319045)))], (18043 ^ _780478) ^ [_1116324, _1116326, _1116328] : [_1116326 = _1116328, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1116324)), _1116326) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1116324)), _1116328))], (43451 ^ _780478) ^ [_1647767, _1647769, _1647771, _1647773] : [hAPP(hAPP(c_List_Oappend(_1647767), _1647769), _1647771) = hAPP(hAPP(c_List_Oappend(_1647767), _1647773), _1647771), -(_1647769 = _1647773)], (49131 ^ _780478) ^ [_1772441, _1772443, _1772445, _1772447] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1772441), _1772443), _1772445), _1772447) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1772441)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1772441), _1772443)))], (12604 ^ _780478) ^ [_1003211, _1003213, _1003215, _1003217] : [12618 ^ _780478 : [(12621 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1003217, 12617 ^ [_1003211, _1003213, _1003215, _1003217])))], (12619 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1003211), 12617 ^ [_1003211, _1003213, _1003215, _1003217]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003211, tc_HOL_Obool)), _1003213), _1003215))))]], 12605 ^ _780478 : [(12612 ^ _780478) ^ [_1003420] : [hBOOL(hAPP(hAPP(c_member(_1003211), _1003420), _1003215)), hBOOL(hAPP(_1003217, _1003420))], (12606 ^ _780478) ^ [_1003324] : [hBOOL(hAPP(hAPP(c_member(_1003211), _1003324), _1003213)), hBOOL(hAPP(_1003217, _1003324))]]], (38828 ^ _780478) ^ [_1530425, _1530427, _1530429, _1530431, _1530433] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530425, _1530427), _1530429), hAPP(hAPP(c_COMBS(_1530425, tc_fun(_1530427, tc_HOL_Obool), tc_fun(_1530427, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530427, tc_HOL_Obool), tc_fun(tc_fun(_1530427, tc_HOL_Obool), tc_fun(_1530427, tc_HOL_Obool)), _1530425), c_Groups_Ominus__class_Ominus(tc_fun(_1530427, tc_HOL_Obool))), _1530431)), _1530433)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1530425, _1530427), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530425, _1530427), _1530429), _1530431)), hAPP(hAPP(c_Product__Type_OSigma(_1530425, _1530427), _1530429), _1530433)))], (49857 ^ _780478) ^ [_1788290, _1788292] : [-(c_Equiv__Relations_Opart__equivp(_1788290, _1788292)), 49860 ^ _780478 : [(49861 ^ _780478) ^ [_1788367] : [hBOOL(hAPP(hAPP(_1788292, _1788367), _1788367))]], c_Predicate_Osymp(_1788290, _1788292), c_Predicate_Otransp(_1788290, _1788292)], (14307 ^ _780478) ^ [_1036005, _1036007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036005), _1036007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036005), _1036007)))], (49596 ^ _780478) ^ [_1783440, _1783442] : [c_Relation_Oantisym(_1783440, _1783442), 49599 ^ _780478 : [(49600 ^ _780478) ^ [_1783552, _1783554] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1783440, _1783440)), hAPP(hAPP(c_Product__Type_OPair(_1783440, _1783440), _1783554), _1783552)), _1783442)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1783440, _1783440)), hAPP(hAPP(c_Product__Type_OPair(_1783440, _1783440), _1783552), _1783554)), _1783442)), -(_1783554 = _1783552)]]], (43001 ^ _780478) ^ [_1638276, _1638278, _1638280] : [hAPP(hAPP(c_List_Olist_OCons(_1638276), _1638278), _1638280) = c_List_Olist_ONil(_1638276)], (27024 ^ _780478) ^ [_1281236, _1281238, _1281240, _1281242] : [class_Fields_Olinordered__field(_1281236), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281236), _1281238), _1281240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281236), c_Groups_Ozero__class_Ozero(_1281236)), _1281242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281236), c_Groups_Ozero__class_Ozero(_1281236)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281236), _1281240), _1281238))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281236), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281236), _1281242), _1281240)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281236), _1281242), _1281238))))], (52081 ^ _780478) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (35888 ^ _780478) ^ [_1461776, _1461778, _1461780, _1461782, _1461784] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1461780, _1461776)), hAPP(hAPP(c_Product__Type_OPair(_1461780, _1461776), _1461784), _1461778)), _1461782)), -(hBOOL(hAPP(hAPP(c_member(_1461776), _1461778), hAPP(c_Relation_OImage(_1461780, _1461776, _1461782), hAPP(hAPP(c_Set_Oinsert(_1461780), _1461784), c_Orderings_Obot__class_Obot(tc_fun(_1461780, tc_HOL_Obool)))))))], (48850 ^ _780478) ^ [_1766016, _1766018, _1766020, _1766022, _1766024] : [48852 ^ _780478 : [(48855 ^ _780478) ^ [] : [c_Relation_Orefl__on(_1766020, hAPP(_1766022, 48851 ^ [_1766016, _1766018, _1766020, _1766022, _1766024]), hAPP(_1766024, 48851 ^ [_1766016, _1766018, _1766020, _1766022, _1766024]))], (48853 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766016), 48851 ^ [_1766016, _1766018, _1766020, _1766022, _1766024]), _1766018)))]], -(c_Relation_Orefl__on(_1766020, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1766016, tc_fun(_1766020, tc_HOL_Obool)), _1766018), _1766022), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1766016, tc_fun(tc_prod(_1766020, _1766020), tc_HOL_Obool)), _1766018), _1766024)))], (52233 ^ _780478) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (5869 ^ _780478) ^ [_873604, _873606, _873608, _873610] : [-(_873604 = c_Orderings_Obot__class_Obot(tc_fun(_873606, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_873606, _873608, hAPP(c_COMBK(_873608, _873606), _873610)), _873604) = hAPP(hAPP(c_Set_Oinsert(_873608), _873610), c_Orderings_Obot__class_Obot(tc_fun(_873608, tc_HOL_Obool))))], (45759 ^ _780478) ^ [_1699339, _1699341] : [-(c_List_Oremdups(_1699339, c_List_Oremdups(_1699339, _1699341)) = c_List_Oremdups(_1699339, _1699341))], (29542 ^ _780478) ^ [_1329129, _1329131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1329129), 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, _1329131, _1329129)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24967 ^ _780478) ^ [_1244073, _1244075, _1244077] : [-(hBOOL(hAPP(_1244073, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1244075), _1244077)))), 24970 ^ _780478 : [(24973 ^ _780478) ^ [] : [hBOOL(hAPP(_1244073, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24971 ^ _780478) ^ [] : [-(_1244077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 24974 ^ _780478 : [(24979 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24977 ^ [_1244073, _1244075, _1244077]), _1244077)))], (24981 ^ _780478) ^ [] : [-(_1244075 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1244077), 24976 ^ [_1244073, _1244075, _1244077])), 24977 ^ [_1244073, _1244075, _1244077]))], (24983 ^ _780478) ^ [] : [hBOOL(hAPP(_1244073, 24976 ^ [_1244073, _1244075, _1244077]))], (24975 ^ _780478) ^ [] : [_1244077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (15834 ^ _780478) ^ [_1067006, _1067008, _1067010] : [class_Lattices_Osemilattice__inf(_1067006), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067006), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067006), _1067008), _1067010)), _1067010)))], (12698 ^ _780478) ^ [_1005129, _1005131] : [class_Lattices_Osemilattice__sup(_1005129), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005129), _1005131), _1005131) = _1005131)], (39074 ^ _780478) ^ [_1538003, _1538005, _1538007, _1538009, _1538011, _1538013] : [class_Groups_Ocomm__monoid__add(_1538003), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538005), _1538007)), 39084 ^ _780478 : [(39087 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538009), hAPP(_1538011, 39083 ^ [_1538003, _1538005, _1538007, _1538009, _1538011, _1538013])))], (39085 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538005), 39083 ^ [_1538003, _1538005, _1538007, _1538009, _1538011, _1538013]), _1538007)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538005, _1538003), hAPP(hAPP(c_COMBS(_1538005, tc_fun(_1538009, tc_HOL_Obool), _1538003), hAPP(hAPP(c_COMBB(tc_fun(_1538009, _1538003), tc_fun(tc_fun(_1538009, tc_HOL_Obool), _1538003), _1538005), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538009, _1538003)), _1538013)), _1538011)), _1538007) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1538005, _1538009), _1538003), hAPP(c_Product__Type_Oprod_Oprod__case(_1538005, _1538009, _1538003), _1538013)), hAPP(hAPP(c_Product__Type_OSigma(_1538005, _1538009), _1538007), _1538011)))], (16344 ^ _780478) ^ [_1077685, _1077687, _1077689, _1077691] : [-(hBOOL(hAPP(hAPP(c_member(_1077685), _1077687), _1077689))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077685, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1077685), _1077687), _1077691)), _1077689) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077685, tc_HOL_Obool)), _1077691), _1077689))], (19160 ^ _780478) ^ [_1140132, _1140134] : [class_Groups_Olinordered__ab__group__add(_1140132), 19163 ^ _780478 : [(19170 ^ _780478) ^ [] : [_1140134 = c_Groups_Ozero__class_Ozero(_1140132), -(c_Groups_Ozero__class_Ozero(_1140132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140132), _1140134), _1140134))], (19164 ^ _780478) ^ [] : [c_Groups_Ozero__class_Ozero(_1140132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140132), _1140134), _1140134), -(_1140134 = c_Groups_Ozero__class_Ozero(_1140132))]]], (17893 ^ _780478) ^ [_1113881, _1113883] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113881), _1113883))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113881), hAPP(c_Nat_OSuc, _1113883))), -(_1113883 = _1113881)], (48653 ^ _780478) ^ [_1761975, _1761977, _1761979, _1761981] : [-(hBOOL(hAPP(_1761975, _1761977))), -(hAPP(c_List_Ofilter(_1761979, _1761975), c_List_Oreplicate(_1761979, _1761981, _1761977)) = c_List_Olist_ONil(_1761979))], (23749 ^ _780478) ^ [_1222077, _1222079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222077)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222079))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1222077), _1222079)))], (10815 ^ _780478) ^ [_969102, _969104, _969106, _969108] : [class_Orderings_Olinorder(_969102), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969102), _969104), _969106)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969102), _969104), hAPP(hAPP(c_Orderings_Oord__class_Omax(_969102), _969106), _969108))))], (49238 ^ _780478) ^ [_1775276] : [-(c_Relation_Otrans(_1775276, c_Relation_OId(_1775276)))], (30665 ^ _780478) ^ [_1349862, _1349864] : [class_Rings_Olinordered__idom(_1349862), -(hAPP(c_Groups_Oabs__class_Oabs(_1349862), _1349864) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349862), _1349864), c_Groups_Osgn__class_Osgn(_1349862, _1349864)))], (18375 ^ _780478) ^ [_1124207, _1124209] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124207), _1124209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1124207)), _1124209)))], (5542 ^ _780478) ^ [_865374, _865376] : [_865376 = _865374, -(c_Divides_Odiv__class_Odiv(_865376) = c_Divides_Odiv__class_Odiv(_865374))], (23747 ^ _780478) ^ [_1222016, _1222018] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222016)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222018)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1222016), _1222018)))], (39159 ^ _780478) ^ [_1540269, _1540271] : [-(c_Product__Type_Omap__pair(_1540269, _1540269, _1540271, _1540271, c_Fun_Oid(_1540269), c_Fun_Oid(_1540271)) = c_Fun_Oid(tc_prod(_1540269, _1540271)))], (47079 ^ _780478) ^ [_1727627, _1727629] : [-(_1727627 = c_List_Olist_ONil(_1727629)), -(hAPP(c_List_Ohd(_1727629), hAPP(c_List_Orev(_1727629), _1727627)) = c_List_Olast(_1727629, _1727627))], (32128 ^ _780478) ^ [_1387256, _1387258, _1387260] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_1387256, _1387258, _1387260)], (51391 ^ _780478) ^ [_1821405, _1821407] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821405, _1821407), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821405), _1821407)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821407), _1821405)))], (50303 ^ _780478) ^ [_1798074, _1798076, _1798078] : [c_Fun_Obij__betw(_1798074, _1798076, _1798078, c_Orderings_Otop__class_Otop(tc_fun(_1798074, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1798076, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1798076, _1798074, c_Orderings_Otop__class_Otop(tc_fun(_1798076, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1798074, _1798076, c_Orderings_Otop__class_Otop(tc_fun(_1798074, tc_HOL_Obool)), _1798078)) = _1798078)], (33841 ^ _780478) ^ [_1419756, _1419758, _1419760] : [class_Int_Onumber__ring(_1419756), 33844 ^ _780478 : [(33851 ^ _780478) ^ [] : [-(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), _1419758)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1419756), hAPP(c_Int_Onumber__class_Onumber__of(_1419756), _1419760)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1419758))) = c_Groups_Oone__class_Oone(_1419756))], (33845 ^ _780478) ^ [] : [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), _1419758))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1419756), hAPP(c_Int_Onumber__class_Onumber__of(_1419756), _1419760)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1419758))) = hAPP(hAPP(c_HOL_OLet(_1419756, _1419756), hAPP(hAPP(c_Power_Opower__class_Opower(_1419756), hAPP(c_Int_Onumber__class_Onumber__of(_1419756), _1419760)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1419758))), hAPP(hAPP(c_COMBS(_1419756, _1419756, _1419756), hAPP(hAPP(c_COMBB(_1419756, tc_fun(_1419756, _1419756), _1419756), c_Groups_Otimes__class_Otimes(_1419756)), hAPP(c_Groups_Otimes__class_Otimes(_1419756), hAPP(c_Int_Onumber__class_Onumber__of(_1419756), _1419760)))), c_COMBI(_1419756))))]]], (41077 ^ _780478) ^ [_1586364, _1586366] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586364, _1586364), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1586364, _1586366)), c_Relation_OId(_1586364)) = c_Transitive__Closure_Ortrancl(_1586364, _1586366))], (1554 ^ _780478) ^ [_802767, _802769] : [-(class_Groups_Oordered__comm__monoid__add(_802767)), _802769 = _802767, class_Groups_Oordered__comm__monoid__add(_802769)], (12281 ^ _780478) ^ [_996780, _996782, _996784] : [class_Lattices_Oab__semigroup__idem__mult(_996780), hAPP(_996782, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996780), 12286 ^ [_996780, _996782, _996784]), 12287 ^ [_996780, _996782, _996784])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996780), hAPP(_996782, 12286 ^ [_996780, _996782, _996784])), hAPP(_996782, 12287 ^ [_996780, _996782, _996784])), hBOOL(hAPP(c_Finite__Set_Ofinite(_996780), _996784)), -(_996784 = c_Orderings_Obot__class_Obot(tc_fun(_996780, tc_HOL_Obool))), -(hAPP(_996782, hAPP(c_Finite__Set_Ofold1(_996780, c_Groups_Otimes__class_Otimes(_996780)), _996784)) = hAPP(c_Finite__Set_Ofold1(_996780, c_Groups_Otimes__class_Otimes(_996780)), hAPP(c_Set_Oimage(_996780, _996780, _996782), _996784)))], (41844 ^ _780478) ^ [_1607558, _1607560, _1607562, _1607564] : [hBOOL(hAPP(hAPP(c_member(_1607558), _1607560), c_Wellfounded_Oacc(_1607558, _1607562))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607558)), _1607564), c_Wellfounded_Oacc(tc_List_Olist(_1607558), c_List_Olistrel1(_1607558, _1607562)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607558)), hAPP(hAPP(c_List_Olist_OCons(_1607558), _1607560), _1607564)), c_Wellfounded_Oacc(tc_List_Olist(_1607558), c_List_Olistrel1(_1607558, _1607562)))))], (25707 ^ _780478) ^ [_1257405, _1257407, _1257409, _1257411] : [class_Fields_Ofield(_1257405), -(_1257407 = c_Groups_Ozero__class_Ozero(_1257405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1257409), _1257411)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1257405), _1257407), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1257411), _1257409)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1257405), hAPP(hAPP(c_Power_Opower__class_Opower(_1257405), _1257407), _1257411)), hAPP(hAPP(c_Power_Opower__class_Opower(_1257405), _1257407), _1257409)))], (34581 ^ _780478) ^ [_1432541] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1432541)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432541))))], (30302 ^ _780478) ^ [_1342647, _1342649, _1342651] : [class_Rings_Olinordered__idom(_1342647), -(hAPP(c_Groups_Oabs__class_Oabs(_1342647), hAPP(hAPP(c_Power_Opower__class_Opower(_1342647), _1342649), _1342651)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1342647), hAPP(c_Groups_Oabs__class_Oabs(_1342647), _1342649)), _1342651))], (2060 ^ _780478) ^ [_810409, _810411, _810413, _810415] : [-(c_Orderings_Oord_Omin(_810415, _810411) = c_Orderings_Oord_Omin(_810413, _810409)), _810415 = _810413, _810411 = _810409], (17995 ^ _780478) ^ [_1115502, _1115504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115502), _1115504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115502)), hAPP(c_Nat_OSuc, _1115504))))], (40490 ^ _780478) ^ [_1572097, _1572099, _1572101, _1572103, _1572105] : [-(_1572097 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1572099, _1572101, _1572097, _1572103), _1572105) = hAPP(hAPP(c_Product__Type_Oscomp(_1572101, _1572099, _1572101, tc_prod(_1572099, _1572101)), hAPP(_1572103, _1572105)), c_Random_Oiterate(_1572099, _1572101, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1572097), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1572103)))], (38843 ^ _780478) ^ [_1530794, _1530796] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530794, _1530796), c_Orderings_Otop__class_Otop(tc_fun(_1530794, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1530796, tc_HOL_Obool), _1530794), c_Orderings_Otop__class_Otop(tc_fun(_1530796, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1530794, _1530796), tc_HOL_Obool)))], (24141 ^ _780478) ^ [_1229982, _1229984] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_1229982, _1229984)) = 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(_1229982)), c_Com_Ocom_Ocom__size(_1229984))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42993 ^ _780478) ^ [_1638145, _1638147, _1638149] : [-(_1638145 = c_List_Olist_ONil(_1638147)), -(c_List_Obutlast(_1638147, hAPP(hAPP(c_List_Olist_OCons(_1638147), _1638149), _1638145)) = hAPP(hAPP(c_List_Olist_OCons(_1638147), _1638149), c_List_Obutlast(_1638147, _1638145)))], (5428 ^ _780478) ^ [_863505, _863507, _863509, _863511] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_863511, _863507) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_863509, _863505)), _863511 = _863509, _863507 = _863505], (23851 ^ _780478) ^ [_1224002, _1224004, _1224006, _1224008] : [class_Groups_Ocomm__monoid__add(_1224002), 23854 ^ _780478 : [(23861 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1224004), _1224006))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1224002), _1224008), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1224006), hAPP(c_Nat_OSuc, _1224004))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1224002), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1224002), _1224008), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1224006), _1224004))), hAPP(_1224008, _1224004)))], (23855 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1224004), _1224006)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1224002), _1224008), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1224006), hAPP(c_Nat_OSuc, _1224004))) = c_Groups_Ozero__class_Ozero(_1224002))]]], (3186 ^ _780478) ^ [_827822, _827824, _827826, _827828] : [-(c_Big__Operators_Olinorder__class_OMax(_827828, _827824) = c_Big__Operators_Olinorder__class_OMax(_827826, _827822)), _827828 = _827826, _827824 = _827822], (46264 ^ _780478) ^ [_1711919, _1711921] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711919), _1711921))), -(c_List_Oupt(_1711919, _1711921) = c_List_Olist_ONil(tc_Nat_Onat))], (50987 ^ _780478) ^ [_1813794, _1813796] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813794), _1813796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1813796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1813794), _1813796)))], (36922 ^ _780478) ^ [_1482795, _1482797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1482797), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1482795, _1482797) = 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), _1482795), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1482797)))))], (38354 ^ _780478) ^ [_1517258, _1517260, _1517262] : [c_Wellfounded_Owf(_1517258, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517258, _1517258), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517258, _1517258), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517258, _1517258, _1517258), _1517260), _1517260)), hAPP(hAPP(c_Relation_Orel__comp(_1517258, _1517258, _1517258), _1517262), _1517260))), _1517262)), -(c_Wellfounded_Owf(_1517258, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517258, _1517258), tc_HOL_Obool)), _1517260), _1517262)))], (16314 ^ _780478) ^ [_1077113, _1077115, _1077117, _1077119] : [hBOOL(hAPP(hAPP(c_member(_1077113), _1077115), _1077117)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077113, tc_HOL_Obool)), _1077117), hAPP(hAPP(c_Set_Oinsert(_1077113), _1077115), _1077119)) = hAPP(hAPP(c_Set_Oinsert(_1077113), _1077115), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077113, tc_HOL_Obool)), _1077117), _1077119)))], (34073 ^ _780478) ^ [_1423719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1423719)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1423719), c_Int_OPls)))], (44686 ^ _780478) ^ [_1674586, _1674588, _1674590, _1674592] : [-(hAPP(hAPP(c_List_Omap(_1674586, _1674588), _1674590), hAPP(c_List_Otl(_1674586), _1674592)) = hAPP(c_List_Otl(_1674588), hAPP(hAPP(c_List_Omap(_1674586, _1674588), _1674590), _1674592)))], (41237 ^ _780478) ^ [_1590403, _1590405] : [-(c_Relation_Ototal__on(_1590403, c_Orderings_Obot__class_Obot(tc_fun(_1590403, tc_HOL_Obool)), _1590405))], (18185 ^ _780478) ^ [_1120455, _1120457, _1120459, _1120461, _1120463, _1120465] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120455, tc_fun(_1120457, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1120459, tc_fun(_1120455, tc_HOL_Obool)), _1120461), _1120463)), _1120465) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120459, tc_fun(_1120457, tc_HOL_Obool)), _1120461), hAPP(hAPP(c_COMBC(_1120459, tc_fun(_1120455, tc_fun(_1120457, tc_HOL_Obool)), tc_fun(_1120457, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1120455, tc_HOL_Obool), tc_fun(tc_fun(_1120455, tc_fun(_1120457, tc_HOL_Obool)), tc_fun(_1120457, tc_HOL_Obool)), _1120459), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120455, tc_fun(_1120457, tc_HOL_Obool))), _1120463)), _1120465)))], (45153 ^ _780478) ^ [_1685618, _1685620] : [hAPP(c_Code__Numeral_Onat__of, _1685618) = hAPP(c_Code__Numeral_Onat__of, _1685620), -(_1685618 = _1685620)], (17366 ^ _780478) ^ [_1101348, _1101350, _1101352, _1101354] : [-(_1101348 = c_Orderings_Obot__class_Obot(tc_fun(_1101350, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101350, tc_fun(_1101352, tc_HOL_Obool)), _1101348), hAPP(c_COMBK(tc_fun(_1101352, tc_HOL_Obool), _1101350), _1101354)) = _1101354)], (17603 ^ _780478) ^ [_1107885, _1107887, _1107889, _1107891, _1107893] : [class_Groups_Ocomm__monoid__mult(_1107885), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107887), _1107889)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107887), _1107891)), 17617 ^ _780478 : [(17620 ^ _780478) ^ [] : [hAPP(_1107893, 17616 ^ [_1107885, _1107887, _1107889, _1107891, _1107893]) = c_Groups_Oone__class_Oone(_1107885)], (17618 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1107887), 17616 ^ [_1107885, _1107887, _1107889, _1107891, _1107893]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107887, tc_HOL_Obool)), _1107889), _1107891))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1107887, _1107885), _1107893), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1107887, tc_HOL_Obool)), _1107889), _1107891)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107885), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1107887, _1107885), _1107893), _1107889)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1107887, _1107885), _1107893), _1107891)))], (50737 ^ _780478) ^ [_1806808, _1806810, _1806812] : [hBOOL(hAPP(hAPP(_1806810, _1806812), _1806812)), -(hBOOL(hAPP(c_Quotient_ORespects(_1806808, _1806810), _1806812)))], (38525 ^ _780478) ^ [_1521407, _1521409, _1521411] : [hAPP(c_Relation_ORange(_1521407, _1521409), _1521411) = c_Orderings_Obot__class_Obot(tc_fun(_1521409, tc_HOL_Obool)), -(_1521411 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521407, _1521409), tc_HOL_Obool)))], (29421 ^ _780478) ^ [_1326859, _1326861] : [class_Divides_Osemiring__div(_1326859), -(c_Divides_Odiv__class_Omod(_1326859, _1326861, c_Groups_Oone__class_Oone(_1326859)) = c_Groups_Ozero__class_Ozero(_1326859))], (35567 ^ _780478) ^ [] : [-(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)))))], (23501 ^ _780478) ^ [] : [-(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))))], (36114 ^ _780478) ^ [_1467058, _1467060, _1467062, _1467064] : [_1467058 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1467060), _1467062)), _1467064), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1467058, _1467060), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1467062), _1467064)))), 36121 ^ _780478 : [(36124 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467064), _1467060))], (36122 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467060)))]], 36129 ^ _780478 : [(36132 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467060), _1467064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1467064), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36130 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467060))]]], (33308 ^ _780478) ^ [_1409653] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1409653), c_Int_OPls) = _1409653)], (5496 ^ _780478) ^ [_864599, _864601, _864603, _864605, _864607, _864609, _864611, _864613, _864615, _864617] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_864617, _864613, _864609, _864605, _864601) = c_SetInterval_Oord_OgreaterThanAtMost(_864615, _864611, _864607, _864603, _864599)), _864617 = _864615, _864613 = _864611, _864609 = _864607, _864605 = _864603, _864601 = _864599], (15605 ^ _780478) ^ [_1062217, _1062219, _1062221, _1062223, _1062225, _1062227, _1062229, _1062231] : [hBOOL(hAPP(hAPP(c_member(_1062217), _1062219), _1062221)), hBOOL(hAPP(hAPP(hAPP(_1062223, _1062219), _1062225), _1062227)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1062217, tc_fun(_1062229, tc_fun(_1062231, tc_HOL_Obool))), _1062221), _1062223), _1062225), _1062227)))], (34819 ^ _780478) ^ [_1436839] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1436839))), 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), _1436839), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (34641 ^ _780478) ^ [_1433570, _1433572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1433570)), c_Int_OBit0(_1433572))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433570), _1433572)))], (52083 ^ _780478) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (6024 ^ _780478) ^ [_876322, _876324] : [-(hBOOL(hAPP(hAPP(c_member(_876322), 6025 ^ [_876322, _876324]), _876324))), -(_876324 = c_Orderings_Obot__class_Obot(tc_fun(_876322, tc_HOL_Obool)))], (10937 ^ _780478) ^ [_971217, _971219, _971221, _971223] : [class_Orderings_Olinorder(_971217), 10940 ^ _780478 : [(10941 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971217), hAPP(hAPP(c_Orderings_Oord__class_Omin(_971217), _971219), _971221)), _971223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971217), _971219), _971223))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971217), _971221), _971223)))], (10951 ^ _780478) ^ [] : [10952 ^ _780478 : [(10955 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971217), _971221), _971223))], (10953 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971217), _971219), _971223))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971217), hAPP(hAPP(c_Orderings_Oord__class_Omin(_971217), _971219), _971221)), _971223)))]]], (37409 ^ _780478) ^ [_1492587, _1492589, _1492591, _1492593, _1492595, _1492597] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1492593, _1492593)), hAPP(hAPP(c_Product__Type_OPair(_1492593, _1492593), hAPP(_1492597, _1492589)), hAPP(_1492597, _1492591))), _1492595)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492587, _1492587)), hAPP(hAPP(c_Product__Type_OPair(_1492587, _1492587), _1492589), _1492591)), hAPP(hAPP(c_Relation_Oinv__image(_1492593, _1492587), _1492595), _1492597))))], (44901 ^ _780478) ^ [_1680237, _1680239] : [class_Groups_Oordered__ab__group__add__abs(_1680237), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1680237), hAPP(c_Groups_Oabs__class_Oabs(_1680237), hAPP(c_List_Omonoid__add__class_Olistsum(_1680237), _1680239))), hAPP(c_List_Omonoid__add__class_Olistsum(_1680237), hAPP(hAPP(c_List_Omap(_1680237, _1680237), c_Groups_Oabs__class_Oabs(_1680237)), _1680239)))))], (50809 ^ _780478) ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1808480, _1808482), tc_prod(_1808480, _1808482))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1808480, _1808482), tc_prod(_1808480, _1808482)), hAPP(hAPP(c_Product__Type_OPair(_1808480, _1808482), _1808484), _1808486)), hAPP(hAPP(c_Product__Type_OPair(_1808480, _1808482), _1808488), _1808490))), c_Transitive__Closure_Ortrancl(tc_prod(_1808480, _1808482), _1808492))), hBOOL(hAPP(hAPP(_1808494, _1808484), _1808486)), 50820 ^ _780478 : [(50825 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1808480, _1808482), tc_prod(_1808480, _1808482))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1808480, _1808482), tc_prod(_1808480, _1808482)), hAPP(hAPP(c_Product__Type_OPair(_1808480, _1808482), 50818 ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494]), 50819 ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494])), hAPP(hAPP(c_Product__Type_OPair(_1808480, _1808482), 50822 ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494]), 50823 ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494]))), _1808492)))], (50827 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1808494, 50818 ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494]), 50819 ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494])))], (50829 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1808494, 50822 ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494]), 50823 ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494]))], (50821 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1808480, _1808482), tc_prod(_1808480, _1808482))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1808480, _1808482), tc_prod(_1808480, _1808482)), hAPP(hAPP(c_Product__Type_OPair(_1808480, _1808482), _1808484), _1808486)), hAPP(hAPP(c_Product__Type_OPair(_1808480, _1808482), 50818 ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494]), 50819 ^ [_1808480, _1808482, _1808484, _1808486, _1808488, _1808490, _1808492, _1808494]))), c_Transitive__Closure_Ortrancl(tc_prod(_1808480, _1808482), _1808492))))]], -(hBOOL(hAPP(hAPP(_1808494, _1808488), _1808490)))], (29608 ^ _780478) ^ [_1330273, _1330275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1330273), _1330275)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330273, _1330275) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1330273), _1330275))], (42562 ^ _780478) ^ [_1628668] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1628668) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42565 ^ _780478 : [(42566 ^ _780478) ^ [_1628743] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1628743), hAPP(c_List_Oset(tc_Nat_Onat), _1628668))), -(_1628743 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (40135 ^ _780478) ^ [_1563642, _1563644, _1563646, _1563648, _1563650] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1563642, _1563644, _1563646), _1563648), _1563650))), hBOOL(hAPP(hAPP(_1563644, _1563648), _1563650)), hBOOL(hAPP(_1563646, _1563650))], (12241 ^ _780478) ^ [_995974, _995976, _995978] : [class_Orderings_Olinorder(_995974), hAPP(_995976, hAPP(hAPP(c_Orderings_Oord__class_Omax(_995974), 12246 ^ [_995974, _995976, _995978]), 12247 ^ [_995974, _995976, _995978])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_995974), hAPP(_995976, 12246 ^ [_995974, _995976, _995978])), hAPP(_995976, 12247 ^ [_995974, _995976, _995978])), hBOOL(hAPP(c_Finite__Set_Ofinite(_995974), _995978)), -(_995978 = c_Orderings_Obot__class_Obot(tc_fun(_995974, tc_HOL_Obool))), -(hAPP(_995976, c_Big__Operators_Olinorder__class_OMax(_995974, _995978)) = c_Big__Operators_Olinorder__class_OMax(_995974, hAPP(c_Set_Oimage(_995974, _995974, _995976), _995978)))], (18001 ^ _780478) ^ [_1115628, _1115630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115628), hAPP(c_Nat_OSuc, _1115630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115628), _1115630))), -(_1115628 = hAPP(c_Nat_OSuc, _1115630))], (36413 ^ _780478) ^ [_1473403, _1473405] : [36414 ^ _780478 : [(36417 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1473405), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36415 ^ _780478) ^ [] : [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), _1473403), _1473405)))]], -(c_Divides_OnegDivAlg(_1473403, _1473405) = 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), _1473403), _1473405)))], (43668 ^ _780478) ^ [_1652364, _1652366, _1652368] : [-(c_List_Obutlast(_1652364, hAPP(hAPP(c_List_Oappend(_1652364), _1652366), hAPP(hAPP(c_List_Olist_OCons(_1652364), _1652368), c_List_Olist_ONil(_1652364)))) = _1652366)], (5875 ^ _780478) ^ [_873677, _873679, _873681, _873683, _873685] : [hBOOL(hAPP(hAPP(c_member(_873677), _873679), _873681)), -(hAPP(hAPP(c_Set_Oinsert(_873683), hAPP(_873685, _873679)), hAPP(c_Set_Oimage(_873677, _873683, _873685), _873681)) = hAPP(c_Set_Oimage(_873677, _873683, _873685), _873681))], (4742 ^ _780478) ^ [_852728, _852730, _852732, _852734, _852736, _852738] : [-(c_Random__Sequence_Oempty(_852738, _852734, _852730) = c_Random__Sequence_Oempty(_852736, _852732, _852728)), _852738 = _852736, _852734 = _852732, _852730 = _852728], (27175 ^ _780478) ^ [_1283865] : [-(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)), _1283865)))], (29786 ^ _780478) ^ [_1333562, _1333564, _1333566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333562)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333564, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1333566), _1333562)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1333566), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333564), _1333566), _1333562))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333564, _1333566)))], (37591 ^ _780478) ^ [_1497830, _1497832, _1497834, _1497836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1497830), _1497832)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1497834), _1497836)), -(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), _1497830), _1497834)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1497832), _1497836))), c_FunDef_Opair__less)))], (17149 ^ _780478) ^ [_1095926, _1095928, _1095930] : [class_Orderings_Olinorder(_1095926), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095926), _1095928)), -(_1095928 = c_Orderings_Obot__class_Obot(tc_fun(_1095926, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095926), _1095930)), -(_1095930 = c_Orderings_Obot__class_Obot(tc_fun(_1095926, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095926, tc_HOL_Obool)), _1095928), _1095930) = c_Orderings_Obot__class_Obot(tc_fun(_1095926, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1095926, c_Orderings_Oord__class_Omax(_1095926), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1095926, tc_HOL_Obool)), _1095928), _1095930)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095926), c_Big__Operators_Olattice_OSup__fin(_1095926, c_Orderings_Oord__class_Omax(_1095926), _1095928)), c_Big__Operators_Olattice_OSup__fin(_1095926, c_Orderings_Oord__class_Omax(_1095926), _1095930)))], (29403 ^ _780478) ^ [_1326500, _1326502, _1326504] : [class_Divides_Osemiring__div(_1326500), -(c_Divides_Odiv__class_Omod(_1326500, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326500), _1326502), _1326504), _1326504) = c_Groups_Ozero__class_Ozero(_1326500))], (43628 ^ _780478) ^ [_1651373, _1651375, _1651377] : [-(_1651373 = c_List_Olist_ONil(_1651375)), -(c_List_Obutlast(_1651375, hAPP(hAPP(c_List_Oappend(_1651375), _1651377), _1651373)) = hAPP(hAPP(c_List_Oappend(_1651375), _1651377), c_List_Obutlast(_1651375, _1651373)))], (52125 ^ _780478) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (6914 ^ _780478) ^ [_895337, _895339, _895341, _895343, _895345] : [-(hAPP(c_Fun_Othe__inv__into(_895337, _895339, _895341, _895343), _895345) = c_HOL_OThe(_895337, hAPP(hAPP(c_COMBS(_895337, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _895337), c_fconj), hAPP(hAPP(c_COMBC(_895337, tc_fun(_895337, tc_HOL_Obool), tc_HOL_Obool), c_member(_895337)), _895341))), hAPP(hAPP(c_COMBC(_895337, _895339, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_895339, tc_fun(_895339, tc_HOL_Obool), _895337), c_fequal), _895343)), _895345))))], (41906 ^ _780478) ^ [_1609616, _1609618, _1609620, _1609622, _1609624, _1609626] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609616), tc_List_Olist(_1609616))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609616), tc_List_Olist(_1609616)), hAPP(hAPP(c_List_Olist_OCons(_1609616), _1609618), _1609620)), hAPP(hAPP(c_List_Olist_OCons(_1609616), _1609622), _1609624))), c_List_Olistrel1(_1609616, _1609626))), 41911 ^ _780478 : [(41914 ^ _780478) ^ [] : [-(_1609620 = _1609624)], (41912 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609616, _1609616)), hAPP(hAPP(c_Product__Type_OPair(_1609616, _1609616), _1609618), _1609622)), _1609626)))]], 41915 ^ _780478 : [(41918 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609616), tc_List_Olist(_1609616))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609616), tc_List_Olist(_1609616)), _1609620), _1609624)), c_List_Olistrel1(_1609616, _1609626))))], (41916 ^ _780478) ^ [] : [-(_1609618 = _1609622)]]], (11687 ^ _780478) ^ [_985492, _985494, _985496] : [class_Orderings_Olinorder(_985492), hBOOL(hAPP(c_Finite__Set_Ofinite(_985492), _985494)), -(hBOOL(hAPP(hAPP(c_member(_985492), _985496), _985494))), -(c_Big__Operators_Olinorder__class_OMax(_985492, hAPP(hAPP(c_Set_Oinsert(_985492), _985496), _985494)) = hAPP(hAPP(c_Finite__Set_Ofold(_985492, _985492, c_Orderings_Oord__class_Omax(_985492)), _985496), _985494))], (35659 ^ _780478) ^ [_1454087, _1454089, _1454091, _1454093] : [hAPP(hAPP(c_COMBC(_1454087, tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_fun(_1454089, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454089, tc_fun(tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_fun(_1454089, tc_HOL_Obool)), _1454087), c_COMBC(_1454089, tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454089, tc_prod(_1454087, _1454089)), tc_fun(_1454089, tc_fun(tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_HOL_Obool)), _1454087), hAPP(c_COMBB(tc_prod(_1454087, _1454089), tc_fun(tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_HOL_Obool), _1454089), c_member(tc_prod(_1454087, _1454089)))), c_Product__Type_OPair(_1454087, _1454089)))), _1454091) = hAPP(hAPP(c_COMBC(_1454087, tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_fun(_1454089, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454089, tc_fun(tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_fun(_1454089, tc_HOL_Obool)), _1454087), c_COMBC(_1454089, tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454089, tc_prod(_1454087, _1454089)), tc_fun(_1454089, tc_fun(tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_HOL_Obool)), _1454087), hAPP(c_COMBB(tc_prod(_1454087, _1454089), tc_fun(tc_fun(tc_prod(_1454087, _1454089), tc_HOL_Obool), tc_HOL_Obool), _1454089), c_member(tc_prod(_1454087, _1454089)))), c_Product__Type_OPair(_1454087, _1454089)))), _1454093), -(_1454091 = _1454093)], (13902 ^ _780478) ^ [_1029011, _1029013, _1029015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029011), _1029013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029011), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029013), _1029015))))], (38714 ^ _780478) ^ [_1526845, _1526847, _1526849, _1526851, _1526853, _1526855] : [hBOOL(hAPP(hAPP(c_member(_1526845), _1526847), _1526849)), hBOOL(hAPP(hAPP(c_member(_1526851), _1526853), hAPP(_1526855, _1526847))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526845, _1526851)), hAPP(hAPP(c_Product__Type_OPair(_1526845, _1526851), _1526847), _1526853)), hAPP(hAPP(c_Product__Type_OSigma(_1526845, _1526851), _1526849), _1526855))))], (20272 ^ _780478) ^ [_1158574, _1158576] : [class_Rings_Olinordered__ring(_1158574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158574), _1158576), _1158576)), c_Groups_Ozero__class_Ozero(_1158574)))], (4976 ^ _780478) ^ [_856417, _856419, _856421, _856423] : [-(c_Relation_Oinv__image(_856423, _856419) = c_Relation_Oinv__image(_856421, _856417)), _856423 = _856421, _856419 = _856417], (42774 ^ _780478) ^ [_1633447, _1633449, _1633451, _1633453] : [hBOOL(hAPP(c_List_Odistinct(_1633447), _1633449)), -(hBOOL(hAPP(hAPP(c_member(_1633447), _1633451), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1633447, tc_HOL_Obool)), hAPP(c_List_Oset(_1633447), _1633449)), hAPP(hAPP(c_Set_Oinsert(_1633447), hAPP(hAPP(c_List_Onth(_1633447), _1633449), _1633453)), c_Orderings_Obot__class_Obot(tc_fun(_1633447, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1633447), hAPP(hAPP(c_List_Olist__update(_1633447, _1633449), _1633453), _1633451))))], (49832 ^ _780478) ^ [_1787919, _1787921] : [49833 ^ _780478 : [(49834 ^ _780478) ^ [_1787975] : [hBOOL(hAPP(hAPP(_1787919, _1787975), _1787975))]], c_Predicate_Osymp(_1787921, _1787919), c_Predicate_Otransp(_1787921, _1787919), -(c_Equiv__Relations_Opart__equivp(_1787921, _1787919))], (17851 ^ _780478) ^ [_1113265, _1113267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113265)), _1113267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113265), _1113267)))], (41178 ^ _780478) ^ [_1588897, _1588899, _1588901] : [c_Relation_Ototal__on(_1588897, _1588899, _1588901), -(c_Relation_Ototal__on(_1588897, _1588899, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1588897, _1588897), tc_HOL_Obool)), _1588901), c_Relation_OId(_1588897))))], (47097 ^ _780478) ^ [_1727892, _1727894, _1727896] : [-(hAPP(c_List_Orev(_1727892), hAPP(hAPP(c_List_Otake(_1727892), _1727894), _1727896)) = hAPP(hAPP(c_List_Odrop(_1727892), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727892)), _1727896)), _1727894)), hAPP(c_List_Orev(_1727892), _1727896)))], (16228 ^ _780478) ^ [_1074785, _1074787, _1074789, _1074791] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074785, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074785, tc_HOL_Obool)), _1074787), _1074789)), _1074791) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074785, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074785, tc_HOL_Obool)), _1074787), _1074791)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074785, tc_HOL_Obool)), _1074789), _1074791)))], (9136 ^ _780478) ^ [_937345, _937347, _937349] : [class_Orderings_Olinorder(_937345), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937345), _937347), _937349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937345), _937349), _937347))], (35365 ^ _780478) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (28424 ^ _780478) ^ [_1306466] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1306466)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1306466))], (7256 ^ _780478) ^ [_901406, _901408, _901410, _901412] : [class_Orderings_Oord(_901406), 7259 ^ _780478 : [(7266 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901406), hAPP(_901410, 7267 ^ [_901406, _901408, _901410, _901412])), hAPP(_901412, 7267 ^ [_901406, _901408, _901410, _901412]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901408, _901406)), _901410), _901412)))], (7260 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901408, _901406)), _901410), _901412)), 7263 ^ _780478 : [(7264 ^ _780478) ^ [_901563] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901406), hAPP(_901410, _901563)), hAPP(_901412, _901563))))]]]]], (52035 ^ _780478) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (23281 ^ _780478) ^ [_1213762, _1213764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213764), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213762), _1213764))), -(_1213762 = _1213764)], (18177 ^ _780478) ^ [_1120016, _1120018, _1120020, _1120022, _1120024] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120016, tc_fun(_1120018, tc_HOL_Obool)), _1120020), hAPP(hAPP(c_COMBC(_1120016, tc_fun(_1120018, tc_HOL_Obool), tc_fun(_1120018, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1120018, tc_HOL_Obool), tc_fun(tc_fun(_1120018, tc_HOL_Obool), tc_fun(_1120018, tc_HOL_Obool)), _1120016), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1120018, tc_HOL_Obool))), _1120022)), _1120024)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1120018, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120016, tc_fun(_1120018, tc_HOL_Obool)), _1120020), _1120022)), _1120024))], (45548 ^ _780478) ^ [_1694553, _1694555, _1694557, _1694559, _1694561] : [c_List_Olist__all2(_1694553, _1694555, _1694557, _1694559, _1694561), 45551 ^ _780478 : [(45554 ^ _780478) ^ [_1694716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1694716), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694553)), _1694559))), -(hBOOL(hAPP(hAPP(_1694557, hAPP(hAPP(c_List_Onth(_1694553), _1694559), _1694716)), hAPP(hAPP(c_List_Onth(_1694555), _1694561), _1694716))))], (45552 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694553)), _1694559) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694555)), _1694561))]]], (27146 ^ _780478) ^ [_1283413, _1283415] : [c_Nat__Transfer_Onat__set(_1283413), c_Nat__Transfer_Onat__set(_1283415), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1283413), _1283415)))], (2232 ^ _780478) ^ [_813103, _813105, _813107, _813109] : [-(c_SMT_Oz3mod(_813109, _813105) = c_SMT_Oz3mod(_813107, _813103)), _813109 = _813107, _813105 = _813103], (50387 ^ _780478) ^ [_1799970, _1799972, _1799974, _1799976, _1799978] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1799970, _1799972, tc_HOL_Obool, _1799974), _1799976), _1799978)), -(hBOOL(hAPP(_1799974, hAPP(hAPP(c_Product__Type_OPair(_1799970, _1799972), _1799976), _1799978))))], (14142 ^ _780478) ^ [_1033198, _1033200, _1033202] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1033198), _1033200)), 14145 ^ _780478 : [(14146 ^ _780478) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1033198, tc_Nat_Onat), _1033202), _1033200) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 14149 ^ _780478 : [(14150 ^ _780478) ^ [_1033360] : [hBOOL(hAPP(hAPP(c_member(_1033198), _1033360), _1033200)), -(hAPP(_1033202, _1033360) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (14156 ^ _780478) ^ [] : [14158 ^ _780478 : [(14161 ^ _780478) ^ [] : [hAPP(_1033202, 14157 ^ [_1033198, _1033200, _1033202]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (14159 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1033198), 14157 ^ [_1033198, _1033200, _1033202]), _1033200)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1033198, tc_Nat_Onat), _1033202), _1033200) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (9408 ^ _780478) ^ [_941662, _941664, _941666, _941668] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_941662), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941662), _941664), _941666)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941662), _941664), _941668))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941662), _941666), _941668)))], (51883 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (4222 ^ _780478) ^ [_844372, _844374] : [_844374 = _844372, -(c_List_Ohd(_844374) = c_List_Ohd(_844372))], (25974 ^ _780478) ^ [_1261931, _1261933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1261931), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1261931), _1261933)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1261931))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1261933))))], (2790 ^ _780478) ^ [_821728, _821730, _821732, _821734, _821736, _821738, _821740, _821742] : [-(c_Random_Oiterate(_821742, _821738, _821734, _821730) = c_Random_Oiterate(_821740, _821736, _821732, _821728)), _821742 = _821740, _821738 = _821736, _821734 = _821732, _821730 = _821728], (41605 ^ _780478) ^ [_1600260, _1600262, _1600264] : [-(c_Nitpick_Oplus__frac(_1600260, _1600262, _1600264) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1600260), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1600260), _1600262), hAPP(c_Nitpick_Odenom(_1600260), _1600264))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1600260), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1600260), tc_Int_Oint), c_Nitpick_Ofrac(_1600260)), 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(_1600260), _1600262))), 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(_1600260), _1600262))))), 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(_1600260), _1600264))), 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(_1600260), _1600264)))))), c_COMBI(tc_Int_Oint))))], (9022 ^ _780478) ^ [_935711, _935713, _935715, _935717] : [class_Orderings_Opreorder(_935711), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935711), _935713), _935715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935711), _935715), _935717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935711), _935713), _935717)))], (29433 ^ _780478) ^ [_1327055, _1327057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327055, _1327057)), _1327055)))], (9194 ^ _780478) ^ [_938240, _938242, _938244] : [class_Orderings_Olinorder(_938240), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938240), _938242), _938244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938240), _938244), _938242)))], (41774 ^ _780478) ^ [_1605017, _1605019, _1605021] : [-(c_List_Oset__Cons(_1605017, _1605019, _1605021) = hAPP(c_Set_OCollect(tc_List_Olist(_1605017)), hAPP(hAPP(c_COMBB(tc_fun(_1605017, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1605017)), c_HOL_OEx(_1605017)), hAPP(hAPP(c_COMBB(tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool)), tc_fun(_1605017, tc_HOL_Obool), tc_List_Olist(_1605017)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), tc_HOL_Obool, _1605017), c_HOL_OEx(tc_List_Olist(_1605017)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1605017), tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool)), tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1605017, tc_fun(tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool))), tc_fun(tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool)), tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool))), tc_List_Olist(_1605017)), c_COMBS(_1605017, tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1605017, tc_fun(tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool))), tc_List_Olist(_1605017)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1605017), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool)), _1605017), c_COMBS(tc_List_Olist(_1605017), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool)), tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1605017)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), tc_fun(tc_List_Olist(_1605017), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1605017), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1605017)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1605017), tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_List_Olist(_1605017))), tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1605017), tc_List_Olist(_1605017)), tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool)), tc_fun(tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_List_Olist(_1605017))), tc_fun(_1605017, tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool))), tc_List_Olist(_1605017)), c_COMBB(tc_fun(tc_List_Olist(_1605017), tc_List_Olist(_1605017)), tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), _1605017)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1605017), tc_List_Olist(_1605017)), tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool)), tc_List_Olist(_1605017)), c_COMBB(tc_List_Olist(_1605017), tc_HOL_Obool, tc_List_Olist(_1605017))), c_fequal))), c_List_Olist_OCons(_1605017)))))), hAPP(hAPP(c_COMBC(_1605017, tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool)), _1605017), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1605017))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1605017), c_fconj), hAPP(hAPP(c_COMBC(_1605017, tc_fun(_1605017, tc_HOL_Obool), tc_HOL_Obool), c_member(_1605017)), _1605019)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1605017), tc_fun(tc_List_Olist(_1605017), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1605017))), _1605021)))))))], (8224 ^ _780478) ^ [_921192, _921194, _921196, _921198, _921200] : [class_Groups_Oordered__ab__semigroup__add(_921192), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921192), _921194), _921196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921192), _921198), _921200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921192), _921194), _921198)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921192), _921196), _921200))))], (13180 ^ _780478) ^ [_1014482] : [c_Orderings_Otop__class_Otop(tc_fun(_1014482, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1014482, tc_HOL_Obool))], (48335 ^ _780478) ^ [] : [-(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)))], (24419 ^ _780478) ^ [_1234291, _1234293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234291), _1234293)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234291), _1234293) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45139 ^ _780478) ^ [_1685383] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1685383)) = _1685383)], (8088 ^ _780478) ^ [_918503, _918505, _918507, _918509] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_918503), _918505)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918503, tc_HOL_Obool)), _918505), _918507)), hBOOL(hAPP(_918509, c_Orderings_Obot__class_Obot(tc_fun(_918503, tc_HOL_Obool)))), 8103 ^ _780478 : [(8104 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_918503), 8102 ^ [_918503, _918505, _918507, _918509])))], (8108 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_918503), 8101 ^ [_918503, _918505, _918507, _918509]), 8102 ^ [_918503, _918505, _918507, _918509]))], (8112 ^ _780478) ^ [] : [hBOOL(hAPP(_918509, hAPP(hAPP(c_Set_Oinsert(_918503), 8101 ^ [_918503, _918505, _918507, _918509]), 8102 ^ [_918503, _918505, _918507, _918509])))], (8110 ^ _780478) ^ [] : [-(hBOOL(hAPP(_918509, 8102 ^ [_918503, _918505, _918507, _918509])))], (8106 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_918503), 8101 ^ [_918503, _918505, _918507, _918509]), _918507)))]], -(hBOOL(hAPP(_918509, _918505)))], (8948 ^ _780478) ^ [_934545, _934547, _934549] : [class_Orderings_Olinorder(_934545), 8951 ^ _780478 : [(8952 ^ _780478) ^ [] : [-(_934547 = _934549), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934545), _934547), _934549))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934545), _934549), _934547)))], (8962 ^ _780478) ^ [] : [8963 ^ _780478 : [(8966 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934545), _934549), _934547))], (8964 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934545), _934547), _934549))]], _934547 = _934549]]], (52197 ^ _780478) ^ [_1832120, _1832122] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1832120, _1832122))), class_Lazy__Sequence_Osmall__lazy(_1832120), class_Lazy__Sequence_Osmall__lazy(_1832122)], (51963 ^ _780478) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (52277 ^ _780478) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (38566 ^ _780478) ^ [_1522405] : [-(c_Nitpick_Oone__frac(_1522405) = c_Nitpick_OAbs__Frac(_1522405, 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))))], (41134 ^ _780478) ^ [_1587750] : [-(c_Relation_OId(_1587750) = hAPP(c_Set_OCollect(tc_prod(_1587750, _1587750)), hAPP(hAPP(c_COMBB(tc_fun(_1587750, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1587750, _1587750)), c_HOL_OEx(_1587750)), hAPP(hAPP(c_COMBC(tc_prod(_1587750, _1587750), tc_fun(_1587750, tc_prod(_1587750, _1587750)), tc_fun(_1587750, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1587750, _1587750), tc_HOL_Obool), tc_fun(tc_fun(_1587750, tc_prod(_1587750, _1587750)), tc_fun(_1587750, tc_HOL_Obool)), tc_prod(_1587750, _1587750)), c_COMBB(tc_prod(_1587750, _1587750), tc_HOL_Obool, _1587750)), c_fequal)), hAPP(hAPP(c_COMBS(_1587750, _1587750, tc_prod(_1587750, _1587750)), c_Product__Type_OPair(_1587750, _1587750)), c_COMBI(_1587750))))))], (45504 ^ _780478) ^ [_1693787, _1693789, _1693791] : [_1693787 = _1693789, -(c_List_Olist__all2(_1693791, _1693791, c_fequal, _1693787, _1693789))], (11715 ^ _780478) ^ [_985920, _985922, _985924, _985926] : [c_Big__Operators_Osemilattice__big(_985920, _985922, _985924), hBOOL(hAPP(c_Finite__Set_Ofinite(_985920), _985926)), -(hAPP(_985924, _985926) = hAPP(c_Finite__Set_Ofold1(_985920, _985922), _985926))], (21245 ^ _780478) ^ [_1175204, _1175206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1175204), _1175206)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1175204), _1175206) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49642 ^ _780478) ^ [_1784475, _1784477] : [c_Relation_Oantisym(_1784475, _1784477), -(c_Relation_Oantisym(_1784475, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1784475, _1784475), tc_HOL_Obool)), _1784477), c_Relation_OId(_1784475))))], (7339 ^ _780478) ^ [_903128, _903130, _903132, _903134] : [c_Fun_Oinj__on(_903128, _903130, _903132, _903134), 7342 ^ _780478 : [(7343 ^ _780478) ^ [_903236] : [hBOOL(hAPP(hAPP(c_member(_903128), _903236), _903134)), 7346 ^ _780478 : [(7347 ^ _780478) ^ [_903338] : [hBOOL(hAPP(hAPP(c_member(_903128), _903338), _903134)), hAPP(_903132, _903236) = hAPP(_903132, _903338), -(_903236 = _903338)]]]]], (15615 ^ _780478) ^ [_1062440, _1062442, _1062444, _1062446] : [hBOOL(hAPP(hAPP(c_member(_1062440), _1062442), _1062444)), hBOOL(hAPP(hAPP(c_member(_1062440), _1062442), _1062446)), -(hBOOL(hAPP(hAPP(c_member(_1062440), _1062442), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062440, tc_HOL_Obool)), _1062444), _1062446))))], (35571 ^ _780478) ^ [_1450078] : [-(c_Int_Oint__ge__less__than2(_1450078) = 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), _1450078)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (12986 ^ _780478) ^ [_1010589, _1010591, _1010593, _1010595] : [class_Lattices_Osemilattice__sup(_1010589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010589), _1010591), _1010593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010589), _1010591), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010589), _1010595), _1010593))))], (35281 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18754 ^ _780478) ^ [_1132690, _1132692, _1132694] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1132690), _1132692)), -(hBOOL(hAPP(hAPP(c_member(_1132690), _1132694), _1132692))), -(hAPP(c_Finite__Set_Ocard(_1132690), hAPP(hAPP(c_Set_Oinsert(_1132690), _1132694), _1132692)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1132690), _1132692)))], (31879 ^ _780478) ^ [_1382484, _1382486, _1382488, _1382490, _1382492, _1382494] : [-(c_Com_Ocom_OCond(_1382484, _1382486, _1382488) = c_Com_Ocom_OCond(_1382490, _1382492, _1382494)), _1382484 = _1382490, _1382486 = _1382492, _1382488 = _1382494], (37760 ^ _780478) ^ [_1501309, _1501311, _1501313] : [-(hAPP(c_Relation_OImage(_1501309, _1501309, c_Relation_OId__on(_1501309, _1501311)), _1501313) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1501309, tc_HOL_Obool)), _1501311), _1501313))], (35067 ^ _780478) ^ [_1441158, _1441160, _1441162] : [class_Int_Onumber__ring(_1441158), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1441158), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1441158), _1441160), _1441162)), 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(_1441158), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1441158), hAPP(hAPP(c_Power_Opower__class_Opower(_1441158), _1441160), 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(_1441158), _1441162), 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(_1441158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1441158), hAPP(c_Int_Onumber__class_Onumber__of(_1441158), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1441160)), _1441162)))], (24245 ^ _780478) ^ [_1231670, _1231672, _1231674] : [class_Divides_Osemiring__div(_1231670), -(_1231672 = c_Groups_Ozero__class_Ozero(_1231670)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231670), _1231674), _1231672)), _1231672) = _1231674)], (34013 ^ _780478) ^ [_1422707] : [-(c_Int_OBit1(_1422707) = 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)), _1422707)), _1422707))], (50550 ^ _780478) ^ [_1803034, _1803036, _1803038] : [c_Fun_Obij__betw(_1803034, _1803034, c_Fun_Oid(_1803034), _1803036, _1803038), -(_1803036 = _1803038)], (22811 ^ _780478) ^ [_1205132, _1205134] : [class_Rings_Olinordered__semidom(_1205132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205132), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205132), _1205134)), c_Groups_Ozero__class_Ozero(_1205132)))], (36104 ^ _780478) ^ [_1466757, _1466759, _1466761, _1466763, _1466765, _1466767] : [c_Equiv__Relations_Oequiv(_1466757, _1466759, _1466761), hBOOL(hAPP(hAPP(c_member(_1466757), _1466763), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466757, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466757, _1466757, _1466761), hAPP(hAPP(c_Set_Oinsert(_1466757), _1466765), c_Orderings_Obot__class_Obot(tc_fun(_1466757, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1466757, _1466757, _1466761), hAPP(hAPP(c_Set_Oinsert(_1466757), _1466767), c_Orderings_Obot__class_Obot(tc_fun(_1466757, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1466757, _1466757)), hAPP(hAPP(c_Product__Type_OPair(_1466757, _1466757), _1466765), _1466767)), _1466761)))], (51817 ^ _780478) ^ [_1828315, _1828317] : [class_Lattices_Olattice(_1828315), -(class_Lattices_Olattice(tc_fun(_1828317, _1828315)))], (50441 ^ _780478) ^ [_1801072, _1801074, _1801076] : [c_Fun_Obij__betw(_1801072, _1801074, _1801076, c_Orderings_Otop__class_Otop(tc_fun(_1801072, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1801074, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1801072, _1801074, _1801076), c_Orderings_Otop__class_Otop(tc_fun(_1801072, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1801074, tc_HOL_Obool)))], (39646 ^ _780478) ^ [_1552359, _1552361, _1552363, _1552365, _1552367, _1552369, _1552371, _1552373, _1552375] : [hAPP(c_Fun_Ocomp(_1552359, _1552361, _1552363, _1552365), _1552367) = hAPP(c_Fun_Ocomp(_1552369, _1552361, _1552363, _1552371), _1552373), -(hAPP(_1552365, hAPP(_1552367, _1552375)) = hAPP(_1552371, hAPP(_1552373, _1552375)))], (29387 ^ _780478) ^ [_1326264, _1326266] : [c_Nat__Transfer_Ois__nat(_1326264), c_Nat__Transfer_Ois__nat(_1326266), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1326264, _1326266)))], (13791 ^ _780478) ^ [_1027087, _1027089, _1027091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027087), _1027089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027091), _1027087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027087), _1027091)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027089), _1027091))))], (38677 ^ _780478) ^ [_1525301, _1525303, _1525305, _1525307] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1525301, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1525301, _1525303), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1525301, _1525303), tc_HOL_Obool)), _1525305), _1525307))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1525301, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1525301, _1525303), _1525305)), hAPP(c_Relation_ODomain(_1525301, _1525303), _1525307)))))], (19776 ^ _780478) ^ [_1149541, _1149543, _1149545] : [class_Rings_Olinordered__ring(_1149541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149541), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149541), _1149543), _1149543)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149541), _1149545), _1149545))), c_Groups_Ozero__class_Ozero(_1149541)))], (20766 ^ _780478) ^ [_1167403, _1167405] : [class_Groups_Oab__group__add(_1167403), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167403), hAPP(c_Groups_Ouminus__class_Ouminus(_1167403), _1167405)), _1167405) = c_Groups_Ozero__class_Ozero(_1167403))], (46923 ^ _780478) ^ [_1724332, _1724334] : [-(c_Fun_Oinj__on(tc_List_Olist(_1724332), tc_List_Olist(_1724332), c_List_Orev(_1724332), _1724334))], (10137 ^ _780478) ^ [_956622, _956624, _956626] : [class_Groups_Ogroup__add(_956622), 10140 ^ _780478 : [(10147 ^ _780478) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_956622), _956626) = _956624, -(hAPP(c_Groups_Ouminus__class_Ouminus(_956622), _956624) = _956626)], (10141 ^ _780478) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_956622), _956624) = _956626, -(hAPP(c_Groups_Ouminus__class_Ouminus(_956622), _956626) = _956624)]]], (49466 ^ _780478) ^ [_1781237, _1781239] : [c_Predicate_Oreflp(_1781237, _1781239), c_Predicate_Osymp(_1781237, _1781239), c_Predicate_Otransp(_1781237, _1781239), -(c_Equiv__Relations_Oequivp(_1781237, _1781239))], (25527 ^ _780478) ^ [_1254441, _1254443] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1254441, _1254443)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1254443), _1254441)))], (6114 ^ _780478) ^ [_877961, _877963, _877965, _877967, _877969] : [-(hBOOL(hAPP(hAPP(c_member(_877961), _877963), hAPP(c_Set_Oimage(_877965, _877961, _877967), _877969)))), 6115 ^ _780478 : [(6116 ^ _780478) ^ [_878031] : [hBOOL(hAPP(hAPP(c_member(_877965), _878031), _877969)), _877963 = hAPP(_877967, _878031)]]], (33869 ^ _780478) ^ [_1420374, _1420376] : [c_Int_Oiszero(_1420374, hAPP(c_Int_Onumber__class_Onumber__of(_1420374), c_Int_OBit1(_1420376))), class_Int_Onumber__ring(_1420374), class_Int_Oring__char__0(_1420374)], (33712 ^ _780478) ^ [_1416525, _1416527] : [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(_1416527))), 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), _1416525)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1416525)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416527))))], (39228 ^ _780478) ^ [_1542184, _1542186] : [c_Wellfounded_OwfP(_1542184, _1542186), -(c_Wellfounded_Owf(_1542184, hAPP(c_Set_OCollect(tc_prod(_1542184, _1542184)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542184, _1542184, tc_HOL_Obool), _1542186))))], (50942 ^ _780478) ^ [_1812883, _1812885, _1812887, _1812889] : [-(hAPP(c_Lazy__Sequence_Obind(_1812883, _1812885, _1812887), _1812889) = c_Lazy__Sequence_Oflat(_1812885, c_Lazy__Sequence_Omap(_1812883, tc_Lazy__Sequence_Olazy__sequence(_1812885), _1812889, _1812887)))], (43431 ^ _780478) ^ [_1647310, _1647312, _1647314, _1647316] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1647310)), hAPP(hAPP(c_List_Oappend(_1647310), _1647312), _1647314)), c_List_Olists(_1647310, _1647316)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1647310)), _1647312), c_List_Olists(_1647310, _1647316))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1647310)), _1647314), c_List_Olists(_1647310, _1647316)))], (45767 ^ _780478) ^ [_1699475, _1699477] : [_1699477 = c_List_Olist_ONil(_1699475), -(c_List_Oremdups(_1699475, _1699477) = c_List_Olist_ONil(_1699475))], (34721 ^ _780478) ^ [_1435205, _1435207] : [class_Int_Onumber__ring(_1435205), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435205), _1435207), hAPP(c_Int_Onumber__class_Onumber__of(_1435205), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1435205), _1435207), _1435207))], (39939 ^ _780478) ^ [_1558737, _1558739, _1558741, _1558743, _1558745, _1558747, _1558749, _1558751, _1558753, _1558755, _1558757] : [c_Finite__Set_Ofolding(_1558737, _1558739, _1558741, _1558743), -(hAPP(c_Fun_Ocomp(_1558745, _1558747, _1558749, _1558751), hAPP(c_Fun_Ocomp(_1558753, _1558745, _1558749, _1558755), _1558757)) = hAPP(c_Fun_Ocomp(_1558753, _1558747, _1558749, hAPP(c_Fun_Ocomp(_1558745, _1558747, _1558753, _1558751), _1558755)), _1558757))], (19048 ^ _780478) ^ [_1138216, _1138218, _1138220, _1138222, _1138224, _1138226, _1138228] : [19050 ^ _780478 : [(19053 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1138224, 19049 ^ [_1138216, _1138218, _1138220, _1138222, _1138224, _1138226, _1138228]), _1138226), _1138228))], (19051 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1138216), 19049 ^ [_1138216, _1138218, _1138220, _1138222, _1138224, _1138226, _1138228]), _1138222)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1138216, tc_fun(_1138218, tc_fun(_1138220, tc_HOL_Obool))), _1138222), _1138224), _1138226), _1138228)))], (10251 ^ _780478) ^ [_958954, _958956, _958958, _958960] : [class_Orderings_Olinorder(_958954), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_958954), _958956), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958954), _958958), _958960)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_958954), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958954), _958956), _958958)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958954), _958956), _958960)))], (51579 ^ _780478) ^ [_1824563, _1824565, _1824567] : [class_Divides_Osemiring__div(_1824563), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824563), _1824565), _1824567)), -(c_Divides_Odiv__class_Omod(_1824563, _1824567, _1824565) = c_Groups_Ozero__class_Ozero(_1824563))], (48798 ^ _780478) ^ [_1764722, _1764724, _1764726, _1764728] : [-(c_Lazy__Sequence_Oappend(_1764722, c_Lazy__Sequence_Olazy__sequence_OInsert(_1764722, _1764724, _1764726), _1764728) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1764722, _1764724, c_Lazy__Sequence_Oappend(_1764722, _1764726, _1764728)))], (15791 ^ _780478) ^ [_1066144, _1066146, _1066148, _1066150] : [-(hAPP(c_Set_Oimage(_1066144, _1066146, _1066148), hAPP(c_Set_Ovimage(_1066144, _1066146, _1066148), _1066150)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1066146, tc_HOL_Obool)), _1066150), hAPP(c_Set_Oimage(_1066144, _1066146, _1066148), c_Orderings_Otop__class_Otop(tc_fun(_1066144, tc_HOL_Obool)))))], (39907 ^ _780478) ^ [_1558075, _1558077, _1558079, _1558081, _1558083, _1558085, _1558087, _1558089] : [c_Finite__Set_Ofolding__image(_1558075, _1558077, _1558079, _1558081, _1558083), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558077), _1558085)), c_Fun_Oinj__on(_1558077, _1558077, _1558087, _1558085), -(hAPP(hAPP(_1558083, _1558089), hAPP(c_Set_Oimage(_1558077, _1558077, _1558087), _1558085)) = hAPP(hAPP(_1558083, hAPP(c_Fun_Ocomp(_1558077, _1558075, _1558077, _1558089), _1558087)), _1558085))], (48073 ^ _780478) ^ [_1749451, _1749453, _1749455] : [-(c_List_Olist__ex(_1749451, _1749453, _1749455)), 48074 ^ _780478 : [(48075 ^ _780478) ^ [_1749508] : [hBOOL(hAPP(hAPP(c_member(_1749451), _1749508), hAPP(c_List_Oset(_1749451), _1749455))), hBOOL(hAPP(_1749453, _1749508))]]], (41894 ^ _780478) ^ [_1609141, _1609143, _1609145, _1609147] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609141), tc_List_Olist(_1609141))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609141), tc_List_Olist(_1609141)), _1609143), _1609145)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1609141), tc_List_Olist(_1609141)), c_List_Olistrel1(_1609141, _1609147)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609141), tc_List_Olist(_1609141))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609141), tc_List_Olist(_1609141)), _1609143), _1609145)), c_List_Olistrel1(_1609141, hAPP(c_Relation_Oconverse(_1609141, _1609141), _1609147)))))], (27978 ^ _780478) ^ [_1297869, _1297871, _1297873, _1297875, _1297877] : [class_Groups_Ocomm__monoid__add(_1297869), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1297869), _1297871), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297873), _1297875), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1297877), _1297875))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1297869), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1297869, tc_Nat_Onat), _1297871), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1297875))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1297873, _1297877)))], (44059 ^ _780478) ^ [_1662617, _1662619, _1662621] : [-(_1662617 = c_List_Olist_ONil(_1662619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662621), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662619)), _1662617))), -(hAPP(c_List_Ohd(_1662619), hAPP(hAPP(c_List_Odrop(_1662619), _1662621), _1662617)) = hAPP(hAPP(c_List_Onth(_1662619), _1662617), _1662621))], (31629 ^ _780478) ^ [_1376700, _1376702, _1376704, _1376706] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1376700), _1376702))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376704), hAPP(c_Set_Oimage(_1376700, _1376704, _1376706), _1376702))), 31637 ^ _780478 : [(31640 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1376700), hAPP(c_Set_OCollect(_1376700), hAPP(hAPP(c_COMBS(_1376700, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1376700), c_fconj), hAPP(hAPP(c_COMBC(_1376700, tc_fun(_1376700, tc_HOL_Obool), tc_HOL_Obool), c_member(_1376700)), _1376702))), hAPP(hAPP(c_COMBC(_1376700, _1376704, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1376704, tc_fun(_1376704, tc_HOL_Obool), _1376700), c_fequal), _1376706)), hAPP(_1376706, 31636 ^ [_1376700, _1376702, _1376704, _1376706]))))))], (31638 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376700), 31636 ^ [_1376700, _1376702, _1376704, _1376706]), _1376702)))]]], (48044 ^ _780478) ^ [_1748975, _1748977] : [c_List_Olist__ex(_1748975, _1748977, c_List_Olist_ONil(_1748975))], (27497 ^ _780478) ^ [_1288883, _1288885, _1288887] : [class_Rings_Olinordered__idom(_1288883), 27500 ^ _780478 : [(27507 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1288885), _1288887)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288883), hAPP(c_Int_Oring__1__class_Oof__int(_1288883), _1288885)), hAPP(c_Int_Oring__1__class_Oof__int(_1288883), _1288887))))], (27501 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288883), hAPP(c_Int_Oring__1__class_Oof__int(_1288883), _1288885)), hAPP(c_Int_Oring__1__class_Oof__int(_1288883), _1288887))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1288885), _1288887)))]]], (30653 ^ _780478) ^ [_1349624, _1349626, _1349628] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1349624, tc_HOL_Obool)), _1349626), _1349628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1349624, tc_HOL_Obool)), _1349626), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349624, tc_HOL_Obool), _1349628))))], (2112 ^ _780478) ^ [_811221, _811223, _811225, _811227, _811229, _811231] : [-(c_SetInterval_Oord_OgreaterThan(_811231, _811227, _811223) = c_SetInterval_Oord_OgreaterThan(_811229, _811225, _811221)), _811231 = _811229, _811227 = _811225, _811223 = _811221], (6314 ^ _780478) ^ [_882225, _882227, _882229, _882231] : [c_Finite__Set_Ofolding__one(_882225, _882227, _882229), -(hAPP(_882229, hAPP(hAPP(c_Set_Oinsert(_882225), _882231), c_Orderings_Obot__class_Obot(tc_fun(_882225, tc_HOL_Obool)))) = _882231)], (40722 ^ _780478) ^ [_1577802, _1577804, _1577806, _1577808] : [-(c_Wellfounded_Owf(_1577802, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1577802, _1577802)), hAPP(hAPP(c_Product__Type_OPair(_1577802, _1577802), _1577804), _1577806)), _1577808))), c_Wellfounded_Owf(_1577802, _1577808), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577802, _1577802)), hAPP(hAPP(c_Product__Type_OPair(_1577802, _1577802), _1577806), _1577804)), c_Transitive__Closure_Ortrancl(_1577802, _1577808))))], (68 ^ _780478) ^ [_781552, _781554, _781556, _781558, _781560, _781562, _781564, _781566, _781568, _781570, _781572, _781574] : [-(c_Finite__Set_Ofolding__image__simple__idem(_781572, _781568, _781564, _781560, _781556, _781552)), c_Finite__Set_Ofolding__image__simple__idem(_781574, _781570, _781566, _781562, _781558, _781554), _781574 = _781572, _781570 = _781568, _781566 = _781564, _781562 = _781560, _781558 = _781556, _781554 = _781552], (4316 ^ _780478) ^ [_845763, _845765] : [_845765 = _845763, -(c_If(_845765) = c_If(_845763))], (3522 ^ _780478) ^ [_833044, _833046, _833048, _833050, _833052, _833054] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_833054, _833050, _833046) = c_SetInterval_Oord__class_OgreaterThanAtMost(_833052, _833048, _833044)), _833054 = _833052, _833050 = _833048, _833046 = _833044], (33080 ^ _780478) ^ [_1405640, _1405642, _1405644, _1405646, _1405648, _1405650, _1405652, _1405654] : [c_Equiv__Relations_Oequiv(_1405640, _1405642, _1405644), c_Equiv__Relations_Ocongruent2(_1405640, _1405646, _1405648, _1405644, _1405650, _1405652), hBOOL(hAPP(hAPP(c_member(_1405640), _1405654), _1405642)), -(c_Equiv__Relations_Ocongruent(_1405646, _1405648, _1405650, hAPP(_1405652, _1405654)))], (19094 ^ _780478) ^ [_1139176, _1139178, _1139180] : [class_Power_Opower(_1139176), class_Rings_Omult__zero(_1139176), class_Rings_Ono__zero__divisors(_1139176), class_Rings_Ozero__neq__one(_1139176), 19109 ^ _780478 : [(19118 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1139176), _1139178), _1139180) = c_Groups_Ozero__class_Ozero(_1139176)), _1139178 = c_Groups_Ozero__class_Ozero(_1139176), -(_1139180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19110 ^ _780478) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1139176), _1139178), _1139180) = c_Groups_Ozero__class_Ozero(_1139176), 19113 ^ _780478 : [(19116 ^ _780478) ^ [] : [_1139180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19114 ^ _780478) ^ [] : [-(_1139178 = c_Groups_Ozero__class_Ozero(_1139176))]]]]], (844 ^ _780478) ^ [_793096, _793098, _793100, _793102] : [-(c_Equiv__Relations_Opart__equivp(_793100, _793096)), c_Equiv__Relations_Opart__equivp(_793102, _793098), _793102 = _793100, _793098 = _793096], (34085 ^ _780478) ^ [_1423915, _1423917] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423915), _1423917), hAPP(c_Int_Onumber__class_Onumber__of(_1423915), c_Int_OBit1(c_Int_OPls))) = _1423917), class_Fields_Ofield(_1423915), class_Int_Onumber__ring(_1423915)], (2406 ^ _780478) ^ [_815718, _815720, _815722, _815724] : [-(c_Set_Othe__elem(_815724, _815720) = c_Set_Othe__elem(_815722, _815718)), _815724 = _815722, _815720 = _815718], (17729 ^ _780478) ^ [_1110596, _1110598, _1110600, _1110602, _1110604, _1110606] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1110596, tc_fun(_1110598, tc_HOL_Obool)), _1110600), _1110602), _1110604)), hBOOL(hAPP(hAPP(c_member(_1110596), _1110606), _1110600)), -(hBOOL(hAPP(hAPP(_1110602, _1110606), _1110604)))], (33742 ^ _780478) ^ [_1417100, _1417102] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1417100)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417102)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417102))), 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, _1417100))), 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), _1417100)), c_Int_Onat)))))], (4510 ^ _780478) ^ [_848896, _848898, _848900, _848902, _848904, _848906, _848908, _848910, _848912, _848914] : [-(c_Nitpick_Opair__box_Opair__box__size(_848914, _848910, _848906, _848902, _848898) = c_Nitpick_Opair__box_Opair__box__size(_848912, _848908, _848904, _848900, _848896)), _848914 = _848912, _848910 = _848908, _848906 = _848904, _848902 = _848900, _848898 = _848896], (31176 ^ _780478) ^ [_1360733, _1360735] : [c_Orderings_Obot__class_Obot(tc_fun(_1360733, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1360733), _1360735), 31179 ^ _780478 : [(31180 ^ _780478) ^ [_1360818] : [hBOOL(hAPP(_1360735, _1360818))]]], (6718 ^ _780478) ^ [_891411, _891413, _891415] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_891411), _891413)), hBOOL(hAPP(_891415, _891413)), 6729 ^ _780478 : [(6732 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_891411), 6727 ^ [_891411, _891413, _891415]), 6728 ^ [_891411, _891413, _891415])))], (6734 ^ _780478) ^ [] : [-(hBOOL(hAPP(_891415, 6728 ^ [_891411, _891413, _891415])))], (6736 ^ _780478) ^ [] : [hBOOL(hAPP(_891415, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891411, tc_HOL_Obool)), 6728 ^ [_891411, _891413, _891415]), hAPP(hAPP(c_Set_Oinsert(_891411), 6727 ^ [_891411, _891413, _891415]), c_Orderings_Obot__class_Obot(tc_fun(_891411, tc_HOL_Obool))))))], (6730 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_891411), 6728 ^ [_891411, _891413, _891415])))]], -(hBOOL(hAPP(_891415, c_Orderings_Obot__class_Obot(tc_fun(_891411, tc_HOL_Obool)))))], (44117 ^ _780478) ^ [_1663432, _1663434, _1663436] : [-(hAPP(c_List_Otl(_1663432), hAPP(hAPP(c_List_Olist_OCons(_1663432), _1663434), _1663436)) = _1663436)], (480 ^ _780478) ^ [_787690, _787692, _787694, _787696, _787698, _787700, _787702, _787704] : [-(c_List_Olistrelp(_787702, _787698, _787694, _787690)), c_List_Olistrelp(_787704, _787700, _787696, _787692), _787704 = _787702, _787700 = _787698, _787696 = _787694, _787692 = _787690], (27996 ^ _780478) ^ [_1298319, _1298321] : [hAPP(_1298319, 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), _1298319), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1298321)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1298319), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1298321)))], (12662 ^ _780478) ^ [_1004521, _1004523, _1004525] : [class_Orderings_Otop(_1004521), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1004523, _1004521)), _1004525) = c_Orderings_Otop__class_Otop(_1004521))], (50050 ^ _780478) ^ [_1792137, _1792139, _1792141, _1792143, _1792145] : [hBOOL(hAPP(hAPP(c_member(_1792137), _1792139), hAPP(c_Set_Oimage(_1792141, _1792137, _1792143), _1792145))), -(hBOOL(hAPP(hAPP(c_member(_1792141), hAPP(c_Hilbert__Choice_Oinv__into(_1792141, _1792137, _1792145, _1792143), _1792139)), _1792145)))], (33302 ^ _780478) ^ [_1409515, _1409517] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409515)), hAPP(c_Nat_OSuc, _1409517)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1409515))), 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)), _1409517)))))], (46308 ^ _780478) ^ [_1712588, _1712590] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1712588), _1712590)) = c_List_Oupt(_1712588, _1712590))], (30175 ^ _780478) ^ [_1340296] : [-(_1340296 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30178 ^ _780478 : [(30185 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340296))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1340296) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30179 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340296)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1340296) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (47167 ^ _780478) ^ [_1729368, _1729370, _1729372] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729368), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1729368))), _1729370))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729372), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1729368))), _1729370))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1729368))), hAPP(c_List_Ofilter(tc_List_Olist(_1729368), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1729368)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1729372)), c_Nat_Osize__class_Osize(tc_List_Olist(_1729368)))), c_List_Otranspose(_1729368, _1729370))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729368)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1729368)), _1729370), _1729372)))], (19884 ^ _780478) ^ [_1151455, _1151457] : [class_Groups_Olinordered__ab__group__add(_1151455), 19887 ^ _780478 : [(19894 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151455), c_Groups_Ozero__class_Ozero(_1151455)), _1151457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151455), c_Groups_Ozero__class_Ozero(_1151455)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151455), _1151457), _1151457))))], (19888 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151455), c_Groups_Ozero__class_Ozero(_1151455)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1151455), _1151457), _1151457))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151455), c_Groups_Ozero__class_Ozero(_1151455)), _1151457)))]]], (13308 ^ _780478) ^ [_1017180, _1017182, _1017184, _1017186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017180, tc_HOL_Obool)), _1017182), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017180, tc_HOL_Obool)), _1017184), _1017186))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017180, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017180, tc_HOL_Obool)), _1017182), _1017184)), _1017186)))], (37921 ^ _780478) ^ [] : [-(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))], (43219 ^ _780478) ^ [_1642241, _1642243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642241)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642243))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642241), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642243)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642241)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642241)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642243))))], (45516 ^ _780478) ^ [_1693955, _1693957, _1693959, _1693961, _1693963] : [c_List_Olist__all2(_1693955, _1693957, _1693959, _1693961, _1693963), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693955)), _1693961) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693957)), _1693963))], (41124 ^ _780478) ^ [] : [-(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))))], (22771 ^ _780478) ^ [_1204416, _1204418, _1204420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1204416), _1204418)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204420)), -(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), _1204420)), _1204416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204420)), _1204418))))], (20622 ^ _780478) ^ [_1164978] : [class_Rings_Olinordered__semidom(_1164978), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164978), c_Groups_Oone__class_Oone(_1164978)), c_Groups_Ozero__class_Ozero(_1164978)))], (29900 ^ _780478) ^ [_1335462, _1335464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1335462), _1335464)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335462, _1335464) = _1335462)], (27854 ^ _780478) ^ [_1295773, _1295775] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1295773), hAPP(c_Nat_OSuc, _1295775)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1295773, _1295775))], (33354 ^ _780478) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (49316 ^ _780478) ^ [_1776858, _1776860] : [49317 ^ _780478 : [(49318 ^ _780478) ^ [_1776924] : [hBOOL(hAPP(_1776860, _1776924))]], 49320 ^ _780478 : [(49323 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1776860, 49319 ^ [_1776858, _1776860])))], (49321 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776858), 49319 ^ [_1776858, _1776860]), c_Orderings_Otop__class_Otop(tc_fun(_1776858, tc_HOL_Obool)))))]]], (16364 ^ _780478) ^ [_1078157, _1078159, _1078161, _1078163] : [hAPP(c_Set_Oimage(_1078157, _1078159, _1078161), c_Orderings_Otop__class_Otop(tc_fun(_1078157, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1078159, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1078157, _1078159, _1078161), hAPP(c_Set_Ovimage(_1078157, _1078159, _1078161), _1078163)) = _1078163)], (3364 ^ _780478) ^ [_830625, _830627] : [_830627 = _830625, -(c_Set_OPow(_830627) = c_Set_OPow(_830625))], (49964 ^ _780478) ^ [_1790223, _1790225] : [c_Equiv__Relations_Opart__equivp(_1790223, _1790225), 49968 ^ _780478 : [(49973 ^ _780478) ^ [] : [-(c_Predicate_Otransp(_1790223, _1790225))], (49971 ^ _780478) ^ [] : [-(c_Predicate_Osymp(_1790223, _1790225))], (49969 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1790225, 49967 ^ [_1790223, _1790225]), 49967 ^ [_1790223, _1790225])))]]], (51983 ^ _780478) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (29914 ^ _780478) ^ [_1335740, _1335742] : [class_Rings_Olinordered__idom(_1335740), -(c_Groups_Osgn__class_Osgn(_1335740, c_Groups_Osgn__class_Osgn(_1335740, _1335742)) = c_Groups_Osgn__class_Osgn(_1335740, _1335742))], (36150 ^ _780478) ^ [_1467742, _1467744, _1467746, _1467748, _1467750, _1467752, _1467754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1467742, _1467744)), hAPP(hAPP(c_Product__Type_OPair(_1467742, _1467744), _1467746), _1467748)), _1467750)), -(hBOOL(hAPP(hAPP(c_member(_1467752), hAPP(hAPP(_1467754, _1467746), _1467748)), hAPP(c_Set_Oimage(tc_prod(_1467742, _1467744), _1467752, hAPP(c_Product__Type_Oprod_Oprod__case(_1467742, _1467744, _1467752), _1467754)), _1467750))))], (28296 ^ _780478) ^ [_1304199, _1304201] : [class_Groups_Oordered__ab__group__add(_1304199), -(hAPP(c_Set_Oimage(_1304199, _1304199, c_Groups_Ouminus__class_Ouminus(_1304199)), hAPP(c_SetInterval_Oord__class_OatLeast(_1304199), _1304201)) = hAPP(c_SetInterval_Oord__class_OatMost(_1304199), hAPP(c_Groups_Ouminus__class_Ouminus(_1304199), _1304201)))], (2252 ^ _780478) ^ [_813401, _813403] : [_813403 = _813401, -(c_Com_Ocom_Ocom__size(_813403) = c_Com_Ocom_Ocom__size(_813401))], (34575 ^ _780478) ^ [_1432390, _1432392] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1432390)), c_Int_OBit1(_1432392)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1432390), _1432392)))], (41953 ^ _780478) ^ [_1610922, _1610924] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1610922), tc_List_Olist(_1610922)), tc_HOL_Obool)), c_List_Olistrel(_1610922, _1610924)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1610922), c_List_Olistrel1(_1610922, _1610924)))))], (11667 ^ _780478) ^ [_985022, _985024, _985026] : [class_Orderings_Olinorder(_985022), hBOOL(hAPP(c_Finite__Set_Ofinite(_985022), _985024)), 11674 ^ _780478 : [(11681 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985022, tc_HOL_Obool)), _985024), hAPP(hAPP(c_Set_Oinsert(_985022), _985026), c_Orderings_Obot__class_Obot(tc_fun(_985022, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_985022, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_985022, hAPP(hAPP(c_Set_Oinsert(_985022), _985026), _985024)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_985022), _985026), c_Big__Operators_Olinorder__class_OMin(_985022, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985022, tc_HOL_Obool)), _985024), hAPP(hAPP(c_Set_Oinsert(_985022), _985026), c_Orderings_Obot__class_Obot(tc_fun(_985022, tc_HOL_Obool)))))))], (11675 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_985022, tc_HOL_Obool)), _985024), hAPP(hAPP(c_Set_Oinsert(_985022), _985026), c_Orderings_Obot__class_Obot(tc_fun(_985022, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_985022, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_985022, hAPP(hAPP(c_Set_Oinsert(_985022), _985026), _985024)) = _985026)]]], (34141 ^ _780478) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (36282 ^ _780478) ^ [_1470483, _1470485, _1470487, _1470489, _1470491, _1470493] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470483, tc_fun(_1470485, tc_HOL_Obool))), _1470487), _1470489), _1470491), _1470493)), -(hBOOL(hAPP(hAPP(_1470489, _1470491), _1470493)))], (38885 ^ _780478) ^ [_1531910, _1531912, _1531914, _1531916, _1531918, _1531920] : [hBOOL(hAPP(hAPP(c_member(_1531910), _1531912), _1531914)), 38888 ^ _780478 : [(38895 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531916, tc_HOL_Obool)), _1531918), _1531920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531916, _1531910), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531916, _1531910), _1531918), hAPP(c_COMBK(tc_fun(_1531910, tc_HOL_Obool), _1531916), _1531914))), hAPP(hAPP(c_Product__Type_OSigma(_1531916, _1531910), _1531920), hAPP(c_COMBK(tc_fun(_1531910, tc_HOL_Obool), _1531916), _1531914)))))], (38889 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531916, _1531910), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1531916, _1531910), _1531918), hAPP(c_COMBK(tc_fun(_1531910, tc_HOL_Obool), _1531916), _1531914))), hAPP(hAPP(c_Product__Type_OSigma(_1531916, _1531910), _1531920), hAPP(c_COMBK(tc_fun(_1531910, tc_HOL_Obool), _1531916), _1531914)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531916, tc_HOL_Obool)), _1531918), _1531920)))]]], (22881 ^ _780478) ^ [_1206362, _1206364, _1206366] : [class_Rings_Osemiring__1(_1206362), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206362), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206364), _1206366)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206362), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206362), _1206364)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206362), _1206366)))], (31967 ^ _780478) ^ [_1384382, _1384384, _1384386, _1384388] : [class_Lattices_Osemilattice__sup(_1384382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384382), _1384384)), 31977 ^ _780478 : [(31980 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384382), 31976 ^ [_1384382, _1384384, _1384386, _1384388]), _1384386))], (31978 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1384382), 31976 ^ [_1384382, _1384384, _1384386, _1384388]), _1384384)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384382), hAPP(hAPP(c_Finite__Set_Ofold(_1384382, _1384382, c_Lattices_Osemilattice__sup__class_Osup(_1384382)), _1384388), _1384384)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1384382), _1384386), _1384388))))], (35299 ^ _780478) ^ [_1445945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1445945))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1445945)))], (13508 ^ _780478) ^ [_1021330, _1021332, _1021334, _1021336] : [c_Fun_Oinj__on(_1021330, _1021332, _1021334, c_Orderings_Otop__class_Otop(tc_fun(_1021330, tc_HOL_Obool))), 13511 ^ _780478 : [(13525 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1021332), _1021336), hAPP(c_Set_Oimage(_1021330, _1021332, _1021334), c_Orderings_Otop__class_Otop(tc_fun(_1021330, tc_HOL_Obool)))))), 13526 ^ _780478 : [(13527 ^ _780478) ^ [_1021733] : [_1021336 = hAPP(_1021334, _1021733), 13531 ^ _780478 : [(13534 ^ _780478) ^ [] : [13530 ^ [_1021330, _1021332, _1021334, _1021336, _1021733] = _1021733], (13532 ^ _780478) ^ [] : [-(_1021336 = hAPP(_1021334, 13530 ^ [_1021330, _1021332, _1021334, _1021336, _1021733]))]]]]], (13512 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1021332), _1021336), hAPP(c_Set_Oimage(_1021330, _1021332, _1021334), c_Orderings_Otop__class_Otop(tc_fun(_1021330, tc_HOL_Obool))))), 13516 ^ _780478 : [(13519 ^ _780478) ^ [_1021595] : [_1021336 = hAPP(_1021334, _1021595), -(_1021595 = 13515 ^ [_1021330, _1021332, _1021334, _1021336])], (13517 ^ _780478) ^ [] : [-(_1021336 = hAPP(_1021334, 13515 ^ [_1021330, _1021332, _1021334, _1021336]))]]]]], (51329 ^ _780478) ^ [_1820294, _1820296, _1820298] : [51330 ^ _780478 : [(51333 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820296), _1820298))], (51331 ^ _780478) ^ [] : [_1820294 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1820294), _1820296)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1820294), _1820298))))], (51753 ^ _780478) ^ [_1827475, _1827477] : [class_Lattices_Obounded__lattice(_1827475), -(class_Lattices_Obounded__lattice(tc_fun(_1827477, _1827475)))], (4756 ^ _780478) ^ [_852949, _852951] : [_852951 = _852949, -(c_DSequence_Oempty(_852951) = c_DSequence_Oempty(_852949))], (18590 ^ _780478) ^ [_1129113, _1129115, _1129117] : [class_Complete__Lattice_Ocomplete__lattice(_1129113), -(c_Complete__Lattice_OInf__class_OInf(_1129113, hAPP(hAPP(c_Set_Oinsert(_1129113), _1129115), _1129117)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1129113), _1129115), c_Complete__Lattice_OInf__class_OInf(_1129113, _1129117)))], (42786 ^ _780478) ^ [_1633695, _1633697, _1633699] : [hBOOL(hAPP(c_List_Odistinct(_1633695), _1633697)), -(hBOOL(hAPP(c_List_Odistinct(_1633695), hAPP(hAPP(c_List_Otake(_1633695), _1633699), _1633697))))], (30915 ^ _780478) ^ [_1354846, _1354848] : [-(c_Nitpick_Oint__lcm(_1354846, _1354848) = 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), _1354846)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1354848)))))], (37754 ^ _780478) ^ [_1501052, _1501054] : [-(c_Relation_OId__on(_1501052, _1501054) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501052, tc_fun(tc_prod(_1501052, _1501052), tc_HOL_Obool)), _1501054), hAPP(hAPP(c_COMBC(_1501052, tc_fun(tc_prod(_1501052, _1501052), tc_HOL_Obool), tc_fun(tc_prod(_1501052, _1501052), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1501052, _1501052), tc_fun(tc_fun(tc_prod(_1501052, _1501052), tc_HOL_Obool), tc_fun(tc_prod(_1501052, _1501052), tc_HOL_Obool)), _1501052), c_Set_Oinsert(tc_prod(_1501052, _1501052))), hAPP(hAPP(c_COMBS(_1501052, _1501052, tc_prod(_1501052, _1501052)), c_Product__Type_OPair(_1501052, _1501052)), c_COMBI(_1501052)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501052, _1501052), tc_HOL_Obool)))))], (33462 ^ _780478) ^ [_1411941, _1411943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411941)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411943)))), 33465 ^ _780478 : [(33468 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1411943))], (33466 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411941), _1411943)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411941), _1411943))], (14008 ^ _780478) ^ [_1030949, _1030951, _1030953] : [_1030951 = _1030953, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030949), _1030951) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030949), _1030953))], (14393 ^ _780478) ^ [_1037581, _1037583] : [-(_1037581 = _1037583), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037581), _1037583))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037583), _1037581)))], (48038 ^ _780478) ^ [_1748803, _1748805, _1748807] : [48039 ^ _780478 : [(48040 ^ _780478) ^ [_1748880, _1748882] : [_1748807 = hAPP(hAPP(c_List_Oappend(_1748803), _1748882), hAPP(hAPP(c_List_Olist_OCons(_1748803), _1748805), _1748880))]], -(hBOOL(hAPP(hAPP(c_member(_1748803), _1748805), hAPP(c_List_Oset(_1748803), _1748807))))], (9570 ^ _780478) ^ [_945025, _945027] : [class_Orderings_Olinorder(_945025), -(c_Big__Operators_Olinorder__class_OMin(_945025, hAPP(hAPP(c_Set_Oinsert(_945025), _945027), c_Orderings_Obot__class_Obot(tc_fun(_945025, tc_HOL_Obool)))) = _945027)], (37991 ^ _780478) ^ [_1508633, _1508635, _1508637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1508633, _1508633), tc_HOL_Obool)), _1508635), _1508637)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1508633, tc_HOL_Obool)), c_Wellfounded_Oacc(_1508633, _1508637)), c_Wellfounded_Oacc(_1508633, _1508635))))], (35774 ^ _780478) ^ [_1458325] : [-(_1458325 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1458325), 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)))))], (3166 ^ _780478) ^ [_827524, _827526, _827528, _827530] : [-(c_Big__Operators_Olattice__class_OInf__fin(_827530, _827526) = c_Big__Operators_Olattice__class_OInf__fin(_827528, _827524)), _827530 = _827528, _827526 = _827524], (31905 ^ _780478) ^ [_1383035, _1383037, _1383039] : [31907 ^ _780478 : [(31912 ^ _780478) ^ [] : [hBOOL(hAPP(_1383037, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 31906 ^ [_1383035, _1383037, _1383039]), _1383035)))], (31910 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1383037, 31906 ^ [_1383035, _1383037, _1383039])))], (31908 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31906 ^ [_1383035, _1383037, _1383039]), _1383035)))]], hBOOL(hAPP(_1383037, _1383039)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1383039), _1383035)), -(hBOOL(hAPP(_1383037, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27156 ^ _780478) ^ [_1283560] : [c_Nat__Transfer_Onat__set(_1283560), 27159 ^ _780478 : [(27160 ^ _780478) ^ [_1283626] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1283626), _1283560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1283626)))]]], (44883 ^ _780478) ^ [_1679899, _1679901, _1679903, _1679905] : [hBOOL(hAPP(c_List_Odistinct(_1679899), hAPP(hAPP(c_List_Omap(_1679901, _1679899), _1679903), _1679905))), 44886 ^ _780478 : [(44889 ^ _780478) ^ [] : [-(c_Fun_Oinj__on(_1679901, _1679899, _1679903, hAPP(c_List_Oset(_1679901), _1679905)))], (44887 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1679901), _1679905)))]]], (38644 ^ _780478) ^ [_1524466, _1524468] : [-(hAPP(c_Relation_ODomain(_1524466, _1524468), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524466, _1524468), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1524466, tc_HOL_Obool)))], (48497 ^ _780478) ^ [_1758385, _1758387, _1758389, _1758391, _1758393] : [hBOOL(hAPP(hAPP(_1758389, _1758393), _1758391)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1758385, _1758387, _1758389), _1758391), _1758393)))], (12806 ^ _780478) ^ [_1007415, _1007417] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1007415, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1007415, tc_HOL_Obool)), _1007417)), _1007417) = c_Orderings_Otop__class_Otop(tc_fun(_1007415, tc_HOL_Obool)))], (6612 ^ _780478) ^ [_888868, _888870, _888872] : [-(hAPP(hAPP(c_Set_Oinsert(_888868), _888870), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888868, tc_HOL_Obool)), _888872), hAPP(hAPP(c_Set_Oinsert(_888868), _888870), c_Orderings_Obot__class_Obot(tc_fun(_888868, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_888868), _888870), _888872))], (8532 ^ _780478) ^ [_927800, _927802, _927804, _927806, _927808] : [class_Groups_Oab__semigroup__mult(_927800), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_927800, _927800, c_Groups_Otimes__class_Otimes(_927800), _927802, _927804), _927806)), hBOOL(hAPP(hAPP(c_member(_927800), _927808), _927804)), -(hBOOL(hAPP(hAPP(c_member(_927800), _927802), _927804))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_927800, _927800, c_Groups_Otimes__class_Otimes(_927800), _927808, hAPP(hAPP(c_Set_Oinsert(_927800), _927802), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_927800, tc_HOL_Obool)), _927804), hAPP(hAPP(c_Set_Oinsert(_927800), _927808), c_Orderings_Obot__class_Obot(tc_fun(_927800, tc_HOL_Obool)))))), _927806)))], (47131 ^ _780478) ^ [_1728744, _1728746, _1728748] : [class_Orderings_Olinorder(_1728744), c_List_Olinorder__class_Osorted(_1728744, hAPP(c_List_Orev(_1728744), _1728746)), 47138 ^ _780478 : [(47145 ^ _780478) ^ [] : [-(_1728746 = c_List_Olist_ONil(_1728744)), -(c_List_Ofoldr(_1728744, _1728744, c_Orderings_Oord__class_Omax(_1728744), _1728746, _1728748) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1728744), hAPP(hAPP(c_List_Onth(_1728744), _1728746), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1728748))], (47139 ^ _780478) ^ [] : [_1728746 = c_List_Olist_ONil(_1728744), -(c_List_Ofoldr(_1728744, _1728744, c_Orderings_Oord__class_Omax(_1728744), _1728746, _1728748) = _1728748)]]], (1164 ^ _780478) ^ [_797892, _797894] : [-(class_Groups_Oordered__ab__group__add(_797892)), _797894 = _797892, class_Groups_Oordered__ab__group__add(_797894)], (18534 ^ _780478) ^ [_1127883, _1127885, _1127887, _1127889, _1127891] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1127883, tc_fun(_1127885, tc_HOL_Obool)), _1127887), hAPP(hAPP(c_COMBB(tc_fun(_1127885, tc_HOL_Obool), tc_fun(_1127885, tc_HOL_Obool), _1127883), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127885, tc_HOL_Obool)), _1127889)), _1127891)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127885, tc_HOL_Obool)), _1127889), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127883, tc_fun(_1127885, tc_HOL_Obool)), _1127887), _1127891)))], (15001 ^ _780478) ^ [_1050172, _1050174, _1050176, _1050178, _1050180, _1050182] : [-(hBOOL(hAPP(hAPP(c_member(_1050172), _1050174), c_SetInterval_Oord_OgreaterThanAtMost(_1050172, _1050176, _1050178, _1050180, _1050182)))), hBOOL(hAPP(hAPP(_1050178, _1050180), _1050174)), hBOOL(hAPP(hAPP(_1050176, _1050174), _1050182))], (24165 ^ _780478) ^ [_1230400, _1230402] : [class_Divides_Osemiring__div(_1230400), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230400), _1230402), c_Groups_Oone__class_Oone(_1230400)) = _1230402)], (17689 ^ _780478) ^ [_1109825, _1109827] : [class_Complete__Lattice_Ocomplete__lattice(_1109825), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109825), _1109827)), -(c_Complete__Lattice_OInf__class_OInf(_1109825, _1109827) = hAPP(hAPP(c_Finite__Set_Ofold(_1109825, _1109825, c_Lattices_Osemilattice__inf__class_Oinf(_1109825)), c_Orderings_Otop__class_Otop(_1109825)), _1109827))], (14313 ^ _780478) ^ [_1036102, _1036104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036102), _1036104)), -(_1036102 = _1036104), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036102), _1036104)))], (2604 ^ _780478) ^ [_818851, _818853] : [_818853 = _818851, -(c_Nitpick_Ozero__frac(_818853) = c_Nitpick_Ozero__frac(_818851))], (29221 ^ _780478) ^ [_1322871, _1322873, _1322875, _1322877] : [class_Divides_Oring__div(_1322871), -(c_Divides_Odiv__class_Omod(_1322871, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322871), _1322873), _1322875), _1322877) = c_Divides_Odiv__class_Omod(_1322871, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322871), _1322873), c_Divides_Odiv__class_Omod(_1322871, _1322875, _1322877)), _1322877))], (46109 ^ _780478) ^ [_1707215, _1707217] : [-(c_List_OremoveAll(_1707215, _1707217) = c_List_Ofilter(_1707215, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1707215), c_fNot), hAPP(c_fequal, _1707217))))], (37399 ^ _780478) ^ [_1492314] : [c_Code__Numeral_OSuc__code__numeral(_1492314) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (3140 ^ _780478) ^ [_827141, _827143] : [_827143 = _827141, -(c_List_Orotate1(_827143) = c_List_Orotate1(_827141))], (1454 ^ _780478) ^ [_801517, _801519] : [-(class_Groups_Ouminus(_801517)), _801519 = _801517, class_Groups_Ouminus(_801519)], (30203 ^ _780478) ^ [_1340782, _1340784, _1340786, _1340788, _1340790] : [class_Groups_Ocomm__monoid__add(_1340782), class_Groups_Ocomm__monoid__mult(_1340782), _1340784 = _1340786, c_Nat__Transfer_Onat__set(_1340786), 30221 ^ _780478 : [(30224 ^ _780478) ^ [] : [hAPP(_1340788, 30220 ^ [_1340782, _1340784, _1340786, _1340788, _1340790]) = hAPP(_1340790, 30220 ^ [_1340782, _1340784, _1340786, _1340788, _1340790])], (30222 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30220 ^ [_1340782, _1340784, _1340786, _1340788, _1340790])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1340782), _1340788), _1340784) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1340782), _1340790), _1340786))], (6264 ^ _780478) ^ [_881159, _881161, _881163, _881165, _881167] : [c_Finite__Set_Ofolding__one__idem(_881159, _881161, _881163), hBOOL(hAPP(c_Finite__Set_Ofinite(_881159), _881165)), -(_881165 = c_Orderings_Obot__class_Obot(tc_fun(_881159, tc_HOL_Obool))), -(hAPP(_881163, hAPP(hAPP(c_Set_Oinsert(_881159), _881167), _881165)) = hAPP(hAPP(_881161, _881167), hAPP(_881163, _881165)))], (13072 ^ _780478) ^ [_1012077, _1012079] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012077, tc_HOL_Obool)), _1012079), c_Orderings_Obot__class_Obot(tc_fun(_1012077, tc_HOL_Obool))) = _1012079)], (44187 ^ _780478) ^ [_1664837, _1664839, _1664841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664837)), _1664839)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1664837, _1664841), _1664839) = _1664839)], (43835 ^ _780478) ^ [_1657064, _1657066, _1657068, _1657070] : [-(hAPP(hAPP(c_List_Odrop(_1657064), hAPP(c_Nat_OSuc, _1657066)), hAPP(hAPP(c_List_Olist_OCons(_1657064), _1657068), _1657070)) = hAPP(hAPP(c_List_Odrop(_1657064), _1657066), _1657070))], (7752 ^ _780478) ^ [_911552, _911554, _911556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911552, tc_HOL_Obool)), _911554), _911556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911552, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_911552, tc_fun(_911552, tc_HOL_Obool), tc_HOL_Obool), c_member(_911552)), _911554)), hAPP(hAPP(c_COMBC(_911552, tc_fun(_911552, tc_HOL_Obool), tc_HOL_Obool), c_member(_911552)), _911556))))], (13872 ^ _780478) ^ [_1028506, _1028508] : [13873 ^ _780478 : [(13874 ^ _780478) ^ [_1028556] : [_1028508 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028506), _1028556)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028506), _1028508)))], (17446 ^ _780478) ^ [_1103998, _1104000, _1104002, _1104004, _1104006] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103998, tc_fun(_1104000, tc_HOL_Obool)), _1104002), hAPP(hAPP(c_COMBC(_1103998, tc_fun(_1104000, tc_HOL_Obool), tc_fun(_1104000, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1104000, tc_HOL_Obool), tc_fun(tc_fun(_1104000, tc_HOL_Obool), tc_fun(_1104000, tc_HOL_Obool)), _1103998), c_Groups_Ominus__class_Ominus(tc_fun(_1104000, tc_HOL_Obool))), _1104004)), _1104006)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1104000, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103998, tc_fun(_1104000, tc_HOL_Obool)), _1104002), _1104004)), _1104006))], (32118 ^ _780478) ^ [_1386971, _1386973, _1386975, _1386977, _1386979, _1386981] : [c_Com_Ocom_OCond(_1386971, _1386973, _1386975) = c_Com_Ocom_OLocal(_1386977, _1386979, _1386981)], (29195 ^ _780478) ^ [_1322310, _1322312, _1322314, _1322316, _1322318, _1322320] : [class_Divides_Oring__div(_1322310), c_Divides_Odiv__class_Omod(_1322310, _1322312, _1322314) = c_Divides_Odiv__class_Omod(_1322310, _1322316, _1322314), c_Divides_Odiv__class_Omod(_1322310, _1322318, _1322314) = c_Divides_Odiv__class_Omod(_1322310, _1322320, _1322314), -(c_Divides_Odiv__class_Omod(_1322310, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322310), _1322312), _1322318), _1322314) = c_Divides_Odiv__class_Omod(_1322310, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322310), _1322316), _1322320), _1322314))], (1684 ^ _780478) ^ [_804392, _804394] : [-(class_Rings_Ocomm__semiring__1(_804392)), _804394 = _804392, class_Rings_Ocomm__semiring__1(_804394)], (32868 ^ _780478) ^ [_1401420, _1401422, _1401424, _1401426] : [class_Fields_Olinordered__field__inverse__zero(_1401420), class_Int_Onumber(_1401420), 32875 ^ _780478 : [(32876 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401420), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1401420), _1401422), _1401424)), hAPP(c_Int_Onumber__class_Onumber__of(_1401420), _1401426))), 32879 ^ _780478 : [(32886 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401420), c_Groups_Ozero__class_Ozero(_1401420)), _1401424))), 32889 ^ _780478 : [(32896 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401420), _1401424), c_Groups_Ozero__class_Ozero(_1401420)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401420), c_Groups_Ozero__class_Ozero(_1401420)), hAPP(c_Int_Onumber__class_Onumber__of(_1401420), _1401426))))], (32890 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401420), _1401424), c_Groups_Ozero__class_Ozero(_1401420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401420), hAPP(c_Int_Onumber__class_Onumber__of(_1401420), _1401426)), _1401424)), _1401422)))]]], (32880 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401420), c_Groups_Ozero__class_Ozero(_1401420)), _1401424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401420), _1401422), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401420), hAPP(c_Int_Onumber__class_Onumber__of(_1401420), _1401426)), _1401424))))]]], (32902 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401420), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1401420), _1401422), _1401424)), hAPP(c_Int_Onumber__class_Onumber__of(_1401420), _1401426)))), 32905 ^ _780478 : [(32908 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401420), _1401422), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401420), hAPP(c_Int_Onumber__class_Onumber__of(_1401420), _1401426)), _1401424)))], (32906 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401420), c_Groups_Ozero__class_Ozero(_1401420)), _1401424)))]], 32909 ^ _780478 : [(32912 ^ _780478) ^ [] : [32913 ^ _780478 : [(32916 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1401420), hAPP(c_Int_Onumber__class_Onumber__of(_1401420), _1401426)), _1401424)), _1401422))], (32914 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401420), _1401424), c_Groups_Ozero__class_Ozero(_1401420))))]], 32917 ^ _780478 : [(32920 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1401420), c_Groups_Ozero__class_Ozero(_1401420)), hAPP(c_Int_Onumber__class_Onumber__of(_1401420), _1401426)))], (32918 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401420), _1401424), c_Groups_Ozero__class_Ozero(_1401420)))]]], (32910 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1401420), c_Groups_Ozero__class_Ozero(_1401420)), _1401424))]]]]], (52343 ^ _780478) ^ [_1833744, _1833746] : [_1833744 = _1833746, -(hBOOL(hAPP(hAPP(c_fequal, _1833744), _1833746)))], (47095 ^ _780478) ^ [_1727826, _1727828, _1727830] : [-(hAPP(c_List_Orev(_1727826), hAPP(hAPP(c_List_Odrop(_1727826), _1727828), _1727830)) = hAPP(hAPP(c_List_Otake(_1727826), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727826)), _1727830)), _1727828)), hAPP(c_List_Orev(_1727826), _1727830)))], (44907 ^ _780478) ^ [_1680378, _1680380, _1680382, _1680384] : [class_Groups_Oab__group__add(_1680378), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1680378), hAPP(c_List_Omonoid__add__class_Olistsum(_1680378), hAPP(hAPP(c_List_Omap(_1680380, _1680378), _1680382), _1680384))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1680378), hAPP(hAPP(c_List_Omap(_1680380, _1680378), hAPP(c_Fun_Ocomp(_1680378, _1680378, _1680380, c_Groups_Ouminus__class_Ouminus(_1680378)), _1680382)), _1680384)))], (33941 ^ _780478) ^ [_1421632] : [c_Int_OPls = c_Int_OBit1(_1421632)], (28410 ^ _780478) ^ [_1306205, _1306207] : [class_Orderings_Olinorder(_1306205), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1306205, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1306205), _1306207)) = hAPP(c_SetInterval_Oord__class_OatMost(_1306205), _1306207))], (26450 ^ _780478) ^ [_1270760, _1270762, _1270764, _1270766] : [class_Fields_Ofield__inverse__zero(_1270760), -(_1270762 = c_Groups_Ozero__class_Ozero(_1270760)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270760), _1270764), _1270762)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270760), _1270766), _1270762)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270760), _1270764), _1270766))], (45333 ^ _780478) ^ [_1689228, _1689230, _1689232, _1689234] : [hBOOL(hAPP(c_List_Olistsp(_1689228, _1689230), hAPP(hAPP(c_List_Oappend(_1689228), _1689232), _1689234))), 45336 ^ _780478 : [(45339 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1689228, _1689230), _1689234)))], (45337 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1689228, _1689230), _1689232)))]]], (1894 ^ _780478) ^ [_807017, _807019] : [-(class_Rings_Odvd(_807017)), _807019 = _807017, class_Rings_Odvd(_807019)], (25645 ^ _780478) ^ [_1256295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256295)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1256295)) = _1256295)], (22289 ^ _780478) ^ [_1194900, _1194902, _1194904, _1194906] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_1194900)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1194900), _1194902), _1194904), _1194906)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14883 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (14269 ^ _780478) ^ [_1035406, _1035408] : [-(hAPP(c_Finite__Set_Ocard(_1035406), _1035408) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1035406, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1035406), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1035408))], (47226 ^ _780478) ^ [_1730720, _1730722, _1730724, _1730726, _1730728] : [-(hAPP(hAPP(c_List_Ozip(_1730720, _1730722), c_List_OtakeWhile(_1730720, _1730724, _1730726)), _1730728) = c_List_OtakeWhile(tc_prod(_1730720, _1730722), hAPP(c_Fun_Ocomp(_1730720, tc_HOL_Obool, tc_prod(_1730720, _1730722), _1730724), c_Product__Type_Ofst(_1730720, _1730722)), hAPP(hAPP(c_List_Ozip(_1730720, _1730722), _1730726), _1730728)))], (43889 ^ _780478) ^ [_1658320, _1658322] : [-(hAPP(hAPP(c_List_Odrop(_1658320), _1658322), c_List_Olist_ONil(_1658320)) = c_List_Olist_ONil(_1658320))], (16999 ^ _780478) ^ [_1093037, _1093039, _1093041] : [class_Orderings_Olinorder(_1093037), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093037), _1093039)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093037), _1093041)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1093037, tc_HOL_Obool)), _1093039), _1093041) = c_Orderings_Obot__class_Obot(tc_fun(_1093037, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093037), c_Big__Operators_Olinorder__class_OMin(_1093037, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1093037, tc_HOL_Obool)), _1093039), _1093041))), c_Big__Operators_Olinorder__class_OMin(_1093037, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1093037, tc_HOL_Obool)), _1093039), _1093041))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093037), c_Big__Operators_Olinorder__class_OMin(_1093037, _1093039)), c_Big__Operators_Olinorder__class_OMin(_1093037, _1093041)))], (50944 ^ _780478) ^ [_1812929, _1812931, _1812933, _1812935, _1812937, _1812939, _1812941, _1812943] : [c_Finite__Set_Ofolding__image(_1812929, _1812931, _1812933, _1812935, _1812937), hBOOL(hAPP(c_Finite__Set_Ofinite(_1812931), _1812939)), 50954 ^ _780478 : [(50957 ^ _780478) ^ [] : [hAPP(_1812941, 50953 ^ [_1812929, _1812931, _1812933, _1812935, _1812937, _1812939, _1812941, _1812943]) = hAPP(_1812943, 50953 ^ [_1812929, _1812931, _1812933, _1812935, _1812937, _1812939, _1812941, _1812943])], (50955 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1812931), 50953 ^ [_1812929, _1812931, _1812933, _1812935, _1812937, _1812939, _1812941, _1812943]), _1812939)))]], -(hAPP(hAPP(_1812937, _1812941), _1812939) = hAPP(hAPP(_1812937, _1812943), _1812939))], (18532 ^ _780478) ^ [_1127851] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1127851)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1127851)], (35407 ^ _780478) ^ [_1447579] : [class_Int_Onumber__ring(_1447579), -(hAPP(c_Int_Onumber__class_Onumber__of(_1447579), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1447579), c_Groups_Oone__class_Oone(_1447579)))], (33376 ^ _780478) ^ [_1410619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410619), 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), _1410619)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (47586 ^ _780478) ^ [_1738207, _1738209] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1738207)), _1738209)), 47592 ^ _780478 : [(47595 ^ _780478) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1738207), 47591 ^ [_1738207, _1738209]))], (47593 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1738207)), 47591 ^ [_1738207, _1738209]), hAPP(c_List_Oset(tc_List_Olist(_1738207)), _1738209))))]], 47599 ^ _780478 : [(47603 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1738207)), 47601 ^ [_1738207, _1738209]), hAPP(c_List_Oset(tc_List_Olist(_1738207)), _1738209))))], (47605 ^ _780478) ^ [] : [47598 ^ [_1738207, _1738209] = 47601 ^ [_1738207, _1738209]], (47607 ^ _780478) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1738207, tc_HOL_Obool)), hAPP(c_List_Oset(_1738207), 47598 ^ [_1738207, _1738209])), hAPP(c_List_Oset(_1738207), 47601 ^ [_1738207, _1738209])) = c_Orderings_Obot__class_Obot(tc_fun(_1738207, tc_HOL_Obool))], (47600 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1738207)), 47598 ^ [_1738207, _1738209]), hAPP(c_List_Oset(tc_List_Olist(_1738207)), _1738209))))]], -(hBOOL(hAPP(c_List_Odistinct(_1738207), c_List_Oconcat(_1738207, _1738209))))], (18049 ^ _780478) ^ [_1116441] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116441, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1116441, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1116441, tc_HOL_Obool)))], (9348 ^ _780478) ^ [_940499, _940501, _940503, _940505] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_940499), 9351 ^ _780478 : [(9358 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940499), _940503), _940505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940499), _940501), _940503)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940499), _940501), _940505))))], (9352 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940499), _940501), _940503)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940499), _940501), _940505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940499), _940503), _940505)))]]], (11125 ^ _780478) ^ [_974812, _974814, _974816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974812, tc_HOL_Obool)), _974814), _974816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974812, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_974812, tc_HOL_Obool)), _974816)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_974812, tc_HOL_Obool)), _974814))))], (37265 ^ _780478) ^ [_1489546, _1489548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489548), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1489546), _1489548) = 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), _1489546), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489548)))))], (19394 ^ _780478) ^ [_1143600, _1143602] : [class_Groups_Ogroup__add(_1143600), 19397 ^ _780478 : [(19404 ^ _780478) ^ [] : [c_Groups_Ozero__class_Ozero(_1143600) = _1143602, -(c_Groups_Ozero__class_Ozero(_1143600) = hAPP(c_Groups_Ouminus__class_Ouminus(_1143600), _1143602))], (19398 ^ _780478) ^ [] : [c_Groups_Ozero__class_Ozero(_1143600) = hAPP(c_Groups_Ouminus__class_Ouminus(_1143600), _1143602), -(c_Groups_Ozero__class_Ozero(_1143600) = _1143602)]]], (13914 ^ _780478) ^ [_1029233, _1029235, _1029237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029233), _1029235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029233), _1029237)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029235), _1029237))))], (45061 ^ _780478) ^ [_1683652, _1683654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1683652), _1683654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1683652)), hAPP(c_Code__Numeral_Oof__nat, _1683654))))], (16831 ^ _780478) ^ [_1089330, _1089332, _1089334, _1089336, _1089338] : [class_Groups_Ocomm__monoid__mult(_1089330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089332), _1089334)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089332), _1089336)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1089332, tc_HOL_Obool)), _1089334), _1089336) = c_Orderings_Obot__class_Obot(tc_fun(_1089332, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089332, _1089330), _1089338), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1089332, tc_HOL_Obool)), _1089334), _1089336)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089330), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089332, _1089330), _1089338), _1089334)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1089332, _1089330), _1089338), _1089336)))], (52117 ^ _780478) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (28324 ^ _780478) ^ [_1304717, _1304719, _1304721] : [class_Orderings_Oord(_1304717), 28327 ^ _780478 : [(28334 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304717), _1304719), _1304721)), -(hBOOL(hAPP(hAPP(c_member(_1304717), _1304719), hAPP(c_SetInterval_Oord__class_OatMost(_1304717), _1304721))))], (28328 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1304717), _1304719), hAPP(c_SetInterval_Oord__class_OatMost(_1304717), _1304721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304717), _1304719), _1304721)))]]], (45285 ^ _780478) ^ [_1688233, _1688235, _1688237, _1688239] : [hBOOL(hAPP(c_List_Olistsp(_1688233, hAPP(hAPP(c_COMBS(_1688233, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1688233), c_fconj), _1688235)), _1688237)), _1688239)), 45288 ^ _780478 : [(45291 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1688233, _1688237), _1688239)))], (45289 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1688233, _1688235), _1688239)))]]], (18037 ^ _780478) ^ [_1116213, _1116215, _1116217] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1116213)), _1116215) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1116213)), _1116217), -(_1116215 = _1116217)], (13244 ^ _780478) ^ [_1015842, _1015844] : [class_Orderings_Otop(_1015842), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1015842), _1015844), c_Orderings_Otop__class_Otop(_1015842))))], (30811 ^ _780478) ^ [_1352840, _1352842] : [class_Complete__Lattice_Ocomplete__lattice(_1352840), -(c_Complete__Lattice_OSup__class_OSup(_1352840, hAPP(hAPP(c_Set_Oinsert(_1352840), _1352842), c_Orderings_Obot__class_Obot(tc_fun(_1352840, tc_HOL_Obool)))) = _1352842)], (50 ^ _780478) ^ [_781283, _781285, _781287, _781289, _781291, _781293] : [-(c_Big__Operators_Osemilattice__big(_781291, _781287, _781283)), c_Big__Operators_Osemilattice__big(_781293, _781289, _781285), _781293 = _781291, _781289 = _781287, _781285 = _781283], (36411 ^ _780478) ^ [_1473359] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1473359) = 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), _1473359), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (35962 ^ _780478) ^ [_1463391, _1463393] : [-(_1463391 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1463393, _1463391), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1463393), _1463391)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1463393, _1463391)))))], (52043 ^ _780478) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (16444 ^ _780478) ^ [_1080550, _1080552, _1080554] : [class_Lattices_Olattice(_1080550), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080550), _1080552)), hBOOL(hAPP(hAPP(c_member(_1080550), _1080554), _1080552)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1080550), _1080554), c_Big__Operators_Olattice__class_OSup__fin(_1080550, _1080552)) = _1080554)], (40558 ^ _780478) ^ [_1573810, _1573812, _1573814] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573810, _1573810), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573810, _1573810), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573810, _1573812)), c_Transitive__Closure_Ortrancl(_1573810, _1573814))), c_Transitive__Closure_Ortrancl(_1573810, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573810, _1573810), tc_HOL_Obool)), _1573812), _1573814)))))], (43692 ^ _780478) ^ [_1653113, _1653115, _1653117] : [hBOOL(hAPP(c_List_Odistinct(_1653113), hAPP(hAPP(c_List_Oappend(_1653113), _1653115), _1653117))), 43695 ^ _780478 : [(43700 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1653113, tc_HOL_Obool)), hAPP(c_List_Oset(_1653113), _1653115)), hAPP(c_List_Oset(_1653113), _1653117)) = c_Orderings_Obot__class_Obot(tc_fun(_1653113, tc_HOL_Obool)))], (43698 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1653113), _1653117)))], (43696 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1653113), _1653115)))]]], (49514 ^ _780478) ^ [_1781917, _1781919, _1781921, _1781923] : [c_Wellfounded_Omax__extp(_1781917, _1781919, _1781921, _1781923), 49517 ^ _780478 : [(49520 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1781917), _1781923)))], (49522 ^ _780478) ^ [] : [_1781923 = c_Orderings_Obot__class_Obot(tc_fun(_1781917, tc_HOL_Obool))], (49524 ^ _780478) ^ [_1782133] : [hBOOL(hAPP(hAPP(c_member(_1781917), _1782133), _1781921)), 49528 ^ _780478 : [(49531 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1781919, _1782133), 49527 ^ [_1781917, _1781919, _1781921, _1781923, _1782133])))], (49529 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1781917), 49527 ^ [_1781917, _1781919, _1781921, _1781923, _1782133]), _1781923)))]]], (49518 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1781917), _1781921)))]]], (5554 ^ _780478) ^ [_865544, _865546, _865548, _865550, _865552, _865554] : [-(c_Divides_Odiv__class_Omod(_865554, _865550, _865546) = c_Divides_Odiv__class_Omod(_865552, _865548, _865544)), _865554 = _865552, _865550 = _865548, _865546 = _865544], (4254 ^ _780478) ^ [_844840, _844842] : [_844842 = _844840, -(c_Orderings_Oord__class_Omin(_844842) = c_Orderings_Oord__class_Omin(_844840))], (50596 ^ _780478) ^ [_1803970, _1803972, _1803974] : [c_Fun_Obij__betw(_1803970, _1803972, _1803974, c_Orderings_Otop__class_Otop(tc_fun(_1803970, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1803972, tc_HOL_Obool))), 50599 ^ _780478 : [(50602 ^ _780478) ^ [] : [-(hAPP(c_Set_Oimage(_1803970, _1803972, _1803974), c_Orderings_Otop__class_Otop(tc_fun(_1803970, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1803972, tc_HOL_Obool)))], (50600 ^ _780478) ^ [] : [-(c_Fun_Oinj__on(_1803970, _1803972, _1803974, c_Orderings_Otop__class_Otop(tc_fun(_1803970, tc_HOL_Obool))))]]], (17955 ^ _780478) ^ [_1114817, _1114819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114819), hAPP(c_Nat_OSuc, _1114817))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114817), _1114819))], (3596 ^ _780478) ^ [_834261, _834263, _834265, _834267] : [-(c_List_Olinorder__class_Osorted__list__of__set(_834267, _834263) = c_List_Olinorder__class_Osorted__list__of__set(_834265, _834261)), _834267 = _834265, _834263 = _834261], (11567 ^ _780478) ^ [_983159, _983161, _983163] : [class_Orderings_Olinorder(_983159), hBOOL(hAPP(c_Finite__Set_Ofinite(_983159), _983161)), -(c_Big__Operators_Olinorder__class_OMin(_983159, hAPP(hAPP(c_Set_Oinsert(_983159), _983163), _983161)) = hAPP(hAPP(c_Finite__Set_Ofold(_983159, _983159, c_Orderings_Oord__class_Omin(_983159)), _983163), _983161))], (30308 ^ _780478) ^ [_1342776, _1342778] : [class_Groups_Oordered__ab__group__add__abs(_1342776), -(hAPP(c_Groups_Oabs__class_Oabs(_1342776), hAPP(c_Groups_Oabs__class_Oabs(_1342776), _1342778)) = hAPP(c_Groups_Oabs__class_Oabs(_1342776), _1342778))], (34361 ^ _780478) ^ [_1428697, _1428699] : [c_Int_OBit0(_1428697) = c_Int_OBit1(_1428699)], (50105 ^ _780478) ^ [_1793466, _1793468, _1793470, _1793472, _1793474] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1793466, _1793468, _1793470, _1793472), _1793474) = c_Hilbert__Choice_OEps(_1793466, hAPP(hAPP(c_COMBS(_1793466, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1793466), c_fconj), hAPP(hAPP(c_COMBC(_1793466, tc_fun(_1793466, tc_HOL_Obool), tc_HOL_Obool), c_member(_1793466)), _1793470))), hAPP(hAPP(c_COMBC(_1793466, _1793468, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1793468, tc_fun(_1793468, tc_HOL_Obool), _1793466), c_fequal), _1793472)), _1793474))))], (27723 ^ _780478) ^ [_1292785, _1292787, _1292789] : [class_Orderings_Olinorder(_1292785), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292785), _1292787), _1292789)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1292785, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1292785, _1292787, _1292789)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1292785), _1292789)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1292785), _1292787))], (48172 ^ _780478) ^ [] : [-(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))))], (41876 ^ _780478) ^ [_1608543, _1608545, _1608547, _1608549] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608543), tc_List_Olist(_1608543))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608543), tc_List_Olist(_1608543)), _1608545), _1608547)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1608543), c_List_Olistrel1(_1608543, _1608549)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608543)), _1608545) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608543)), _1608547))], (48739 ^ _780478) ^ [_1763676, _1763678, _1763680] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1763676, _1763678), _1763680) = c_Lazy__Sequence_Oproduct(_1763676, _1763678, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1763676, _1763680), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1763678, _1763680))), class_Lazy__Sequence_Osmall__lazy(_1763676), class_Lazy__Sequence_Osmall__lazy(_1763678)], (5899 ^ _780478) ^ [_874197, _874199, _874201, _874203] : [_874197 = _874199, 5904 ^ _780478 : [(5907 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_874201), _874203), _874199)))], (5905 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_874201), _874203), _874197)))]], 5908 ^ _780478 : [(5911 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874201), _874203), _874199))], (5909 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874201), _874203), _874197))]]], (28164 ^ _780478) ^ [_1301743, _1301745, _1301747] : [class_Orderings_Olinorder(_1301743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301743), _1301745), _1301747)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301743, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1301743, _1301745), _1301747)), hAPP(hAPP(c_Set_Oinsert(_1301743), _1301747), c_Orderings_Obot__class_Obot(tc_fun(_1301743, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1301743, _1301745, _1301747))], (44400 ^ _780478) ^ [_1669564, _1669566, _1669568, _1669570, _1669572] : [class_Orderings_Olinorder(_1669564), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669566)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669566, _1669564, _1669568), _1669570), _1669572)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1669566)), _1669572)))], (16428 ^ _780478) ^ [_1080182, _1080184, _1080186, _1080188, _1080190] : [hAPP(_1080188, _1080184) = _1080190, -(hBOOL(hAPP(hAPP(c_member(_1080182), _1080184), hAPP(c_Set_Ovimage(_1080182, _1080186, _1080188), hAPP(hAPP(c_Set_Oinsert(_1080186), _1080190), c_Orderings_Obot__class_Obot(tc_fun(_1080186, tc_HOL_Obool)))))))], (45727 ^ _780478) ^ [_1698752, _1698754, _1698756] : [hBOOL(hAPP(c_List_Odistinct(_1698752), _1698754)), -(hBOOL(hAPP(c_List_Odistinct(_1698752), hAPP(c_List_OremoveAll(_1698752, _1698756), _1698754))))], (33342 ^ _780478) ^ [_1410125, _1410127] : [class_Int_Onumber__ring(_1410125), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1410125), _1410127), hAPP(c_Int_Onumber__class_Onumber__of(_1410125), c_Int_OPls)) = _1410127)], (6650 ^ _780478) ^ [_889868, _889870, _889872] : [hBOOL(hAPP(hAPP(c_member(_889868), _889870), _889872)), -(hAPP(hAPP(c_Set_Oinsert(_889868), _889870), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889868, tc_HOL_Obool)), _889872), hAPP(hAPP(c_Set_Oinsert(_889868), _889870), c_Orderings_Obot__class_Obot(tc_fun(_889868, tc_HOL_Obool))))) = _889872)], (42955 ^ _780478) ^ [_1637424, _1637426, _1637428] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637424), tc_List_Olist(_1637424))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637424), tc_List_Olist(_1637424)), c_List_Olist_ONil(_1637424)), _1637426)), c_List_Olistrel(_1637424, _1637428))), -(_1637426 = c_List_Olist_ONil(_1637424))], (3480 ^ _780478) ^ [_832419, _832421, _832423, _832425] : [-(c_Random_Opick(_832425, _832421) = c_Random_Opick(_832423, _832419)), _832425 = _832423, _832421 = _832419], (6380 ^ _780478) ^ [_883796, _883798, _883800, _883802, _883804, _883806, _883808] : [c_Hoare__Mirabelle_Ohoare__derivs(_883796, _883798, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883796)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883796), _883800), _883802), _883804)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883796), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_883796, _883798, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883796)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883796), _883804), _883806), _883808)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883796), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_883796, _883798, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883796)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883796), _883800), c_Com_Ocom_OSemi(_883802, _883806)), _883808)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883796), tc_HOL_Obool)))))], (17282 ^ _780478) ^ [_1099304, _1099306, _1099308, _1099310, _1099312] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099304, tc_fun(_1099306, tc_HOL_Obool)), _1099308), _1099310), _1099312)), 17286 ^ _780478 : [(17289 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1099310, 17285 ^ [_1099304, _1099306, _1099308, _1099310, _1099312]), _1099312)))], (17287 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099304), 17285 ^ [_1099304, _1099306, _1099308, _1099310, _1099312]), _1099308)))]]], (14475 ^ _780478) ^ [_1038754, _1038756, _1038758, _1038760, _1038762] : [class_Groups_Ocomm__monoid__mult(_1038754), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038756), _1038758)), 14482 ^ _780478 : [(14489 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1038756), _1038760), _1038758))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038756, _1038754), hAPP(hAPP(c_COMBC(_1038756, _1038754, _1038754), hAPP(hAPP(c_COMBS(_1038756, _1038754, tc_fun(_1038754, _1038754)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1038754, tc_fun(_1038754, _1038754)), _1038756), c_If(_1038754)), hAPP(hAPP(c_COMBC(_1038756, _1038756, tc_HOL_Obool), c_fequal), _1038760))), _1038762)), c_Groups_Oone__class_Oone(_1038754))), _1038758) = c_Groups_Oone__class_Oone(_1038754))], (14483 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1038756), _1038760), _1038758)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038756, _1038754), hAPP(hAPP(c_COMBC(_1038756, _1038754, _1038754), hAPP(hAPP(c_COMBS(_1038756, _1038754, tc_fun(_1038754, _1038754)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1038754, tc_fun(_1038754, _1038754)), _1038756), c_If(_1038754)), hAPP(hAPP(c_COMBC(_1038756, _1038756, tc_HOL_Obool), c_fequal), _1038760))), _1038762)), c_Groups_Oone__class_Oone(_1038754))), _1038758) = hAPP(_1038762, _1038760))]]], (45199 ^ _780478) ^ [_1686384, _1686386] : [-(c_Code__Numeral_Onat__of__aux(_1686384, _1686386) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686384)), _1686386))], (16098 ^ _780478) ^ [_1071915, _1071917, _1071919, _1071921] : [hBOOL(hAPP(hAPP(c_member(_1071915), _1071917), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1071915, tc_HOL_Obool)), _1071919), _1071921))), 16101 ^ _780478 : [(16104 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071915), _1071917), _1071921)))], (16102 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071915), _1071917), _1071919)))]]], (18666 ^ _780478) ^ [_1130991, _1130993, _1130995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130991), _1130993)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130995), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1130993), _1130991))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1130995), _1130991)), hAPP(c_Nat_OSuc, _1130993)))], (48709 ^ _780478) ^ [_1762946, _1762948, _1762950] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1762946), hAPP(c_COMBK(_1762946, tc_Nat_Onat), _1762948)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1762950)) = c_List_Oreplicate(_1762946, _1762950, _1762948))], (50965 ^ _780478) ^ [_1813422, _1813424, _1813426, _1813428, _1813430] : [-(c_New__DSequence_Opos__map(_1813422, _1813424, _1813426, _1813428, _1813430) = c_Lazy__Sequence_Omap(_1813422, _1813424, _1813426, hAPP(_1813428, _1813430)))], (46390 ^ _780478) ^ [_1714149, _1714151, _1714153, _1714155] : [class_Groups_Ocomm__monoid__add(_1714149), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1714149), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1714149), _1714151), c_List_Oupt(_1714153, _1714155))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1714149), _1714151), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1714153, _1714155))))], (35387 ^ _780478) ^ [_1447229] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1447229), c_Int_OMin) = c_Int_Osucc(_1447229))], (14603 ^ _780478) ^ [_1041582, _1041584, _1041586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041582), _1041584)), 14606 ^ _780478 : [(14613 ^ _780478) ^ [] : [_1041584 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041586), _1041582), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041584), _1041582) = _1041586)], (14607 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041584), _1041582) = _1041586, -(_1041584 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041586), _1041582))]]], (16554 ^ _780478) ^ [_1082979, _1082981, _1082983] : [class_Lattices_Oboolean__algebra(_1082979), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1082979), _1082981), _1082983) = c_Orderings_Obot__class_Obot(_1082979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1082979), _1082981), _1082983) = c_Orderings_Otop__class_Otop(_1082979), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1082979), _1082981) = _1082983)], (44664 ^ _780478) ^ [_1674174, _1674176] : [-(_1674174 = c_List_Olist_ONil(_1674176)), -(c_Random_Oselect__weight(_1674176, hAPP(hAPP(c_List_Omap(_1674176, tc_prod(tc_Code__Numeral_Ocode__numeral, _1674176)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1674176), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1674174)) = c_Random_Oselect(_1674176, _1674174))], (23653 ^ _780478) ^ [_1220014, _1220016, _1220018, _1220020] : [class_Orderings_Olinorder(_1220014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220014), _1220016), _1220018)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220014), _1220018), _1220020)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1220014, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220014, _1220016), _1220018)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220014, _1220018), _1220020)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220014, _1220016), _1220020))], (4604 ^ _780478) ^ [_850513, _850515, _850517, _850519, _850521, _850523] : [-(c_FunDef_OTHE__default(_850523, _850519, _850515) = c_FunDef_OTHE__default(_850521, _850517, _850513)), _850523 = _850521, _850519 = _850517, _850515 = _850513], (12770 ^ _780478) ^ [_1006631, _1006633, _1006635, _1006637] : [class_Lattices_Olattice(_1006631), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006631), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006631), _1006633), _1006635)), _1006637) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006631), _1006633), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006631), _1006635), _1006637)))], (1504 ^ _780478) ^ [_802142, _802144] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_802142)), _802144 = _802142, class_Groups_Oordered__ab__semigroup__add__imp__le(_802144)], (52145 ^ _780478) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (5358 ^ _780478) ^ [_862390, _862392] : [_862392 = _862390, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_862392) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_862390))], (25485 ^ _780478) ^ [_1253610] : [25486 ^ _780478 : [(25487 ^ _780478) ^ [_1253667] : [hBOOL(hAPP(_1253610, _1253667))]], 25489 ^ _780478 : [(25492 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1253610, hAPP(c_Int_Onat, 25488 ^ [_1253610]))))], (25490 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25488 ^ [_1253610])))]]], (43929 ^ _780478) ^ [_1659211, _1659213, _1659215, _1659217] : [hAPP(hAPP(c_List_Oappend(_1659211), _1659213), _1659215) = _1659217, 43932 ^ _780478 : [(43935 ^ _780478) ^ [] : [-(_1659215 = hAPP(hAPP(c_List_Odrop(_1659211), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659211)), _1659213)), _1659217))], (43933 ^ _780478) ^ [] : [-(_1659213 = hAPP(hAPP(c_List_Otake(_1659211), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659211)), _1659213)), _1659217))]]], (33706 ^ _780478) ^ [_1416380, _1416382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1416380)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416382))), -(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(_1416382))), 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), _1416380)), c_Int_Onat))))))], (7303 ^ _780478) ^ [_902470, _902472, _902474] : [_902470 = _902472, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902474, tc_HOL_Obool)), _902470), _902472)))], (24897 ^ _780478) ^ [_1242896, _1242898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242896)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242898), _1242896)), _1242896) = _1242898)], (25190 ^ _780478) ^ [_1248546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248546)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248546) = 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, _1248546))))], (19824 ^ _780478) ^ [_1150446, _1150448, _1150450] : [class_Groups_Oordered__comm__monoid__add(_1150446), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150446), c_Groups_Ozero__class_Ozero(_1150446)), _1150448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150446), c_Groups_Ozero__class_Ozero(_1150446)), _1150450)), 19835 ^ _780478 : [(19844 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150446), _1150448), _1150450) = c_Groups_Ozero__class_Ozero(_1150446)), _1150448 = c_Groups_Ozero__class_Ozero(_1150446), _1150450 = c_Groups_Ozero__class_Ozero(_1150446)], (19836 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150446), _1150448), _1150450) = c_Groups_Ozero__class_Ozero(_1150446), 19839 ^ _780478 : [(19842 ^ _780478) ^ [] : [-(_1150450 = c_Groups_Ozero__class_Ozero(_1150446))], (19840 ^ _780478) ^ [] : [-(_1150448 = c_Groups_Ozero__class_Ozero(_1150446))]]]]], (52207 ^ _780478) ^ [_1832249, _1832251] : [-(class_Finite__Set_Ofinite(tc_prod(_1832249, _1832251))), class_Finite__Set_Ofinite(_1832249), class_Finite__Set_Ofinite(_1832251)], (41666 ^ _780478) ^ [_1601644, _1601646, _1601648, _1601650] : [class_Rings_Olinordered__semidom(_1601644), 41672 ^ _780478 : [(41675 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1601644), c_Groups_Ozero__class_Ozero(_1601644)), hAPP(_1601650, 41671 ^ [_1601644, _1601646, _1601648, _1601650])))], (41673 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601646), 41671 ^ [_1601644, _1601646, _1601648, _1601650]), _1601648)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1601644), c_Groups_Ozero__class_Ozero(_1601644)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1601646, _1601644), _1601650), _1601648))))], (15183 ^ _780478) ^ [_1053825, _1053827, _1053829] : [class_Lattices_Olattice(_1053825), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053825), _1053827)), -(_1053827 = c_Orderings_Obot__class_Obot(tc_fun(_1053825, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053825), _1053829)), -(_1053829 = c_Orderings_Obot__class_Obot(tc_fun(_1053825, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1053825, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1053825, tc_HOL_Obool)), _1053827), _1053829)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1053825), c_Big__Operators_Olattice__class_OSup__fin(_1053825, _1053827)), c_Big__Operators_Olattice__class_OSup__fin(_1053825, _1053829)))], (44318 ^ _780478) ^ [_1667577, _1667579, _1667581] : [class_Orderings_Olinorder(_1667577), -(c_Big__Operators_Olattice_OInf__fin(_1667577, c_Orderings_Oord__class_Omin(_1667577), hAPP(c_List_Oset(_1667577), hAPP(hAPP(c_List_Olist_OCons(_1667577), _1667579), _1667581))) = hAPP(c_List_Ofoldl(_1667577, _1667577, c_Orderings_Oord__class_Omin(_1667577), _1667579), _1667581))], (34153 ^ _780478) ^ [] : [-(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)))], (11913 ^ _780478) ^ [_989822, _989824] : [class_Orderings_Olinorder(_989822), -(c_Big__Operators_Olattice_OInf__fin(_989822, c_Orderings_Oord__class_Omin(_989822), hAPP(hAPP(c_Set_Oinsert(_989822), _989824), c_Orderings_Obot__class_Obot(tc_fun(_989822, tc_HOL_Obool)))) = _989824)], (12704 ^ _780478) ^ [_1005220, _1005222, _1005224, _1005226, _1005228] : [class_Lattices_Olattice(_1005220), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1005222, _1005220)), _1005224), _1005226), _1005228) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005220), hAPP(_1005224, _1005228)), hAPP(_1005226, _1005228)))], (7545 ^ _780478) ^ [_907284, _907286, _907288, _907290, _907292] : [class_Groups_Oab__group__add(_907284), hBOOL(hAPP(c_Finite__Set_Ofinite(_907286), _907288)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907286, tc_HOL_Obool)), _907290), _907288)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_907286, _907284), _907292), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_907286, tc_HOL_Obool)), _907288), _907290)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_907284), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_907286, _907284), _907292), _907288)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_907286, _907284), _907292), _907290)))], (13120 ^ _780478) ^ [_1013001, _1013003, _1013005, _1013007] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013001, tc_HOL_Obool)), _1013003), hAPP(hAPP(c_Set_Oinsert(_1013001), _1013005), _1013007)) = hAPP(hAPP(c_Set_Oinsert(_1013001), _1013005), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013001, tc_HOL_Obool)), _1013003), _1013007)))], (51535 ^ _780478) ^ [_1823847, _1823849, _1823851] : [class_Rings_Ocomm__ring__1(_1823847), 51538 ^ _780478 : [(51545 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823847), _1823849), _1823851)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823847), hAPP(c_Groups_Ouminus__class_Ouminus(_1823847), _1823849)), _1823851)))], (51539 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823847), hAPP(c_Groups_Ouminus__class_Ouminus(_1823847), _1823849)), _1823851)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823847), _1823849), _1823851)))]]], (46402 ^ _780478) ^ [_1714455, _1714457, _1714459] : [46403 ^ _780478 : [(46406 ^ _780478) ^ [] : [_1714459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46404 ^ _780478) ^ [] : [-(_1714455 = c_List_Olist_ONil(tc_List_Olist(_1714457)))]], 46410 ^ _780478 : [(46413 ^ _780478) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1714457)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714457)), _1714455), 46409 ^ [_1714455, _1714457, _1714459])) = _1714459], (46411 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46409 ^ [_1714455, _1714457, _1714459]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714457))), _1714455))))]], -(c_List_Otranspose(_1714457, _1714455) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1714457)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1714457)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1714457), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1714457)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1714457)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1714457), hAPP(hAPP(c_COMBB(tc_List_Olist(_1714457), tc_fun(tc_Nat_Onat, _1714457), tc_Nat_Onat), c_List_Onth(_1714457)), hAPP(c_List_Onth(tc_List_Olist(_1714457)), _1714455))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714457))), _1714455)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1714459)))], (52093 ^ _780478) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (3490 ^ _780478) ^ [_832568, _832570] : [_832570 = _832568, -(c_List_Otranspose__rel(_832570) = c_List_Otranspose__rel(_832568))], (40849 ^ _780478) ^ [_1580281, _1580283, _1580285, _1580287, _1580289] : [-(hAPP(c_Relation_Oconverse(_1580281, _1580283), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1580285, tc_fun(tc_prod(_1580281, _1580283), tc_HOL_Obool)), _1580287), _1580289)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1580285, tc_fun(tc_prod(_1580283, _1580281), tc_HOL_Obool)), _1580287), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1580281, _1580283), tc_HOL_Obool), tc_fun(tc_prod(_1580283, _1580281), tc_HOL_Obool), _1580285), c_Relation_Oconverse(_1580281, _1580283)), _1580289)))], (28566 ^ _780478) ^ [_1309356, _1309358, _1309360] : [class_Orderings_Olinorder(_1309356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309356), _1309358), _1309360)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309356, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1309356), _1309358)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1309356, _1309358, _1309360)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1309356), _1309360))], (33442 ^ _780478) ^ [_1411612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411612), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411612))], (11479 ^ _780478) ^ [_981663, _981665, _981667, _981669] : [class_Orderings_Olinorder(_981663), hBOOL(hAPP(c_Finite__Set_Ofinite(_981663), _981665)), hBOOL(hAPP(hAPP(c_member(_981663), _981667), _981665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981663), hAPP(hAPP(c_Finite__Set_Ofold(_981663, _981663, c_Orderings_Oord__class_Omin(_981663)), _981669), _981665)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_981663), _981667), _981669))))], (23521 ^ _780478) ^ [_1217705, _1217707, _1217709, _1217711, _1217713] : [class_Orderings_Olinorder(_1217705), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217705, _1217707), _1217709) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217705, _1217711), _1217713), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217705), _1217707), _1217709)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217705), _1217711), _1217713)), -(_1217707 = _1217711)], (37792 ^ _780478) ^ [_1501949, _1501951, _1501953, _1501955, _1501957, _1501959] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1501949, tc_HOL_Obool), tc_fun(_1501949, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1501949, tc_HOL_Obool), tc_fun(_1501949, tc_HOL_Obool)), _1501951), _1501953)), c_Wellfounded_Omax__ext(_1501949, _1501955))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1501949, tc_HOL_Obool), tc_fun(_1501949, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1501949, tc_HOL_Obool), tc_fun(_1501949, tc_HOL_Obool)), _1501957), _1501959)), c_Wellfounded_Omax__ext(_1501949, _1501955))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1501949, tc_HOL_Obool), tc_fun(_1501949, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1501949, tc_HOL_Obool), tc_fun(_1501949, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501949, tc_HOL_Obool)), _1501951), _1501957)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1501949, tc_HOL_Obool)), _1501953), _1501959))), c_Wellfounded_Omax__ext(_1501949, _1501955))))], (37997 ^ _780478) ^ [_1508788, _1508790, _1508792] : [hBOOL(hAPP(hAPP(c_member(_1508788), _1508790), c_Wellfounded_Oacc(_1508788, _1508792))), 38000 ^ _780478 : [(38001 ^ _780478) ^ [_1508902] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508788, _1508788)), hAPP(hAPP(c_Product__Type_OPair(_1508788, _1508788), _1508902), _1508790)), _1508792)), -(hBOOL(hAPP(hAPP(c_member(_1508788), _1508902), c_Wellfounded_Oacc(_1508788, _1508792))))]]], (51475 ^ _780478) ^ [_1822882, _1822884] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822882), _1822884)), -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822884, _1822882) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (46378 ^ _780478) ^ [_1713884, _1713886] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1713884, _1713886) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1713884), _1713886)))], (44330 ^ _780478) ^ [_1667847, _1667849, _1667851, _1667853] : [class_Complete__Lattice_Ocomplete__lattice(_1667847), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1667849, _1667847), hAPP(c_List_Oset(_1667849), _1667851)), _1667853) = hAPP(c_List_Ofoldl(_1667847, _1667849, hAPP(c_COMBC(_1667849, _1667847, _1667847), hAPP(hAPP(c_COMBB(_1667847, tc_fun(_1667847, _1667847), _1667849), c_Lattices_Osemilattice__sup__class_Osup(_1667847)), _1667853)), c_Orderings_Obot__class_Obot(_1667847)), _1667851))], (41979 ^ _780478) ^ [_1611729, _1611731, _1611733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1611729, _1611729), tc_HOL_Obool)), _1611731), _1611733)), c_Relation_Orefl__on(_1611729, c_Orderings_Otop__class_Otop(tc_fun(_1611729, tc_HOL_Obool)), _1611733), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1611729), tc_List_Olist(_1611729)), tc_HOL_Obool)), c_List_Olistrel1(_1611729, _1611731)), c_List_Olistrel(_1611729, _1611733))))], (39017 ^ _780478) ^ [_1536806, _1536808] : [-(hAPP(c_Set_Oimage(_1536806, _1536806, c_Fun_Oid(_1536806)), _1536808) = _1536808)], (37672 ^ _780478) ^ [_1499517] : [-(_1499517 = 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)), _1499517), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (34067 ^ _780478) ^ [_1423618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1423618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1423618))))], (41049 ^ _780478) ^ [_1585810, _1585812] : [-(hAPP(c_Relation_OImage(_1585810, _1585810, c_Relation_OId(_1585810)), _1585812) = _1585812)], (25930 ^ _780478) ^ [_1261208, _1261210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261210)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1261208)), hAPP(c_Int_Onat, _1261210)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1261208, _1261210)))], (10257 ^ _780478) ^ [_959113, _959115, _959117, _959119] : [class_Orderings_Olinorder(_959113), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_959113), _959115), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959113), _959117), _959119)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_959113), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959113), _959115), _959117)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959113), _959115), _959119)))], (23839 ^ _780478) ^ [_1223826] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1223826)), -(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)), _1223826))))], (47003 ^ _780478) ^ [_1726037, _1726039, _1726041, _1726043, _1726045] : [c_List_Olist__all2(_1726037, _1726039, _1726041, hAPP(c_List_Orev(_1726037), _1726043), hAPP(c_List_Orev(_1726039), _1726045)), -(c_List_Olist__all2(_1726037, _1726039, _1726041, _1726043, _1726045))], (44753 ^ _780478) ^ [_1676702, _1676704, _1676706, _1676708] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676702)), hAPP(hAPP(c_List_Omap(_1676704, _1676702), _1676706), _1676708)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676704)), _1676708))], (35423 ^ _780478) ^ [_1447821, _1447823] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1447821), _1447823), hAPP(c_Int_Onumber__class_Onumber__of(_1447821), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1447821), _1447823)), class_Fields_Ofield__inverse__zero(_1447821), class_Int_Onumber__ring(_1447821)], (47778 ^ _780478) ^ [_1743035, _1743037] : [class_Orderings_Olinorder(_1743035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1743035), _1743037)), 47786 ^ _780478 : [(47789 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743035, 47785 ^ [_1743035, _1743037]))], (47791 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1743035), 47785 ^ [_1743035, _1743037])))], (47793 ^ _780478) ^ [_1743361] : [-(_1743361 = 47785 ^ [_1743035, _1743037]), hAPP(c_List_Oset(_1743035), _1743361) = _1743037, c_List_Olinorder__class_Osorted(_1743035, _1743361), hBOOL(hAPP(c_List_Odistinct(_1743035), _1743361))], (47787 ^ _780478) ^ [] : [-(hAPP(c_List_Oset(_1743035), 47785 ^ [_1743035, _1743037]) = _1743037)]]], (44648 ^ _780478) ^ [_1673812, _1673814, _1673816] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1673812)), _1673814), c_List_Olists(_1673812, _1673816)))), 44649 ^ _780478 : [(44652 ^ _780478) ^ [_1673940, _1673942] : [_1673814 = hAPP(hAPP(c_List_Olist_OCons(_1673812), _1673942), _1673940), hBOOL(hAPP(hAPP(c_member(_1673812), _1673942), _1673816)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1673812)), _1673940), c_List_Olists(_1673812, _1673816)))], (44650 ^ _780478) ^ [] : [_1673814 = c_List_Olist_ONil(_1673812)]]], (18688 ^ _780478) ^ [_1131480, _1131482, _1131484] : [class_Lattices_Olattice(_1131480), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131480), _1131482)), hBOOL(hAPP(hAPP(c_member(_1131480), _1131484), _1131482)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1131480), _1131484), c_Big__Operators_Olattice__class_OInf__fin(_1131480, _1131482)) = _1131484)], (7605 ^ _780478) ^ [_908471, _908473] : [class_Orderings_Obot(_908471), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908471), c_Orderings_Obot__class_Obot(_908471)), _908473)))], (47692 ^ _780478) ^ [_1741077, _1741079, _1741081] : [class_Enum_Oenum(_1741077), class_Enum_Oenum(_1741079), 47699 ^ _780478 : [(47706 ^ _780478) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1741079), hAPP(hAPP(c_COMBB(tc_fun(_1741077, tc_HOL_Obool), tc_HOL_Obool, _1741079), c_Enum_Oenum__class_Oenum__ex(_1741077)), hAPP(hAPP(c_COMBB(tc_fun(_1741077, tc_prod(_1741079, _1741077)), tc_fun(_1741077, tc_HOL_Obool), _1741079), hAPP(c_COMBB(tc_prod(_1741079, _1741077), tc_HOL_Obool, _1741077), _1741081)), c_Product__Type_OPair(_1741079, _1741077))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1741079, _1741077)), _1741081)))], (47700 ^ _780478) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1741079, _1741077)), _1741081)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1741079), hAPP(hAPP(c_COMBB(tc_fun(_1741077, tc_HOL_Obool), tc_HOL_Obool, _1741079), c_Enum_Oenum__class_Oenum__ex(_1741077)), hAPP(hAPP(c_COMBB(tc_fun(_1741077, tc_prod(_1741079, _1741077)), tc_fun(_1741077, tc_HOL_Obool), _1741079), hAPP(c_COMBB(tc_prod(_1741079, _1741077), tc_HOL_Obool, _1741077), _1741081)), c_Product__Type_OPair(_1741079, _1741077))))))]]], (41822 ^ _780478) ^ [_1606850, _1606852, _1606854, _1606856] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606850), tc_List_Olist(_1606850))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606850), tc_List_Olist(_1606850)), _1606852), _1606854)), c_List_Olex(_1606850, _1606856)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606850), tc_List_Olist(_1606850))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606850), tc_List_Olist(_1606850)), _1606852), _1606854)), c_List_Olexord(_1606850, _1606856))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606850)), _1606852) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606850)), _1606854)], (6518 ^ _780478) ^ [_886844, _886846, _886848] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_886844), _886846)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_886844), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886844, tc_HOL_Obool)), _886846), _886848))))], (9064 ^ _780478) ^ [_936410, _936412, _936414] : [class_Orderings_Oorder(_936410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936410), _936412), _936414)), -(_936414 = _936412), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936410), _936412), _936414)))], (42999 ^ _780478) ^ [_1638224, _1638226, _1638228] : [c_List_Olist_ONil(_1638224) = hAPP(hAPP(c_List_Olist_OCons(_1638224), _1638226), _1638228)], (43823 ^ _780478) ^ [_1656683, _1656685] : [-(hAPP(c_List_Orotate1(_1656683), _1656685) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1656683), _1656683, c_List_Olist_ONil(_1656683), hAPP(hAPP(c_COMBB(tc_List_Olist(_1656683), tc_fun(tc_List_Olist(_1656683), tc_List_Olist(_1656683)), _1656683), hAPP(c_COMBC(tc_List_Olist(_1656683), tc_List_Olist(_1656683), tc_List_Olist(_1656683)), c_List_Oappend(_1656683))), hAPP(hAPP(c_COMBC(_1656683, tc_List_Olist(_1656683), tc_List_Olist(_1656683)), c_List_Olist_OCons(_1656683)), c_List_Olist_ONil(_1656683)))), _1656685))], (40522 ^ _780478) ^ [_1572956, _1572958] : [-(hAPP(c_Relation_ORange(_1572956, _1572956), c_Transitive__Closure_Ortrancl(_1572956, _1572958)) = c_Orderings_Otop__class_Otop(tc_fun(_1572956, tc_HOL_Obool)))], (41245 ^ _780478) ^ [_1590543, _1590545, _1590547] : [c_Relation_Ototal__on(_1590543, _1590545, _1590547), -(c_Relation_Ototal__on(_1590543, _1590545, hAPP(c_Relation_Oconverse(_1590543, _1590543), _1590547)))], (31869 ^ _780478) ^ [_1382337, _1382339, _1382341, _1382343, _1382345, _1382347] : [c_Com_Ocom_OCond(_1382337, _1382339, _1382341) = c_Com_Ocom_OCond(_1382343, _1382345, _1382347), 31872 ^ _780478 : [(31877 ^ _780478) ^ [] : [-(_1382341 = _1382347)], (31875 ^ _780478) ^ [] : [-(_1382339 = _1382345)], (31873 ^ _780478) ^ [] : [-(_1382337 = _1382343)]]], (13294 ^ _780478) ^ [_1016820, _1016822, _1016824, _1016826] : [c_Fun_Oinj__on(_1016820, _1016822, _1016824, _1016826), -(hAPP(c_Finite__Set_Ocard(_1016822), hAPP(c_Set_Oimage(_1016820, _1016822, _1016824), _1016826)) = hAPP(c_Finite__Set_Ocard(_1016820), _1016826))], (17424 ^ _780478) ^ [_1103037, _1103039, _1103041, _1103043, _1103045] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103037, tc_fun(_1103039, tc_HOL_Obool)), _1103041), hAPP(hAPP(c_COMBC(_1103037, tc_fun(_1103039, tc_HOL_Obool), tc_fun(_1103039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1103039, tc_HOL_Obool), tc_fun(tc_fun(_1103039, tc_HOL_Obool), tc_fun(_1103039, tc_HOL_Obool)), _1103037), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103039, tc_HOL_Obool))), _1103043)), _1103045)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103039, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103037, tc_fun(_1103039, tc_HOL_Obool)), _1103041), _1103043)), _1103045))], (32924 ^ _780478) ^ [_1402489, _1402491, _1402493, _1402495] : [class_Fields_Olinordered__field__inverse__zero(_1402489), class_Int_Onumber(_1402489), 32931 ^ _780478 : [(32932 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402489), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1402489), _1402491), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493))), _1402495)), 32935 ^ _780478 : [(32942 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402489), c_Groups_Ozero__class_Ozero(_1402489)), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493)))), 32945 ^ _780478 : [(32952 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402489), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493)), c_Groups_Ozero__class_Ozero(_1402489)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402489), c_Groups_Ozero__class_Ozero(_1402489)), _1402495)))], (32946 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402489), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493)), c_Groups_Ozero__class_Ozero(_1402489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402489), _1402495), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493))), _1402491)))]]], (32936 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402489), c_Groups_Ozero__class_Ozero(_1402489)), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402489), _1402491), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402489), _1402495), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493)))))]]], (32958 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402489), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1402489), _1402491), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493))), _1402495))), 32961 ^ _780478 : [(32964 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402489), _1402491), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402489), _1402495), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493))))], (32962 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402489), c_Groups_Ozero__class_Ozero(_1402489)), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493))))]], 32965 ^ _780478 : [(32968 ^ _780478) ^ [] : [32969 ^ _780478 : [(32972 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1402489), _1402495), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493))), _1402491))], (32970 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402489), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493)), c_Groups_Ozero__class_Ozero(_1402489))))]], 32973 ^ _780478 : [(32976 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1402489), c_Groups_Ozero__class_Ozero(_1402489)), _1402495))], (32974 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402489), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493)), c_Groups_Ozero__class_Ozero(_1402489)))]]], (32966 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1402489), c_Groups_Ozero__class_Ozero(_1402489)), hAPP(c_Int_Onumber__class_Onumber__of(_1402489), _1402493)))]]]]], (26360 ^ _780478) ^ [_1269101, _1269103, _1269105] : [class_Fields_Olinordered__field(_1269101), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269101), _1269103), c_Groups_Ozero__class_Ozero(_1269101))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269101), c_Groups_Ozero__class_Ozero(_1269101)), _1269105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269101), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269101), _1269103), _1269105)), c_Groups_Ozero__class_Ozero(_1269101))))], (17189 ^ _780478) ^ [_1096895, _1096897, _1096899, _1096901, _1096903, _1096905] : [hBOOL(hAPP(hAPP(c_member(_1096895), _1096897), _1096899)), hBOOL(hAPP(hAPP(c_member(_1096901), _1096903), hAPP(_1096905, _1096897))), -(hBOOL(hAPP(hAPP(c_member(_1096901), _1096903), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1096895, tc_fun(_1096901, tc_HOL_Obool)), _1096899), _1096905))))], (25476 ^ _780478) ^ [_1253432] : [25478 ^ _780478 : [(25481 ^ _780478) ^ [] : [hBOOL(hAPP(_1253432, hAPP(c_Int_Onat, 25477 ^ [_1253432])))], (25479 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25477 ^ [_1253432])))]], 25482 ^ _780478 : [(25483 ^ _780478) ^ [_1253565] : [-(hBOOL(hAPP(_1253432, _1253565)))]]], (816 ^ _780478) ^ [_792710, _792712, _792714, _792716] : [-(c_Predicate_Osymp(_792714, _792710)), c_Predicate_Osymp(_792716, _792712), _792716 = _792714, _792712 = _792710], (48133 ^ _780478) ^ [_1750703, _1750705, _1750707] : [hBOOL(hAPP(hAPP(c_member(_1750703), _1750705), hAPP(c_List_Oset(_1750703), _1750707))), 48138 ^ _780478 : [(48141 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1750703), _1750705), hAPP(c_List_Oset(_1750703), 48137 ^ [_1750703, _1750705, _1750707])))], (48139 ^ _780478) ^ [] : [-(_1750707 = hAPP(hAPP(c_List_Oappend(_1750703), 48136 ^ [_1750703, _1750705, _1750707]), hAPP(hAPP(c_List_Olist_OCons(_1750703), _1750705), 48137 ^ [_1750703, _1750705, _1750707])))]]], (52323 ^ _780478) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (45205 ^ _780478) ^ [_1686501] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1686501), 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, _1686501)) = _1686501)], (30228 ^ _780478) ^ [_1341245, _1341247] : [class_Complete__Lattice_Ocomplete__lattice(_1341245), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341245), _1341247)), -(c_Complete__Lattice_OSup__class_OSup(_1341245, _1341247) = hAPP(hAPP(c_Finite__Set_Ofold(_1341245, _1341245, c_Lattices_Osemilattice__sup__class_Osup(_1341245)), c_Orderings_Obot__class_Obot(_1341245)), _1341247))], (1394 ^ _780478) ^ [_800767, _800769] : [-(class_Lattices_Osemilattice__inf(_800767)), _800769 = _800767, class_Lattices_Osemilattice__inf(_800769)], (49891 ^ _780478) ^ [_1788802, _1788804, _1788806, _1788808] : [c_Equiv__Relations_Opart__equivp(_1788802, _1788804), hBOOL(hAPP(hAPP(_1788804, _1788806), _1788808)), -(hBOOL(hAPP(hAPP(_1788804, _1788808), _1788806)))], (37525 ^ _780478) ^ [_1496583, _1496585] : [c_Equiv__Relations_Oequivp(_1496583, _1496585), 37528 ^ _780478 : [(37535 ^ _780478) ^ [_1496776, _1496778] : [hAPP(_1496585, _1496778) = hAPP(_1496585, _1496776), -(hBOOL(hAPP(hAPP(_1496585, _1496778), _1496776)))], (37529 ^ _780478) ^ [_1496677, _1496679] : [hBOOL(hAPP(hAPP(_1496585, _1496679), _1496677)), -(hAPP(_1496585, _1496679) = hAPP(_1496585, _1496677))]]], (30901 ^ _780478) ^ [_1354674, _1354676] : [class_Complete__Lattice_Ocomplete__lattice(_1354674), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354674), _1354676)), -(_1354676 = c_Orderings_Obot__class_Obot(tc_fun(_1354674, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1354674, _1354676) = c_Complete__Lattice_OSup__class_OSup(_1354674, _1354676))], (34587 ^ _780478) ^ [_1432636] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432636))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1432636)))))], (27136 ^ _780478) ^ [_1283278, _1283280] : [c_Nat__Transfer_Onat__set(_1283278), c_Nat__Transfer_Onat__set(_1283280), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1283278), _1283280)))], (33674 ^ _780478) ^ [_1415548, _1415550] : [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(_1415550))), 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)), _1415548))))), -(hAPP(c_Nat_OSuc, _1415548) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415550))], (40402 ^ _780478) ^ [_1569945, _1569947, _1569949] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569945, _1569945)), _1569947), _1569949)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569945, _1569945)), _1569947), c_Transitive__Closure_Otrancl(_1569945, _1569949))))], (5738 ^ _780478) ^ [_868308, _868310] : [_868310 = _868308, -(tc_Hoare__Mirabelle_Otriple(_868310) = tc_Hoare__Mirabelle_Otriple(_868308))], (43887 ^ _780478) ^ [_1658265, _1658267, _1658269] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1658265, tc_HOL_Obool)), hAPP(c_List_Oset(_1658265), hAPP(hAPP(c_List_Odrop(_1658265), _1658267), _1658269))), hAPP(c_List_Oset(_1658265), _1658269))))], (21051 ^ _780478) ^ [_1171973, _1171975] : [21052 ^ _780478 : [(21055 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171975))], (21053 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171973))]], -(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), _1171973), _1171975))))], (34151 ^ _780478) ^ [] : [-(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)))))], (36228 ^ _780478) ^ [_1469308, _1469310, _1469312, _1469314, _1469316] : [hBOOL(hAPP(hAPP(_1469308, _1469310), _1469312)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1469314, _1469316, tc_HOL_Obool), _1469308), hAPP(hAPP(c_Product__Type_OPair(_1469314, _1469316), _1469310), _1469312))))], (17384 ^ _780478) ^ [_1101724, _1101726, _1101728, _1101730] : [17386 ^ _780478 : [(17389 ^ _780478) ^ [] : [hAPP(_1101730, 17385 ^ [_1101724, _1101726, _1101728, _1101730]) = c_Orderings_Obot__class_Obot(tc_fun(_1101724, tc_HOL_Obool))], (17387 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1101726), 17385 ^ [_1101724, _1101726, _1101728, _1101730]), _1101728)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1101724, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101726, tc_fun(_1101724, tc_HOL_Obool)), _1101728), _1101730))], (36522 ^ _780478) ^ [_1475206, _1475208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475206)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475208)), -(c_Divides_OposDivAlg(_1475206, _1475208) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1475206), _1475208)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1475206, _1475208)))], (38576 ^ _780478) ^ [_1522842, _1522844, _1522846, _1522848] : [hBOOL(hAPP(hAPP(c_member(_1522844), _1522848), hAPP(c_Relation_ORange(_1522842, _1522844), _1522846))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1522842, _1522844, hAPP(hAPP(c_COMBC(_1522842, tc_fun(tc_prod(_1522842, _1522844), tc_HOL_Obool), tc_fun(_1522844, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522844, tc_fun(tc_fun(tc_prod(_1522842, _1522844), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1522842, _1522844), tc_HOL_Obool), tc_fun(_1522844, tc_HOL_Obool)), _1522842), c_COMBC(_1522844, tc_fun(tc_prod(_1522842, _1522844), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522844, tc_prod(_1522842, _1522844)), tc_fun(_1522844, tc_fun(tc_fun(tc_prod(_1522842, _1522844), tc_HOL_Obool), tc_HOL_Obool)), _1522842), hAPP(c_COMBB(tc_prod(_1522842, _1522844), tc_fun(tc_fun(tc_prod(_1522842, _1522844), tc_HOL_Obool), tc_HOL_Obool), _1522844), c_member(tc_prod(_1522842, _1522844)))), c_Product__Type_OPair(_1522842, _1522844)))), _1522846)), _1522848)))], (25265 ^ _780478) ^ [_1250059, _1250061, _1250063, _1250065] : [class_Rings_Odivision__ring(_1250059), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1250059), _1250061), _1250063)), _1250065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1250059), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250059), _1250061), _1250065)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250059), _1250063), _1250065)))], (9092 ^ _780478) ^ [_936758, _936760, _936762] : [class_Orderings_Oorder(_936758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936758), _936760), _936762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936758), _936760), _936762))), -(_936760 = _936762)], (3918 ^ _780478) ^ [_839374, _839376, _839378, _839380, _839382, _839384, _839386, _839388] : [-(c_New__DSequence_Oneg__decr__bind(_839388, _839384, _839380, _839376) = c_New__DSequence_Oneg__decr__bind(_839386, _839382, _839378, _839374)), _839388 = _839386, _839384 = _839382, _839380 = _839378, _839376 = _839374], (51677 ^ _780478) ^ [_1826221, _1826223, _1826225, _1826227] : [class_Divides_Osemiring__div(_1826221), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826221), _1826223), _1826225)), 51684 ^ _780478 : [(51691 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826221), _1826223), _1826227)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826221), _1826223), c_Divides_Odiv__class_Omod(_1826221, _1826227, _1826225))))], (51685 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826221), _1826223), c_Divides_Odiv__class_Omod(_1826221, _1826227, _1826225))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826221), _1826223), _1826227)))]]], (45115 ^ _780478) ^ [_1684721, _1684723, _1684725, _1684727] : [class_Groups_Ocomm__monoid__add(_1684721), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1684721), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1684721), _1684723), c_List_Oupto(_1684725, _1684727))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1684721), _1684723), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1684725, _1684727))))], (13182 ^ _780478) ^ [_1014515] : [class_Finite__Set_Ofinite(_1014515), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1014515), c_Orderings_Otop__class_Otop(tc_fun(_1014515, tc_HOL_Obool)))))], (28100 ^ _780478) ^ [_1300291, _1300293, _1300295, _1300297] : [class_Orderings_Oorder(_1300291), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300291, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1300291, _1300293, _1300295)), c_SetInterval_Oord__class_OatLeastAtMost(_1300291, _1300295, _1300297)) = c_Orderings_Obot__class_Obot(tc_fun(_1300291, tc_HOL_Obool)))], (12365 ^ _780478) ^ [_998694, _998696, _998698, _998700, _998702, _998704] : [class_Groups_Oab__semigroup__mult(_998694), hBOOL(hAPP(c_Finite__Set_Ofinite(_998696), _998698)), -(hBOOL(hAPP(hAPP(c_member(_998696), _998700), _998698))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_998694, _998696, c_Groups_Otimes__class_Otimes(_998694)), _998702), _998704), hAPP(hAPP(c_Set_Oinsert(_998696), _998700), _998698)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998694), hAPP(_998702, _998700)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_998694, _998696, c_Groups_Otimes__class_Otimes(_998694)), _998702), _998704), _998698)))], (15729 ^ _780478) ^ [_1064740, _1064742, _1064744] : [class_Lattices_Osemilattice__inf(_1064740), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064740), _1064742), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064740), _1064742), _1064744)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064740), _1064742), _1064744))], (23577 ^ _780478) ^ [_1218683] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218683) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1218683))], (30538 ^ _780478) ^ [_1347386, _1347388, _1347390] : [class_Groups_Oordered__ab__group__add__abs(_1347386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347386), hAPP(c_Groups_Oabs__class_Oabs(_1347386), _1347388)), _1347390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347386), hAPP(c_Groups_Ouminus__class_Ouminus(_1347386), _1347388)), _1347390)))], (45197 ^ _780478) ^ [_1686355] : [-(hAPP(c_Code__Numeral_Onat__of, _1686355) = c_Code__Numeral_Onat__of__aux(_1686355, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10329 ^ _780478) ^ [_960671, _960673, _960675] : [class_Orderings_Olinorder(_960671), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_960671), _960673), _960675) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_960671), _960675), _960673))], (44726 ^ _780478) ^ [_1675954, _1675956, _1675958, _1675960, _1675962, _1675964] : [-(hAPP(hAPP(c_List_Omap(_1675954, _1675956), _1675958), hAPP(hAPP(c_List_Olist__update(_1675954, _1675960), _1675962), _1675964)) = hAPP(hAPP(c_List_Olist__update(_1675956, hAPP(hAPP(c_List_Omap(_1675954, _1675956), _1675958), _1675960)), _1675962), hAPP(_1675958, _1675964)))], (45522 ^ _780478) ^ [_1694093, _1694095, _1694097, _1694099] : [c_List_Olist__all2(_1694093, _1694095, _1694097, c_List_Olist_ONil(_1694093), _1694099), -(_1694099 = c_List_Olist_ONil(_1694095))], (10429 ^ _780478) ^ [_962434, _962436, _962438, _962440] : [class_Orderings_Olinorder(_962434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962434), _962436), _962438)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962434), _962440), _962438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962434), hAPP(hAPP(c_Orderings_Oord__class_Omax(_962434), _962436), _962440)), _962438)))], (2084 ^ _780478) ^ [_810779, _810781, _810783, _810785, _810787, _810789] : [-(c_SetInterval_Oord_OatLeast(_810789, _810785, _810781) = c_SetInterval_Oord_OatLeast(_810787, _810783, _810779)), _810789 = _810787, _810785 = _810783, _810781 = _810779], (21386 ^ _780478) ^ [_1177573, _1177575, _1177577] : [class_Groups_Oordered__comm__monoid__add(_1177573), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177573), c_Groups_Ozero__class_Ozero(_1177573)), _1177575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177573), c_Groups_Ozero__class_Ozero(_1177573)), _1177577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177573), c_Groups_Ozero__class_Ozero(_1177573)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177573), _1177575), _1177577))))], (40776 ^ _780478) ^ [_1578984, _1578986] : [40777 ^ _780478 : [(40780 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1578986), _1578984))], (40778 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1578984), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1578984, _1578986) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (38500 ^ _780478) ^ [_1520775, _1520777, _1520779, _1520781] : [38502 ^ _780478 : [(38505 ^ _780478) ^ [] : [c_Wellfounded_Owf(_1520777, hAPP(_1520779, 38501 ^ [_1520775, _1520777, _1520779, _1520781]))], (38503 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1520775, 38501 ^ [_1520775, _1520777, _1520779, _1520781])))]], -(c_Wellfounded_Owf(tc_prod(_1520781, _1520777), c_Recdef_Osame__fst(_1520781, _1520777, _1520775, _1520779)))], (38348 ^ _780478) ^ [_1517059, _1517061, _1517063] : [c_Wellfounded_Owf(_1517059, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517059, _1517059), tc_HOL_Obool)), _1517061), _1517063)), -(c_Wellfounded_Owf(_1517059, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517059, _1517059), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517059, _1517059), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517059, _1517059, _1517059), _1517061), _1517061)), hAPP(hAPP(c_Relation_Orel__comp(_1517059, _1517059, _1517059), _1517063), _1517061))), _1517063)))], (37082 ^ _780478) ^ [_1485897, _1485899, _1485901] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1485897, _1485899), _1485901)), 37085 ^ _780478 : [(37086 ^ _780478) ^ [_1485982] : [hBOOL(hAPP(hAPP(_1485899, _1485982), _1485901)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1485897, _1485899), _1485982)))]]], (30143 ^ _780478) ^ [_1339812, _1339814] : [class_Rings_Olinordered__idom(_1339812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339812), c_Groups_Ozero__class_Ozero(_1339812)), _1339814)), -(c_Groups_Osgn__class_Osgn(_1339812, _1339814) = c_Groups_Oone__class_Oone(_1339812))], (20278 ^ _780478) ^ [_1158684, _1158686, _1158688, _1158690] : [class_Rings_Olinordered__ring__strict(_1158684), 20281 ^ _780478 : [(20296 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158684), _1158686), _1158688)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158684), _1158690), _1158688)))), 20297 ^ _780478 : [(20304 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158684), _1158688), c_Groups_Ozero__class_Ozero(_1158684))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158684), _1158690), _1158686))], (20298 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158684), c_Groups_Ozero__class_Ozero(_1158684)), _1158688)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158684), _1158686), _1158690))]]], (20282 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158684), _1158686), _1158688)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158684), _1158690), _1158688))), 20287 ^ _780478 : [(20290 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158684), _1158686), _1158690)))], (20288 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158684), c_Groups_Ozero__class_Ozero(_1158684)), _1158688)))]], 20291 ^ _780478 : [(20294 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158684), _1158690), _1158686)))], (20292 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158684), _1158688), c_Groups_Ozero__class_Ozero(_1158684))))]]]]], (8892 ^ _780478) ^ [_933901, _933903, _933905] : [class_Orderings_Olinorder(_933901), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933901), _933903), _933905))), 8899 ^ _780478 : [(8906 ^ _780478) ^ [] : [_933905 = _933903, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933901), _933905), _933903))], (8900 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933901), _933905), _933903))), -(_933905 = _933903)]]], (34913 ^ _780478) ^ [_1438464, _1438466] : [class_Rings_Olinordered__idom(_1438464), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1438464), hAPP(hAPP(c_Power_Opower__class_Opower(_1438464), _1438466), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1438464)))], (116 ^ _780478) ^ [_782366, _782368, _782370, _782372, _782374, _782376, _782378, _782380, _782382, _782384] : [-(c_Big__Operators_Ocomm__monoid__big(_782382, _782378, _782374, _782370, _782366)), c_Big__Operators_Ocomm__monoid__big(_782384, _782380, _782376, _782372, _782368), _782384 = _782382, _782380 = _782378, _782376 = _782374, _782372 = _782370, _782368 = _782366], (7657 ^ _780478) ^ [_909484, _909486, _909488, _909490, _909492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909484, tc_HOL_Obool)), _909486), _909488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909490, tc_HOL_Obool)), hAPP(c_Set_Oimage(_909484, _909490, _909492), _909486)), hAPP(c_Set_Oimage(_909484, _909490, _909492), _909488))))], (45753 ^ _780478) ^ [_1699220, _1699222] : [c_List_Oremdups(_1699220, _1699222) = _1699222, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699220)), c_List_Oremdups(_1699220, _1699222)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699220)), _1699222))], (39163 ^ _780478) ^ [_1540433, _1540435, _1540437, _1540439, _1540441, _1540443, _1540445, _1540447, _1540449, _1540451] : [hAPP(c_Set_Oimage(_1540433, _1540435, _1540437), _1540439) = _1540441, hAPP(c_Set_Oimage(_1540443, _1540445, _1540447), _1540449) = _1540451, -(hAPP(c_Set_Oimage(tc_prod(_1540433, _1540443), tc_prod(_1540435, _1540445), c_Product__Type_Omap__pair(_1540433, _1540435, _1540443, _1540445, _1540437, _1540447)), hAPP(hAPP(c_Product__Type_OSigma(_1540433, _1540443), _1540439), hAPP(c_COMBK(tc_fun(_1540443, tc_HOL_Obool), _1540433), _1540449))) = hAPP(hAPP(c_Product__Type_OSigma(_1540435, _1540445), _1540441), hAPP(c_COMBK(tc_fun(_1540445, tc_HOL_Obool), _1540435), _1540451)))], (52309 ^ _780478) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (26044 ^ _780478) ^ [_1263274, _1263276, _1263278, _1263280] : [class_Fields_Olinordered__field__inverse__zero(_1263274), 26047 ^ _780478 : [(26048 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263274), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1263274), _1263276), _1263278)), _1263280)), 26051 ^ _780478 : [(26058 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263274), c_Groups_Ozero__class_Ozero(_1263274)), _1263278))), 26061 ^ _780478 : [(26068 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263274), _1263278), c_Groups_Ozero__class_Ozero(_1263274)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263274), c_Groups_Ozero__class_Ozero(_1263274)), _1263280)))], (26062 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263274), _1263278), c_Groups_Ozero__class_Ozero(_1263274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263274), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263274), _1263280), _1263278)), _1263276)))]]], (26052 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263274), c_Groups_Ozero__class_Ozero(_1263274)), _1263278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263274), _1263276), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263274), _1263280), _1263278))))]]], (26074 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263274), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1263274), _1263276), _1263278)), _1263280))), 26077 ^ _780478 : [(26080 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263274), _1263276), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263274), _1263280), _1263278)))], (26078 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263274), c_Groups_Ozero__class_Ozero(_1263274)), _1263278)))]], 26081 ^ _780478 : [(26084 ^ _780478) ^ [] : [26085 ^ _780478 : [(26088 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263274), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1263274), _1263280), _1263278)), _1263276))], (26086 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263274), _1263278), c_Groups_Ozero__class_Ozero(_1263274))))]], 26089 ^ _780478 : [(26092 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263274), c_Groups_Ozero__class_Ozero(_1263274)), _1263280))], (26090 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263274), _1263278), c_Groups_Ozero__class_Ozero(_1263274)))]]], (26082 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1263274), c_Groups_Ozero__class_Ozero(_1263274)), _1263278))]]]]], (42266 ^ _780478) ^ [_1619962, _1619964] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1619962), hAPP(c_List_Oset(_1619962), _1619964))))], (44608 ^ _780478) ^ [_1673072, _1673074, _1673076, _1673078] : [hAPP(hAPP(c_List_Oappend(_1673072), _1673074), hAPP(hAPP(c_List_Olist_OCons(_1673072), _1673076), c_List_Olist_ONil(_1673072))) = _1673078, 44611 ^ _780478 : [(44616 ^ _780478) ^ [] : [-(c_List_Olast(_1673072, _1673078) = _1673076)], (44614 ^ _780478) ^ [] : [-(c_List_Obutlast(_1673072, _1673078) = _1673074)], (44612 ^ _780478) ^ [] : [_1673078 = c_List_Olist_ONil(_1673072)]]], (10679 ^ _780478) ^ [_966795, _966797, _966799, _966801] : [class_Orderings_Olinorder(_966795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966795), _966797), _966799)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966795), _966797), _966801)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966795), _966797), hAPP(hAPP(c_Orderings_Oord__class_Omin(_966795), _966799), _966801))))], (18165 ^ _780478) ^ [_1119370, _1119372, _1119374, _1119376, _1119378, _1119380] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119370, tc_fun(_1119372, tc_HOL_Obool)), _1119374), hAPP(hAPP(c_COMBB(_1119376, tc_fun(_1119372, tc_HOL_Obool), _1119370), _1119378), _1119380)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119376, tc_fun(_1119372, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1119370, _1119376, _1119380), _1119374)), _1119378))], (13364 ^ _780478) ^ [_1018502, _1018504, _1018506, _1018508, _1018510] : [c_Fun_Oinj__on(_1018502, _1018504, _1018506, c_Orderings_Otop__class_Otop(tc_fun(_1018502, tc_HOL_Obool))), 13367 ^ _780478 : [(13374 ^ _780478) ^ [] : [_1018508 = _1018510, -(hAPP(c_Set_Oimage(_1018502, _1018504, _1018506), _1018508) = hAPP(c_Set_Oimage(_1018502, _1018504, _1018506), _1018510))], (13368 ^ _780478) ^ [] : [hAPP(c_Set_Oimage(_1018502, _1018504, _1018506), _1018508) = hAPP(c_Set_Oimage(_1018502, _1018504, _1018506), _1018510), -(_1018508 = _1018510)]]], (27229 ^ _780478) ^ [_1284609] : [c_Nat__Transfer_Onat__set(_1284609), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1284609) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1284609)))], (44025 ^ _780478) ^ [_1661611, _1661613, _1661615, _1661617] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1661611) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1661613), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1661611)), hAPP(hAPP(c_List_Olist_OCons(_1661613), _1661615), _1661617)) = hAPP(hAPP(c_List_Odrop(_1661613), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1661611)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1661617))], (46027 ^ _780478) ^ [_1705676, _1705678, _1705680] : [46029 ^ _780478 : [(46032 ^ _780478) ^ [] : [hBOOL(hAPP(_1705678, 46028 ^ [_1705676, _1705678, _1705680]))], (46030 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1705676), 46028 ^ [_1705676, _1705678, _1705680]), hAPP(c_List_Oset(_1705676), _1705680))))]], -(hAPP(c_List_Ofilter(_1705676, _1705678), _1705680) = _1705680)], (38782 ^ _780478) ^ [_1528751, _1528753, _1528755, _1528757, _1528759] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528751, _1528753), _1528755), hAPP(hAPP(c_COMBS(_1528751, tc_fun(_1528753, tc_HOL_Obool), tc_fun(_1528753, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528753, tc_HOL_Obool), tc_fun(tc_fun(_1528753, tc_HOL_Obool), tc_fun(_1528753, tc_HOL_Obool)), _1528751), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528753, tc_HOL_Obool))), _1528757)), _1528759)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528751, _1528753), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528751, _1528753), _1528755), _1528757)), hAPP(hAPP(c_Product__Type_OSigma(_1528751, _1528753), _1528755), _1528759)))], (46003 ^ _780478) ^ [_1705173, _1705175, _1705177, _1705179, _1705181] : [class_Orderings_Olinorder(_1705173), -(hAPP(c_List_Ofilter(_1705175, _1705177), c_List_Olinorder__class_Osort__key(_1705175, _1705173, _1705179, _1705181)) = c_List_Olinorder__class_Osort__key(_1705175, _1705173, _1705179, hAPP(c_List_Ofilter(_1705175, _1705177), _1705181)))], (39642 ^ _780478) ^ [_1552242, _1552244, _1552246, _1552248, _1552250, _1552252, _1552254] : [-(hAPP(c_Fun_Ocomp(_1552242, _1552244, _1552246, _1552248), hAPP(c_Fun_Ocomp(_1552250, _1552242, _1552246, _1552252), _1552254)) = hAPP(c_Fun_Ocomp(_1552250, _1552244, _1552246, hAPP(c_Fun_Ocomp(_1552242, _1552244, _1552250, _1552248), _1552252)), _1552254))], (10199 ^ _780478) ^ [_957823, _957825, _957827, _957829] : [class_Orderings_Olinorder(_957823), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_957823), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957823), _957825), _957827)), _957829) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_957823), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957823), _957825), _957829)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957823), _957827), _957829)))], (45893 ^ _780478) ^ [_1701789, _1701791, _1701793] : [-(c_List_Oconcat(_1701789, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1701789)), _1701791), _1701793)) = hAPP(hAPP(c_List_Oappend(_1701789), _1701791), c_List_Oconcat(_1701789, _1701793)))], (25505 ^ _780478) ^ [_1253932, _1253934, _1253936] : [class_Fields_Ofield__inverse__zero(_1253932), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253932), c_Groups_Oone__class_Oone(_1253932)), hAPP(hAPP(c_Power_Opower__class_Opower(_1253932), _1253934), _1253936)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1253932), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1253932), c_Groups_Oone__class_Oone(_1253932)), _1253934)), _1253936))], (42358 ^ _780478) ^ [_1622109, _1622111, _1622113, _1622115, _1622117] : [hBOOL(hAPP(hAPP(c_member(_1622109), _1622111), hAPP(c_List_Oset(_1622109), _1622113))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622115), hAPP(_1622117, _1622111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622115), c_List_Olist_Olist__size(_1622109, _1622117, _1622113))))], (5805 ^ _780478) ^ [_872351, _872353, _872355, _872357] : [c_Hoare__Mirabelle_Ohoare__derivs(_872351, _872353, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872351)), _872355), _872357)), 5808 ^ _780478 : [(5811 ^ _780478) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_872351, _872353, _872357))], (5809 ^ _780478) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_872351, _872353, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872351)), _872355), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872351), tc_HOL_Obool)))))]]], (4180 ^ _780478) ^ [_843747, _843749, _843751, _843753] : [-(c_New__DSequence_Opos__single(_843753, _843749) = c_New__DSequence_Opos__single(_843751, _843747)), _843753 = _843751, _843749 = _843747], (49177 ^ _780478) ^ [_1773646, _1773648, _1773650, _1773652, _1773654] : [c_Relation_Otrans(_1773646, _1773648), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773646, _1773646)), hAPP(hAPP(c_Product__Type_OPair(_1773646, _1773646), _1773650), _1773652)), _1773648)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773646, _1773646)), hAPP(hAPP(c_Product__Type_OPair(_1773646, _1773646), _1773652), _1773654)), _1773648)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773646, _1773646)), hAPP(hAPP(c_Product__Type_OPair(_1773646, _1773646), _1773650), _1773654)), _1773648)))], (4676 ^ _780478) ^ [_851655, _851657] : [_851657 = _851655, -(c_Code__Numeral_OSuc__code__numeral(_851657) = c_Code__Numeral_OSuc__code__numeral(_851655))], (13146 ^ _780478) ^ [_1013610, _1013612, _1013614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013610, tc_HOL_Obool)), _1013612), _1013614)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013610, tc_HOL_Obool)), _1013614), _1013612) = _1013614)], (28524 ^ _780478) ^ [_1308521, _1308523] : [c_Nat__Transfer_Ois__nat(_1308521), c_Nat__Transfer_Ois__nat(_1308523), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1308521, _1308523) = 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, _1308521), hAPP(c_Int_Onat, _1308523))))], (11107 ^ _780478) ^ [_974375, _974377, _974379, _974381] : [class_Groups_Oordered__ab__group__add(_974375), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974375), hAPP(hAPP(c_Orderings_Oord__class_Omax(_974375), _974377), _974379)), _974381) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_974375), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974375), _974377), _974381)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974375), _974379), _974381)))], (18169 ^ _780478) ^ [_1119524, _1119526, _1119528, _1119530, _1119532, _1119534, _1119536] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119524, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119526, tc_fun(_1119524, tc_HOL_Obool)), _1119528), _1119530)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119532, tc_fun(_1119524, tc_HOL_Obool)), _1119534), _1119536)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119526, tc_fun(_1119524, tc_HOL_Obool)), _1119528), hAPP(hAPP(c_COMBB(tc_fun(_1119532, tc_fun(_1119524, tc_HOL_Obool)), tc_fun(_1119524, tc_HOL_Obool), _1119526), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119532, tc_fun(_1119524, tc_HOL_Obool)), _1119534)), hAPP(hAPP(c_COMBC(_1119526, tc_fun(_1119532, tc_fun(_1119524, tc_HOL_Obool)), tc_fun(_1119532, tc_fun(_1119524, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1119524, tc_HOL_Obool), tc_fun(_1119524, tc_HOL_Obool)), tc_fun(tc_fun(_1119532, tc_fun(_1119524, tc_HOL_Obool)), tc_fun(_1119532, tc_fun(_1119524, tc_HOL_Obool))), _1119526), c_COMBB(tc_fun(_1119524, tc_HOL_Obool), tc_fun(_1119524, tc_HOL_Obool), _1119532)), hAPP(hAPP(c_COMBB(tc_fun(_1119524, tc_HOL_Obool), tc_fun(tc_fun(_1119524, tc_HOL_Obool), tc_fun(_1119524, tc_HOL_Obool)), _1119526), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119524, tc_HOL_Obool))), _1119530))), _1119536))))], (47816 ^ _780478) ^ [_1743826, _1743828, _1743830, _1743832, _1743834] : [class_Orderings_Olinorder(_1743826), 47822 ^ _780478 : [(47825 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743826), hAPP(_1743832, _1743834)), hAPP(_1743832, 47821 ^ [_1743826, _1743828, _1743830, _1743832, _1743834])))], (47823 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743828), 47821 ^ [_1743826, _1743828, _1743830, _1743832, _1743834]), hAPP(c_List_Oset(_1743828), _1743830))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1743828, _1743826, _1743832), _1743834), _1743830) = hAPP(hAPP(c_List_Olist_OCons(_1743828), _1743834), _1743830))], (43003 ^ _780478) ^ [_1638328, _1638330, _1638332, _1638334] : [_1638328 = _1638330, -(c_List_Oremove1(_1638332, _1638328, hAPP(hAPP(c_List_Olist_OCons(_1638332), _1638330), _1638334)) = _1638334)], (39795 ^ _780478) ^ [_1555579, _1555581, _1555583, _1555585, _1555587, _1555589] : [class_Groups_Ocomm__monoid__add(_1555579), c_Fun_Oinj__on(_1555581, _1555583, _1555585, _1555587), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1555583, _1555579), _1555589), hAPP(c_Set_Oimage(_1555581, _1555583, _1555585), _1555587)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1555581, _1555579), hAPP(c_Fun_Ocomp(_1555583, _1555579, _1555581, _1555589), _1555585)), _1555587))], (32336 ^ _780478) ^ [_1391479, _1391481, _1391483, _1391485] : [class_Fields_Ofield__inverse__zero(_1391479), class_Int_Onumber(_1391479), 32343 ^ _780478 : [(32344 ^ _780478) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391479), _1391481), hAPP(c_Int_Onumber__class_Onumber__of(_1391479), _1391483)) = _1391485, 32347 ^ _780478 : [(32354 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1391479), _1391483) = c_Groups_Ozero__class_Ozero(_1391479), -(_1391485 = c_Groups_Ozero__class_Ozero(_1391479))], (32348 ^ _780478) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1391479), _1391483) = c_Groups_Ozero__class_Ozero(_1391479)), -(_1391481 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391479), _1391485), hAPP(c_Int_Onumber__class_Onumber__of(_1391479), _1391483)))]]], (32360 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391479), _1391481), hAPP(c_Int_Onumber__class_Onumber__of(_1391479), _1391483)) = _1391485), 32363 ^ _780478 : [(32366 ^ _780478) ^ [] : [_1391481 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391479), _1391485), hAPP(c_Int_Onumber__class_Onumber__of(_1391479), _1391483))], (32364 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1391479), _1391483) = c_Groups_Ozero__class_Ozero(_1391479)]], 32367 ^ _780478 : [(32370 ^ _780478) ^ [] : [_1391485 = c_Groups_Ozero__class_Ozero(_1391479)], (32368 ^ _780478) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1391479), _1391483) = c_Groups_Ozero__class_Ozero(_1391479))]]]]], (26542 ^ _780478) ^ [_1272165, _1272167, _1272169] : [class_Fields_Olinordered__field(_1272165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272165), c_Groups_Ozero__class_Ozero(_1272165)), _1272167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272165), _1272169), c_Groups_Ozero__class_Ozero(_1272165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272165), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272165), _1272167), _1272169)), c_Groups_Ozero__class_Ozero(_1272165))))], (16362 ^ _780478) ^ [_1078104, _1078106, _1078108, _1078110] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1078104, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1078106, _1078104, _1078108), hAPP(c_Set_Ovimage(_1078106, _1078104, _1078108), _1078110))), _1078110)))], (24285 ^ _780478) ^ [_1232250, _1232252] : [class_Divides_Osemiring__div(_1232250), -(_1232252 = c_Groups_Ozero__class_Ozero(_1232250)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1232250), _1232252), _1232252) = c_Groups_Oone__class_Oone(_1232250))], (52047 ^ _780478) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (36447 ^ _780478) ^ [_1473898, _1473900] : [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), _1473898))), 36450 ^ _780478 : [(36457 ^ _780478) ^ [] : [-(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), _1473900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473898))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473900), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473898)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473898)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473900), 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), _1473898)))))], (36451 ^ _780478) ^ [] : [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), _1473900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473898)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473900), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473898)) = 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), _1473900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1473898))))]]], (52033 ^ _780478) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (11731 ^ _780478) ^ [_986186] : [class_Orderings_Olinorder(_986186), -(c_Orderings_Oord_Omax(_986186, hAPP(c_COMBC(_986186, _986186, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_986186))) = c_Orderings_Oord__class_Omin(_986186))], (50833 ^ _780478) ^ [_1809610, _1809612, _1809614, _1809616, _1809618, _1809620, _1809622] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1809610, _1809612), tc_prod(_1809610, _1809612))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1809610, _1809612), tc_prod(_1809610, _1809612)), hAPP(hAPP(c_Product__Type_OPair(_1809610, _1809612), _1809614), _1809616)), hAPP(hAPP(c_Product__Type_OPair(_1809610, _1809612), _1809618), _1809620))), c_Transitive__Closure_Ortrancl(tc_prod(_1809610, _1809612), _1809622))), -(hAPP(hAPP(c_Product__Type_OPair(_1809610, _1809612), _1809614), _1809616) = hAPP(hAPP(c_Product__Type_OPair(_1809610, _1809612), _1809618), _1809620)), 50842 ^ _780478 : [(50845 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1809610, _1809612), tc_prod(_1809610, _1809612))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1809610, _1809612), tc_prod(_1809610, _1809612)), hAPP(hAPP(c_Product__Type_OPair(_1809610, _1809612), 50840 ^ [_1809610, _1809612, _1809614, _1809616, _1809618, _1809620, _1809622]), 50841 ^ [_1809610, _1809612, _1809614, _1809616, _1809618, _1809620, _1809622])), hAPP(hAPP(c_Product__Type_OPair(_1809610, _1809612), _1809618), _1809620))), c_Transitive__Closure_Ortrancl(tc_prod(_1809610, _1809612), _1809622))))], (50843 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1809610, _1809612), tc_prod(_1809610, _1809612))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1809610, _1809612), tc_prod(_1809610, _1809612)), hAPP(hAPP(c_Product__Type_OPair(_1809610, _1809612), _1809614), _1809616)), hAPP(hAPP(c_Product__Type_OPair(_1809610, _1809612), 50840 ^ [_1809610, _1809612, _1809614, _1809616, _1809618, _1809620, _1809622]), 50841 ^ [_1809610, _1809612, _1809614, _1809616, _1809618, _1809620, _1809622]))), _1809622)))]]], (34683 ^ _780478) ^ [_1434334, _1434336] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1434334)), c_Int_OBit1(_1434336)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1434334), c_Int_Osucc(_1434336))))], (40365 ^ _780478) ^ [_1569083, _1569085, _1569087, _1569089, _1569091, _1569093, _1569095] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1569083, _1569085, _1569087, _1569089), _1569091), _1569093), _1569095) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1569085, _1569087, _1569089), _1569093), hAPP(_1569091, _1569095)))], (6774 ^ _780478) ^ [_892585, _892587, _892589, _892591, _892593, _892595, _892597] : [-(_892585 = _892587), -(c_Fun_Ofun__upd(_892589, _892591, c_Fun_Ofun__upd(_892589, _892591, _892593, _892585, _892595), _892587, _892597) = c_Fun_Ofun__upd(_892589, _892591, c_Fun_Ofun__upd(_892589, _892591, _892593, _892587, _892597), _892585, _892595))], (24577 ^ _780478) ^ [_1237092, _1237094] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1237092, _1237094)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1237094), hAPP(c_Nat_OSuc, _1237092)))], (22217 ^ _780478) ^ [_1193405, _1193407, _1193409, _1193411, _1193413] : [class_Groups_Ocomm__monoid__add(_1193405), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193407), _1193409)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193407, _1193405), _1193411), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1193407, tc_HOL_Obool)), _1193409), _1193413)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193407, _1193405), hAPP(hAPP(c_COMBC(_1193407, _1193405, _1193405), hAPP(hAPP(c_COMBS(_1193407, _1193405, tc_fun(_1193405, _1193405)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1193405, tc_fun(_1193405, _1193405)), _1193407), c_If(_1193405)), hAPP(hAPP(c_COMBC(_1193407, tc_fun(_1193407, tc_HOL_Obool), tc_HOL_Obool), c_member(_1193407)), _1193413))), _1193411)), c_Groups_Ozero__class_Ozero(_1193405))), _1193409))], (46062 ^ _780478) ^ [_1706359, _1706361, _1706363, _1706365, _1706367] : [-(hAPP(c_List_Ofilter(_1706359, _1706361), hAPP(hAPP(c_List_Omap(_1706363, _1706359), _1706365), _1706367)) = hAPP(hAPP(c_List_Omap(_1706363, _1706359), _1706365), hAPP(c_List_Ofilter(_1706363, hAPP(c_Fun_Ocomp(_1706359, tc_HOL_Obool, _1706363, _1706361), _1706365)), _1706367)))], (23161 ^ _780478) ^ [_1211661] : [23163 ^ _780478 : [(23166 ^ _780478) ^ [] : [hBOOL(hAPP(_1211661, 23162 ^ [_1211661]))], (23164 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23162 ^ [_1211661])))]], 23167 ^ _780478 : [(23168 ^ _780478) ^ [_1211788] : [-(hBOOL(hAPP(_1211661, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211788))))]]], (47486 ^ _780478) ^ [_1736254, _1736256, _1736258, _1736260] : [47488 ^ _780478 : [(47491 ^ _780478) ^ [] : [hBOOL(hAPP(_1736256, hAPP(hAPP(c_List_Onth(_1736258), _1736260), 47487 ^ [_1736254, _1736256, _1736258, _1736260])))], (47489 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47487 ^ [_1736254, _1736256, _1736258, _1736260]), _1736254)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736254), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736258)), _1736260))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736254), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736258)), c_List_OtakeWhile(_1736258, _1736256, _1736260)))))], (19228 ^ _780478) ^ [_1141192, _1141194] : [class_Rings_Omult__zero(_1141192), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141192), _1141194), c_Groups_Ozero__class_Ozero(_1141192)) = c_Groups_Ozero__class_Ozero(_1141192))], (45773 ^ _780478) ^ [_1699568, _1699570] : [-(hAPP(c_List_OremoveAll(_1699568, _1699570), c_List_Olist_ONil(_1699568)) = c_List_Olist_ONil(_1699568))], (39273 ^ _780478) ^ [_1542936] : [-(c_Relation_Orefl__on(_1542936, c_Orderings_Obot__class_Obot(tc_fun(_1542936, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1542936, _1542936), tc_HOL_Obool))))], (40943 ^ _780478) ^ [_1582648, _1582650, _1582652, _1582654] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582648, _1582648)), hAPP(hAPP(c_Product__Type_OPair(_1582648, _1582648), _1582650), _1582652)), c_Transitive__Closure_Ortrancl(_1582648, hAPP(c_Relation_Oconverse(_1582648, _1582648), _1582654)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582648, _1582648)), hAPP(hAPP(c_Product__Type_OPair(_1582648, _1582648), _1582652), _1582650)), c_Transitive__Closure_Ortrancl(_1582648, _1582654))))], (24565 ^ _780478) ^ [_1236802, _1236804, _1236806, _1236808] : [class_Orderings_Oorder(_1236802), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1236802, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1236802, _1236804, _1236806)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1236802, _1236806), _1236808)) = c_Orderings_Obot__class_Obot(tc_fun(_1236802, tc_HOL_Obool)))], (33943 ^ _780478) ^ [_1421657] : [class_Int_Onumber__ring(_1421657), c_Int_Oiszero(_1421657, hAPP(c_Int_Onumber__class_Onumber__of(_1421657), c_Int_OBit1(c_Int_OPls)))], (12318 ^ _780478) ^ [_997567, _997569, _997571, _997573] : [class_Orderings_Olinorder(_997567), hBOOL(hAPP(c_Finite__Set_Ofinite(_997567), _997569)), 12328 ^ _780478 : [(12331 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997567), _997571), 12327 ^ [_997567, _997569, _997571, _997573]))], (12329 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_997567), 12327 ^ [_997567, _997569, _997571, _997573]), _997569)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997567), hAPP(hAPP(c_Orderings_Oord__class_Omin(_997567), _997571), _997573)), hAPP(hAPP(c_Finite__Set_Ofold(_997567, _997567, c_Orderings_Oord__class_Omin(_997567)), _997573), _997569))))], (24839 ^ _780478) ^ [_1241868, _1241870, _1241872] : [class_Orderings_Oorder(_1241868), 24842 ^ _780478 : [(24849 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241868), _1241870), _1241872))), -(c_Orderings_Obot__class_Obot(tc_fun(_1241868, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1241868, _1241870, _1241872))], (24843 ^ _780478) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1241868, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1241868, _1241870, _1241872), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241868), _1241870), _1241872))]]], (40534 ^ _780478) ^ [_1573271, _1573273] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1573271, _1573271, _1573271), c_Transitive__Closure_Ortrancl(_1573271, _1573273)), c_Transitive__Closure_Ortrancl(_1573271, _1573273)) = c_Transitive__Closure_Ortrancl(_1573271, _1573273))], (45837 ^ _780478) ^ [_1700677, _1700679, _1700681, _1700683, _1700685] : [c_Fun_Oinj__on(_1700677, _1700679, _1700681, c_Orderings_Otop__class_Otop(tc_fun(_1700677, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1700677, _1700679), _1700681), hAPP(c_List_OremoveAll(_1700677, _1700683), _1700685)) = hAPP(c_List_OremoveAll(_1700679, hAPP(_1700681, _1700683)), hAPP(hAPP(c_List_Omap(_1700677, _1700679), _1700681), _1700685)))], (12506 ^ _780478) ^ [_1001152, _1001154, _1001156, _1001158] : [hBOOL(hAPP(hAPP(c_member(_1001152), _1001154), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001152, tc_HOL_Obool)), _1001156), _1001158))), -(hBOOL(hAPP(hAPP(c_member(_1001152), _1001154), _1001156))), -(hBOOL(hAPP(hAPP(c_member(_1001152), _1001154), _1001158)))], (8489 ^ _780478) ^ [_926720, _926722, _926724, _926726, _926728] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_926720, _926722, hAPP(hAPP(c_Set_Oinsert(_926720), _926724), _926726)), _926728))), 8490 ^ _780478 : [(8491 ^ _780478) ^ [_926824, _926826] : [hAPP(hAPP(c_Set_Oinsert(_926720), _926724), _926726) = hAPP(hAPP(c_Set_Oinsert(_926720), _926826), _926824), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_926720, _926720, _926722, _926826, _926824), _926728)), -(hBOOL(hAPP(hAPP(c_member(_926720), _926826), _926824)))]]], (27207 ^ _780478) ^ [_1284304] : [c_Nat__Transfer_Onat__set(_1284304), -(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), _1284304)) = _1284304)], (27371 ^ _780478) ^ [] : [-(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))))], (41622 ^ _780478) ^ [_1600758, _1600760, _1600762] : [-(c_Nitpick_Oof__frac(_1600760, _1600758, _1600762) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1600758), hAPP(c_Int_Oring__1__class_Oof__int(_1600758), hAPP(c_Nitpick_Onum(_1600760), _1600762))), hAPP(c_Int_Oring__1__class_Oof__int(_1600758), hAPP(c_Nitpick_Odenom(_1600760), _1600762)))), class_Rings_Oinverse(_1600758), class_Rings_Oring__1(_1600758)], (42039 ^ _780478) ^ [_1613884, _1613886, _1613888, _1613890, _1613892, _1613894] : [c_List_Olistrelp(_1613884, _1613886, hAPP(hAPP(c_List_Olist_OCons(_1613884), _1613888), _1613890), hAPP(hAPP(c_List_Olist_OCons(_1613884), _1613892), _1613894)), 42042 ^ _780478 : [(42045 ^ _780478) ^ [] : [-(c_List_Olistrelp(_1613884, _1613886, _1613890, _1613894))], (42043 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1613886, _1613888), _1613892)))]]], (16222 ^ _780478) ^ [_1074533, _1074535, _1074537, _1074539] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074533, tc_HOL_Obool)), _1074535), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074533, tc_HOL_Obool)), _1074537), _1074539)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074533, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074533, tc_HOL_Obool)), _1074535), _1074537)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074533, tc_HOL_Obool)), _1074535), _1074539)))], (25229 ^ _780478) ^ [_1249335, _1249337] : [class_Rings_Odivision__ring(_1249335), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249335), c_Groups_Ozero__class_Ozero(_1249335)), _1249337) = c_Groups_Ozero__class_Ozero(_1249335))], (51089 ^ _780478) ^ [_1815970, _1815972, _1815974, _1815976] : [class_Divides_Osemiring__div(_1815970), -(_1815972 = c_Groups_Ozero__class_Ozero(_1815970)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815970), _1815972), _1815974)), 51100 ^ _780478 : [(51107 ^ _780478) ^ [] : [_1815974 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815970), _1815976), _1815972), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1815970), _1815974), _1815972) = _1815976)], (51101 ^ _780478) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1815970), _1815974), _1815972) = _1815976, -(_1815974 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815970), _1815976), _1815972))]]], (47276 ^ _780478) ^ [_1731648, _1731650, _1731652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731648)), c_List_OtakeWhile(_1731648, _1731650, _1731652))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731648)), _1731652))), hBOOL(hAPP(_1731650, hAPP(hAPP(c_List_Onth(_1731648), _1731652), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731648)), c_List_OtakeWhile(_1731648, _1731650, _1731652)))))], (38662 ^ _780478) ^ [_1524913, _1524915, _1524917, _1524919] : [hBOOL(hAPP(hAPP(c_member(_1524913), _1524915), hAPP(c_Relation_ODomain(_1524913, _1524917), _1524919))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524913, _1524917)), hAPP(hAPP(c_Product__Type_OPair(_1524913, _1524917), _1524915), 38665 ^ [_1524913, _1524915, _1524917, _1524919])), _1524919)))], (36361 ^ _780478) ^ [_1472409, _1472411, _1472413, _1472415, _1472417] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1472409, _1472411, _1472413), _1472415), _1472417)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472409, _1472411)), hAPP(hAPP(c_Product__Type_OPair(_1472409, _1472411), _1472415), _1472417)), _1472413)))], (39446 ^ _780478) ^ [_1546378, _1546380] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1546378), c_Int_OInteg)), hBOOL(hAPP(_1546380, hAPP(c_Int_ORep__Integ, 39451 ^ [_1546378, _1546380]))), -(hBOOL(hAPP(_1546380, _1546378)))], (11069 ^ _780478) ^ [_973739, _973741, _973743] : [hBOOL(hAPP(hAPP(c_member(_973739), _973741), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973739, tc_HOL_Obool)), _973743))), hBOOL(hAPP(hAPP(c_member(_973739), _973741), _973743))], (12668 ^ _780478) ^ [_1004618, _1004620, _1004622, _1004624] : [hBOOL(hAPP(_1004618, _1004620)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004622, tc_HOL_Obool)), _1004618), _1004624), _1004620)))], (16022 ^ _780478) ^ [_1070354, _1070356, _1070358, _1070360] : [class_Lattices_Odistrib__lattice(_1070354), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070354), _1070356), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070354), _1070358), _1070360)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070354), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070354), _1070356), _1070358)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070354), _1070356), _1070360)))], (47411 ^ _780478) ^ [_1734516, _1734518, _1734520, _1734522, _1734524] : [-(c_List_OdropWhile(_1734516, _1734518, _1734520) = hAPP(hAPP(c_List_Olist_OCons(_1734516), _1734522), _1734524)), _1734520 = hAPP(hAPP(c_List_Oappend(_1734516), c_List_OtakeWhile(_1734516, _1734518, _1734520)), hAPP(hAPP(c_List_Olist_OCons(_1734516), _1734522), _1734524)), -(hBOOL(hAPP(_1734518, _1734522)))], (40029 ^ _780478) ^ [_1560958, _1560960, _1560962, _1560964, _1560966, _1560968] : [c_Finite__Set_Ofolding(_1560958, _1560960, _1560962, _1560964), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560958), _1560966)), -(hAPP(hAPP(_1560964, _1560966), _1560968) = hAPP(hAPP(c_Finite__Set_Ofold(_1560958, _1560960, _1560962), _1560968), _1560966))], (17669 ^ _780478) ^ [_1109381, _1109383, _1109385, _1109387] : [class_Complete__Lattice_Ocomplete__lattice(_1109381), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109383), _1109385)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1109383, _1109381), _1109385), _1109387) = hAPP(hAPP(c_Finite__Set_Ofold(_1109383, _1109381, hAPP(hAPP(c_COMBB(_1109381, tc_fun(_1109381, _1109381), _1109383), c_Lattices_Osemilattice__inf__class_Oinf(_1109381)), _1109387)), c_Orderings_Otop__class_Otop(_1109381)), _1109385))], (43875 ^ _780478) ^ [_1657981, _1657983, _1657985] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657981)), hAPP(hAPP(c_List_Odrop(_1657981), _1657983), _1657985)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657981)), _1657985)), _1657983))], (32618 ^ _780478) ^ [_1396527, _1396529, _1396531, _1396533] : [class_Fields_Olinordered__field__inverse__zero(_1396527), class_Int_Onumber(_1396527), 32625 ^ _780478 : [(32626 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), hAPP(c_Int_Onumber__class_Onumber__of(_1396527), _1396529)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1396527), _1396531), _1396533))), 32629 ^ _780478 : [(32636 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), c_Groups_Ozero__class_Ozero(_1396527)), _1396533))), 32639 ^ _780478 : [(32646 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), _1396533), c_Groups_Ozero__class_Ozero(_1396527)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), hAPP(c_Int_Onumber__class_Onumber__of(_1396527), _1396529)), c_Groups_Ozero__class_Ozero(_1396527))))], (32640 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), _1396533), c_Groups_Ozero__class_Ozero(_1396527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), _1396531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396527), hAPP(c_Int_Onumber__class_Onumber__of(_1396527), _1396529)), _1396533))))]]], (32630 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), c_Groups_Ozero__class_Ozero(_1396527)), _1396533)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396527), hAPP(c_Int_Onumber__class_Onumber__of(_1396527), _1396529)), _1396533)), _1396531)))]]], (32652 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), hAPP(c_Int_Onumber__class_Onumber__of(_1396527), _1396529)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1396527), _1396531), _1396533)))), 32655 ^ _780478 : [(32658 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396527), hAPP(c_Int_Onumber__class_Onumber__of(_1396527), _1396529)), _1396533)), _1396531))], (32656 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), c_Groups_Ozero__class_Ozero(_1396527)), _1396533)))]], 32659 ^ _780478 : [(32662 ^ _780478) ^ [] : [32663 ^ _780478 : [(32666 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), _1396531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396527), hAPP(c_Int_Onumber__class_Onumber__of(_1396527), _1396529)), _1396533)))], (32664 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), _1396533), c_Groups_Ozero__class_Ozero(_1396527))))]], 32667 ^ _780478 : [(32670 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), hAPP(c_Int_Onumber__class_Onumber__of(_1396527), _1396529)), c_Groups_Ozero__class_Ozero(_1396527)))], (32668 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), _1396533), c_Groups_Ozero__class_Ozero(_1396527)))]]], (32660 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396527), c_Groups_Ozero__class_Ozero(_1396527)), _1396533))]]]]], (45997 ^ _780478) ^ [_1704749, _1704751, _1704753, _1704755] : [-(c_List_Otranspose(_1704749, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704749)), hAPP(hAPP(c_List_Olist_OCons(_1704749), _1704751), _1704753)), _1704755)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704749)), hAPP(hAPP(c_List_Olist_OCons(_1704749), _1704751), c_List_Oconcat(_1704749, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704749), tc_List_Olist(_1704749)), c_List_Olist_Olist__case(tc_List_Olist(_1704749), _1704749, c_List_Olist_ONil(_1704749), hAPP(hAPP(c_COMBB(tc_List_Olist(_1704749), tc_fun(tc_List_Olist(_1704749), tc_List_Olist(_1704749)), _1704749), c_COMBK(tc_List_Olist(_1704749), tc_List_Olist(_1704749))), hAPP(hAPP(c_COMBC(_1704749, tc_List_Olist(_1704749), tc_List_Olist(_1704749)), c_List_Olist_OCons(_1704749)), c_List_Olist_ONil(_1704749))))), _1704755)))), c_List_Otranspose(_1704749, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1704749)), _1704753), c_List_Oconcat(tc_List_Olist(_1704749), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704749), tc_List_Olist(tc_List_Olist(_1704749))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1704749)), _1704749, c_List_Olist_ONil(tc_List_Olist(_1704749)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1704749), tc_List_Olist(tc_List_Olist(_1704749))), _1704749), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704749), tc_List_Olist(tc_List_Olist(_1704749)), tc_List_Olist(tc_List_Olist(_1704749))), c_List_Olist_OCons(tc_List_Olist(_1704749))), c_List_Olist_ONil(tc_List_Olist(_1704749)))))), _1704755))))))], (43562 ^ _780478) ^ [_1650223, _1650225, _1650227] : [_1650223 = hAPP(hAPP(c_List_Oappend(_1650225), _1650227), _1650223), -(_1650227 = c_List_Olist_ONil(_1650225))], (50255 ^ _780478) ^ [_1797163, _1797165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1797163), _1797165)), -(c_Quickcheck_Obeyond(_1797163, _1797165) = _1797165)], (4080 ^ _780478) ^ [_842155, _842157] : [_842157 = _842155, -(c_New__Random__Sequence_Oneg__single(_842157) = c_New__Random__Sequence_Oneg__single(_842155))], (43043 ^ _780478) ^ [_1638931, _1638933] : [-(c_List_Osublist(_1638931, c_List_Olist_ONil(_1638931), _1638933) = c_List_Olist_ONil(_1638931))], (9610 ^ _780478) ^ [_945706, _945708, _945710] : [class_Orderings_Olinorder(_945706), hBOOL(hAPP(c_Finite__Set_Ofinite(_945706), _945708)), hBOOL(hAPP(hAPP(c_member(_945706), _945710), _945708)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_945706), _945710), c_Big__Operators_Olinorder__class_OMax(_945706, _945708))))], (19034 ^ _780478) ^ [_1137825, _1137827, _1137829, _1137831] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1137825, tc_fun(_1137827, tc_HOL_Obool)), _1137829), _1137831) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1137827, tc_HOL_Obool), hAPP(c_Set_Oimage(_1137825, tc_fun(_1137827, tc_HOL_Obool), _1137831), _1137829)))], (5404 ^ _780478) ^ [_863165, _863167] : [_863167 = _863165, -(c_Power_Opower__class_Opower(_863167) = c_Power_Opower__class_Opower(_863165))], (39879 ^ _780478) ^ [_1557451, _1557453, _1557455, _1557457, _1557459, _1557461, _1557463] : [class_Groups_Oab__semigroup__mult(_1557451), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557453), _1557455)), c_Fun_Oinj__on(_1557453, _1557457, _1557459, _1557455), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1557451, _1557457, c_Groups_Otimes__class_Otimes(_1557451)), _1557461), _1557463), hAPP(c_Set_Oimage(_1557453, _1557457, _1557459), _1557455)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1557451, _1557453, c_Groups_Otimes__class_Otimes(_1557451)), hAPP(c_Fun_Ocomp(_1557457, _1557451, _1557453, _1557461), _1557459)), _1557463), _1557455))], (41888 ^ _780478) ^ [_1608912, _1608914, _1608916, _1608918] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608912), tc_List_Olist(_1608912))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608912), tc_List_Olist(_1608912)), _1608914), _1608916)), c_List_Olistrel1(_1608912, hAPP(c_Relation_Oconverse(_1608912, _1608912), _1608918)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608912), tc_List_Olist(_1608912))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608912), tc_List_Olist(_1608912)), _1608914), _1608916)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1608912), tc_List_Olist(_1608912)), c_List_Olistrel1(_1608912, _1608918)))))], (12201 ^ _780478) ^ [_995144, _995146, _995148] : [class_Orderings_Olinorder(_995144), hAPP(_995146, hAPP(hAPP(c_Orderings_Oord__class_Omax(_995144), 12206 ^ [_995144, _995146, _995148]), 12207 ^ [_995144, _995146, _995148])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_995144), hAPP(_995146, 12206 ^ [_995144, _995146, _995148])), hAPP(_995146, 12207 ^ [_995144, _995146, _995148])), hBOOL(hAPP(c_Finite__Set_Ofinite(_995144), _995148)), -(_995148 = c_Orderings_Obot__class_Obot(tc_fun(_995144, tc_HOL_Obool))), -(hAPP(_995146, c_Big__Operators_Olattice_OSup__fin(_995144, c_Orderings_Oord__class_Omax(_995144), _995148)) = c_Big__Operators_Olattice_OSup__fin(_995144, c_Orderings_Oord__class_Omax(_995144), hAPP(c_Set_Oimage(_995144, _995144, _995146), _995148)))], (12950 ^ _780478) ^ [_1009916, _1009918, _1009920, _1009922, _1009924] : [class_Lattices_Osemilattice__sup(_1009916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009916), _1009918), _1009920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009916), _1009922), _1009924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009916), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009916), _1009918), _1009922)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009916), _1009920), _1009924))))], (1734 ^ _780478) ^ [_805017, _805019] : [-(class_Rings_Ozero__neq__one(_805017)), _805019 = _805017, class_Rings_Ozero__neq__one(_805019)], (48105 ^ _780478) ^ [_1749984, _1749986, _1749988, _1749990] : [48106 ^ _780478 : [(48109 ^ _780478) ^ [] : [c_List_Olist__ex(_1749984, _1749986, _1749990)], (48107 ^ _780478) ^ [] : [hBOOL(hAPP(_1749986, _1749988))]], -(c_List_Olist__ex(_1749984, _1749986, hAPP(hAPP(c_List_Olist_OCons(_1749984), _1749988), _1749990)))], (35451 ^ _780478) ^ [_1448273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448273), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1448273)), c_Int_OMin)))], (52013 ^ _780478) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (5973 ^ _780478) ^ [_875440, _875442] : [class_Finite__Set_Ofinite(_875440), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_875440), _875442)))], (7008 ^ _780478) ^ [_897496, _897498, _897500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897496, tc_HOL_Obool)), _897498), _897500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897496, tc_HOL_Obool)), _897500), _897498)), -(_897498 = _897500)], (52303 ^ _780478) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (15651 ^ _780478) ^ [_1063172, _1063174] : [class_Lattices_Olattice(_1063172), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1063172), _1063174), _1063174) = _1063174)], (42642 ^ _780478) ^ [_1630240, _1630242, _1630244] : [-(hAPP(hAPP(c_List_Olist__update(_1630240, _1630242), _1630244), hAPP(hAPP(c_List_Onth(_1630240), _1630242), _1630244)) = _1630242)], (49282 ^ _780478) ^ [_1775939, _1775941, _1775943, _1775945] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1775939), _1775941)), 49285 ^ _780478 : [(49286 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1775943), hAPP(c_Set_OCollect(_1775943), hAPP(hAPP(c_COMBB(tc_fun(_1775939, tc_HOL_Obool), tc_HOL_Obool, _1775943), c_HOL_OEx(_1775939)), hAPP(hAPP(c_COMBB(tc_fun(_1775939, tc_HOL_Obool), tc_fun(_1775939, tc_HOL_Obool), _1775943), hAPP(c_COMBS(_1775939, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1775939), c_fconj), hAPP(hAPP(c_COMBC(_1775939, tc_fun(_1775939, tc_HOL_Obool), tc_HOL_Obool), c_member(_1775939)), _1775941)))), _1775945))))), 49289 ^ _780478 : [(49290 ^ _780478) ^ [_1776247] : [hBOOL(hAPP(hAPP(c_member(_1775939), _1776247), _1775941)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1775943), hAPP(c_Set_OCollect(_1775943), hAPP(hAPP(c_COMBC(_1775943, _1775939, tc_HOL_Obool), _1775945), _1776247)))))]]], (49296 ^ _780478) ^ [] : [49298 ^ _780478 : [(49301 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1775943), hAPP(c_Set_OCollect(_1775943), hAPP(hAPP(c_COMBC(_1775943, _1775939, tc_HOL_Obool), _1775945), 49297 ^ [_1775939, _1775941, _1775943, _1775945]))))], (49299 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775939), 49297 ^ [_1775939, _1775941, _1775943, _1775945]), _1775941)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1775943), hAPP(c_Set_OCollect(_1775943), hAPP(hAPP(c_COMBB(tc_fun(_1775939, tc_HOL_Obool), tc_HOL_Obool, _1775943), c_HOL_OEx(_1775939)), hAPP(hAPP(c_COMBB(tc_fun(_1775939, tc_HOL_Obool), tc_fun(_1775939, tc_HOL_Obool), _1775943), hAPP(c_COMBS(_1775939, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1775939), c_fconj), hAPP(hAPP(c_COMBC(_1775939, tc_fun(_1775939, tc_HOL_Obool), tc_HOL_Obool), c_member(_1775939)), _1775941)))), _1775945))))))]]], (36532 ^ _780478) ^ [_1475381, _1475383] : [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), _1475381))), 36535 ^ _780478 : [(36542 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1475383)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1475381)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1475383), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1475381)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1475381)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1475383), 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), _1475381)))))], (36536 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1475383)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1475381))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1475383), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1475381)) = 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), _1475383)))]]], (48778 ^ _780478) ^ [_1764383] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1764383) = c_Lazy__Sequence_Osmall__lazy_H(_1764383, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1764383)))], (25940 ^ _780478) ^ [_1261393] : [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, _1261393))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1261393)))], (43812 ^ _780478) ^ [_1656364, _1656366, _1656368, _1656370, _1656372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656364), tc_List_Olist(_1656364))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656364), tc_List_Olist(_1656364)), hAPP(hAPP(c_List_Oappend(_1656364), _1656366), _1656368)), hAPP(hAPP(c_List_Oappend(_1656364), _1656366), _1656370))), c_List_Olexord(_1656364, _1656372))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1656364, _1656364)), hAPP(hAPP(c_Product__Type_OPair(_1656364, _1656364), 43817 ^ [_1656364, _1656366, _1656368, _1656370, _1656372]), 43817 ^ [_1656364, _1656366, _1656368, _1656370, _1656372])), _1656372))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656364), tc_List_Olist(_1656364))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656364), tc_List_Olist(_1656364)), _1656368), _1656370)), c_List_Olexord(_1656364, _1656372))))], (27213 ^ _780478) ^ [_1284389] : [c_Nat__Transfer_Onat__set(_1284389), 27216 ^ _780478 : [(27223 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1284389))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1284389)))], (27217 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1284389)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1284389))))]]], (25517 ^ _780478) ^ [_1254174, _1254176, _1254178, _1254180, _1254182] : [class_Fields_Ofield__inverse__zero(_1254174), hBOOL(hAPP(c_Finite__Set_Ofinite(_1254176), _1254178)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1254176, _1254174), hAPP(hAPP(c_COMBS(_1254176, _1254174, _1254174), hAPP(hAPP(c_COMBB(_1254174, tc_fun(_1254174, _1254174), _1254176), c_Rings_Oinverse__class_Odivide(_1254174)), _1254180)), _1254182)), _1254178) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1254174), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1254176, _1254174), _1254180), _1254178)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1254176, _1254174), _1254182), _1254178)))], (6017 ^ _780478) ^ [_876256, _876258] : [-(_876258 = c_Orderings_Obot__class_Obot(tc_fun(_876256, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_876256), 6020 ^ [_876256, _876258]), _876258)))], (45847 ^ _780478) ^ [_1700973, _1700975] : [class_Orderings_Olinorder(_1700973), -(c_List_Olinorder__class_Osorted__list__of__set(_1700973, hAPP(c_List_Oset(_1700973), _1700975)) = c_List_Olinorder__class_Osort__key(_1700973, _1700973, c_COMBI(_1700973), c_List_Oremdups(_1700973, _1700975)))], (12838 ^ _780478) ^ [_1007995, _1007997, _1007999] : [class_Lattices_Osemilattice__sup(_1007995), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007995), _1007997), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007995), _1007999), _1007997))))], (34027 ^ _780478) ^ [_1422949] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1422949)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1422949))))], (25693 ^ _780478) ^ [_1257174, _1257176] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1257174), _1257176)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1257176), _1257174)))], (39173 ^ _780478) ^ [_1540734, _1540736, _1540738, _1540740] : [c_Wellfounded_Owf(_1540734, _1540736), c_Fun_Oinj__on(_1540734, _1540738, _1540740, c_Orderings_Otop__class_Otop(tc_fun(_1540734, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1540738, hAPP(c_Set_Oimage(tc_prod(_1540734, _1540734), tc_prod(_1540738, _1540738), c_Product__Type_Omap__pair(_1540734, _1540738, _1540734, _1540738, _1540740, _1540740)), _1540736)))], (22652 ^ _780478) ^ [_1202303, _1202305] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202303)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202305))))), _1202303 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1202305 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24045 ^ _780478) ^ [_1227640, _1227642] : [24053 ^ _780478 : [(24056 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1227642, 24052 ^ [_1227640, _1227642])))], (24054 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24052 ^ [_1227640, _1227642]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227640))))]], 24046 ^ _780478 : [(24047 ^ _780478) ^ [_1227708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227708), _1227640)), hBOOL(hAPP(_1227642, _1227708))]]], (46384 ^ _780478) ^ [_1714006, _1714008, _1714010, _1714012] : [class_Groups_Ocomm__monoid__add(_1714006), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1714006), _1714008), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1714010, _1714012))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1714006), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1714006), _1714008), c_List_Oupt(_1714010, _1714012))))], (15898 ^ _780478) ^ [_1068107, _1068109, _1068111] : [class_Lattices_Osemilattice__inf(_1068107), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068107), _1068109), _1068111)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068107), _1068109), _1068111) = _1068109)], (29307 ^ _780478) ^ [_1324654, _1324656] : [class_Divides_Osemiring__div(_1324654), -(c_Divides_Odiv__class_Omod(_1324654, _1324656, _1324656) = c_Groups_Ozero__class_Ozero(_1324654))], (26250 ^ _780478) ^ [_1267142, _1267144, _1267146, _1267148] : [class_Fields_Olinordered__field__inverse__zero(_1267142), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267142), _1267144), _1267146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267142), _1267148), c_Groups_Ozero__class_Ozero(_1267142))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1267142), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267142), _1267146), _1267148)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267142), _1267144), _1267148))))], (33682 ^ _780478) ^ [_1415794, _1415796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415794)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415796))), -(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(_1415796))), 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), _1415794)), c_Int_Onat))))))], (49276 ^ _780478) ^ [_1775848, _1775850] : [c_Relation_Otrans(_1775848, _1775850), -(c_Relation_Otrans(_1775848, hAPP(c_Relation_Oconverse(_1775848, _1775848), _1775850)))], (51319 ^ _780478) ^ [_1820162, _1820164, _1820166] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1820162), _1820164)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1820162), _1820166))), -(_1820162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820164), _1820166)))], (36642 ^ _780478) ^ [_1477284] : [-(c_Divides_Odivmod__nat(_1477284, 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)), _1477284))], (16929 ^ _780478) ^ [_1091705, _1091707, _1091709] : [class_Groups_Oab__semigroup__mult(_1091705), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091705), _1091707)), -(_1091707 = c_Orderings_Obot__class_Obot(tc_fun(_1091705, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091705), _1091709)), -(_1091709 = c_Orderings_Obot__class_Obot(tc_fun(_1091705, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1091705, tc_HOL_Obool)), _1091707), _1091709) = c_Orderings_Obot__class_Obot(tc_fun(_1091705, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1091705, c_Groups_Otimes__class_Otimes(_1091705)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1091705, tc_HOL_Obool)), _1091707), _1091709)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091705), hAPP(c_Finite__Set_Ofold1(_1091705, c_Groups_Otimes__class_Otimes(_1091705)), _1091707)), hAPP(c_Finite__Set_Ofold1(_1091705, c_Groups_Otimes__class_Otimes(_1091705)), _1091709)))], (21275 ^ _780478) ^ [_1175634, _1175636, _1175638] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1175634), _1175636)), 21278 ^ _780478 : [(21279 ^ _780478) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1175634, tc_Nat_Onat), _1175638), _1175636) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 21282 ^ _780478 : [(21283 ^ _780478) ^ [_1175796] : [hBOOL(hAPP(hAPP(c_member(_1175634), _1175796), _1175636)), -(hAPP(_1175638, _1175796) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21289 ^ _780478) ^ [] : [21291 ^ _780478 : [(21294 ^ _780478) ^ [] : [hAPP(_1175638, 21290 ^ [_1175634, _1175636, _1175638]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21292 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1175634), 21290 ^ [_1175634, _1175636, _1175638]), _1175636)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1175634, tc_Nat_Onat), _1175638), _1175636) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (33310 ^ _780478) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (30362 ^ _780478) ^ [_1343800, _1343802, _1343804, _1343806] : [class_Groups_Oordered__ab__group__add__abs(_1343800), -(hAPP(c_Groups_Oabs__class_Oabs(_1343800), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343802, _1343800), hAPP(hAPP(c_COMBB(_1343800, _1343800, _1343802), c_Groups_Oabs__class_Oabs(_1343800)), _1343804)), _1343806)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1343802, _1343800), hAPP(hAPP(c_COMBB(_1343800, _1343800, _1343802), c_Groups_Oabs__class_Oabs(_1343800)), _1343804)), _1343806))], (29690 ^ _780478) ^ [_1331708, _1331710, _1331712, _1331714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331708)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331710)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331710), _1331712)), -(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), _1331712), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331714, _1331708))), _1331710))))], (15267 ^ _780478) ^ [_1055280, _1055282, _1055284, _1055286] : [class_Rings_Olinordered__semidom(_1055280), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055280), c_Groups_Oone__class_Oone(_1055280)), _1055282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055280), hAPP(hAPP(c_Power_Opower__class_Opower(_1055280), _1055282), _1055284)), hAPP(hAPP(c_Power_Opower__class_Opower(_1055280), _1055282), _1055286))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055284), _1055286)))], (33939 ^ _780478) ^ [_1421598] : [c_Int_OBit1(_1421598) = c_Int_OPls], (51949 ^ _780478) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (30478 ^ _780478) ^ [_1346134, _1346136] : [class_Groups_Oordered__ab__group__add__abs(_1346134), 30481 ^ _780478 : [(30488 ^ _780478) ^ [] : [-(_1346136 = c_Groups_Ozero__class_Ozero(_1346134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346134), c_Groups_Ozero__class_Ozero(_1346134)), hAPP(c_Groups_Oabs__class_Oabs(_1346134), _1346136))))], (30482 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346134), c_Groups_Ozero__class_Ozero(_1346134)), hAPP(c_Groups_Oabs__class_Oabs(_1346134), _1346136))), _1346136 = c_Groups_Ozero__class_Ozero(_1346134)]]], (31759 ^ _780478) ^ [_1380548, _1380550] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1380548))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1380550)), hAPP(c_Int_Onat, _1380548)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1380550), _1380548)), 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)))], (37947 ^ _780478) ^ [_1507217, _1507219, _1507221, _1507223, _1507225, _1507227, _1507229] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507217, _1507219, _1507221), _1507223), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1507225, tc_fun(tc_prod(_1507219, _1507221), tc_HOL_Obool)), _1507227), _1507229)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1507225, tc_fun(tc_prod(_1507217, _1507221), tc_HOL_Obool)), _1507227), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1507219, _1507221), tc_HOL_Obool), tc_fun(tc_prod(_1507217, _1507221), tc_HOL_Obool), _1507225), hAPP(c_Relation_Orel__comp(_1507217, _1507219, _1507221), _1507223)), _1507229)))], (46366 ^ _780478) ^ [_1713642, _1713644] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1713642, _1713644) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1713642, hAPP(c_Nat_OSuc, _1713644))))], (37149 ^ _780478) ^ [_1487162] : [-(hAPP(c_Int_Onat, _1487162) = 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, _1487162)), 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)))))))], (40367 ^ _780478) ^ [_1569145, _1569147, _1569149, _1569151, _1569153, _1569155, _1569157] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1569145, _1569147, _1569149, _1569151), _1569153), _1569155), _1569157) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1569147, _1569149, _1569151), _1569155), hAPP(_1569153, _1569157)))], (17558 ^ _780478) ^ [_1106749, _1106751, _1106753, _1106755, _1106757] : [_1106749 = c_Orderings_Obot__class_Obot(tc_fun(_1106751, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106753, tc_HOL_Obool)), _1106755), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106751, tc_fun(_1106753, tc_HOL_Obool)), _1106749), _1106757)) = _1106755)], (36564 ^ _780478) ^ [_1475948, _1475950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475948)), 36567 ^ _780478 : [(36574 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475950))), 36577 ^ _780478 : [(36584 ^ _780478) ^ [] : [-(_1475948 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1475948, _1475950) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1475948), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1475950))))], (36578 ^ _780478) ^ [] : [_1475948 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1475948, _1475950) = 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)))]]], (36568 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475950)), -(c_Divides_Odivmod__int(_1475948, _1475950) = c_Divides_OposDivAlg(_1475948, _1475950))]]], (27794 ^ _780478) ^ [_1294531, _1294533] : [class_Rings_Ocomm__semiring__1(_1294531), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294531), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1294531), c_Groups_Oone__class_Oone(_1294531)), c_Groups_Oone__class_Oone(_1294531))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1294531), c_Nat_Osemiring__1__class_Oof__nat(_1294531)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1294533))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294531), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1294531), _1294533)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1294531), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1294531), _1294533)), c_Groups_Oone__class_Oone(_1294531))))], (52265 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (49252 ^ _780478) ^ [_1775468, _1775470] : [c_Relation_Otrans(_1775468, _1775470), -(c_Relation_Otrans(tc_List_Olist(_1775468), c_List_Olexord(_1775468, _1775470)))], (16404 ^ _780478) ^ [_1079436, _1079438, _1079440, _1079442] : [hBOOL(hAPP(hAPP(c_member(_1079438), _1079442), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1079436, tc_fun(_1079438, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1079436, tc_HOL_Obool))), _1079440))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1079436, tc_fun(_1079438, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1079436, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1079438, tc_HOL_Obool), tc_fun(_1079438, tc_HOL_Obool), _1079436), hAPP(c_COMBC(_1079438, tc_fun(_1079438, tc_HOL_Obool), tc_HOL_Obool), c_member(_1079438))), _1079440)), _1079442)))], (31027 ^ _780478) ^ [_1357601, _1357603] : [_1357601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1357603, _1357601) = _1357603)], (31226 ^ _780478) ^ [_1361674, _1361676] : [-(hAPP(c_Set_OCollect(_1361674), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1361674), c_fNot), _1361676)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1361674, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1361674), _1361676)))], (38943 ^ _780478) ^ [_1533352, _1533354, _1533356, _1533358] : [_1533352 = c_Orderings_Obot__class_Obot(tc_fun(_1533354, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1533354, _1533356), _1533356, c_Product__Type_Osnd(_1533354, _1533356)), hAPP(hAPP(c_Product__Type_OSigma(_1533354, _1533356), _1533352), hAPP(c_COMBK(tc_fun(_1533356, tc_HOL_Obool), _1533354), _1533358))) = c_Orderings_Obot__class_Obot(tc_fun(_1533356, tc_HOL_Obool)))], (37135 ^ _780478) ^ [_1486858, _1486860, _1486862, _1486864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1486864, _1486860)), hAPP(_1486864, _1486862))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486858, _1486858)), hAPP(hAPP(c_Product__Type_OPair(_1486858, _1486858), _1486860), _1486862)), hAPP(c_Wellfounded_Omeasure(_1486858), _1486864))))], (41382 ^ _780478) ^ [_1594163, _1594165] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594163, _1594163)), hAPP(hAPP(c_Product__Type_OPair(_1594163, _1594163), 41383 ^ [_1594163, _1594165]), 41383 ^ [_1594163, _1594165])), c_Transitive__Closure_Otrancl(_1594163, _1594165)))), -(c_Wellfounded_Oacyclic(_1594163, _1594165))], (6001 ^ _780478) ^ [_875915, _875917, _875919, _875921, _875923, _875925] : [-(hAPP(c_Set_Oimage(_875915, _875917, _875919), hAPP(c_Set_Oimage(_875921, _875915, _875923), _875925)) = hAPP(c_Set_Oimage(_875921, _875917, hAPP(hAPP(c_COMBB(_875915, _875917, _875921), _875919), _875923)), _875925))], (17322 ^ _780478) ^ [_1100259, _1100261, _1100263, _1100265, _1100267] : [hBOOL(hAPP(hAPP(c_member(_1100259), _1100261), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1100263, tc_fun(_1100259, tc_HOL_Obool)), _1100265), _1100267))), 17326 ^ _780478 : [(17329 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1100259), _1100261), hAPP(_1100267, 17325 ^ [_1100259, _1100261, _1100263, _1100265, _1100267]))))], (17327 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1100263), 17325 ^ [_1100259, _1100261, _1100263, _1100265, _1100267]), _1100265)))]]], (38313 ^ _780478) ^ [_1516411, _1516413, _1516415] : [c_Wellfounded_Owf(_1516411, _1516413), hBOOL(hAPP(hAPP(c_member(tc_prod(_1516411, _1516411)), hAPP(hAPP(c_Product__Type_OPair(_1516411, _1516411), _1516415), _1516415)), _1516413))], (52393 ^ _780478) ^ [_1834386, _1834388] : [hBOOL(_1834386), -(hBOOL(hAPP(hAPP(c_fdisj, _1834388), _1834386)))], (35804 ^ _780478) ^ [_1460362, _1460364, _1460366] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1460362, _1460362), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1460364), _1460366))), -(_1460362 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1460364 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (16128 ^ _780478) ^ [_1072547] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1072547) = c_Orderings_Oord__class_Omin(_1072547)), class_Lattices_Osemilattice__inf(_1072547), class_Orderings_Olinorder(_1072547)], (43909 ^ _780478) ^ [_1658741, _1658743, _1658745] : [hAPP(hAPP(c_List_Odrop(_1658741), _1658743), _1658745) = c_List_Olist_ONil(_1658741), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658741)), _1658745)), _1658743)))], (29480 ^ _780478) ^ [_1327828, _1327830] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327828, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1327830)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327828, _1327830) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (15111 ^ _780478) ^ [_1052605, _1052607] : [class_Lattices_Olattice(_1052605), -(c_Big__Operators_Olattice__class_OSup__fin(_1052605, hAPP(hAPP(c_Set_Oinsert(_1052605), _1052607), c_Orderings_Obot__class_Obot(tc_fun(_1052605, tc_HOL_Obool)))) = _1052607)], (38190 ^ _780478) ^ [_1514203] : [-(c_Wellfounded_Owf(_1514203, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1514203, _1514203), tc_HOL_Obool))))], (51205 ^ _780478) ^ [_1818169, _1818171, _1818173] : [class_Rings_Ocomm__semiring__1(_1818169), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818169), _1818171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1818169), _1818173), _1818171))))], (27990 ^ _780478) ^ [_1298186, _1298188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1298186), hAPP(c_Nat_OSuc, _1298188))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1298186, hAPP(c_Nat_OSuc, _1298188)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1298188)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1298186, _1298188)))], (37030 ^ _780478) ^ [_1484823, _1484825] : [c_Relation_Oirrefl(_1484823, _1484825), 37033 ^ _780478 : [(37034 ^ _780478) ^ [_1484905] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1484823, _1484823)), hAPP(hAPP(c_Product__Type_OPair(_1484823, _1484823), _1484905), _1484905)), _1484825))]]], (35597 ^ _780478) ^ [_1450666, _1450668, _1450670, _1450672, _1450674] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450666, _1450668), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1450670), _1450672))), -(_1450668 = 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)), _1450674)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450666, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1450668), _1450674)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1450670), _1450674)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1450668), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1450670, _1450674))), _1450672)))))], (10597 ^ _780478) ^ [_965307, _965309, _965311] : [class_Groups_Oordered__ab__group__add(_965307), 10600 ^ _780478 : [(10607 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965307), hAPP(c_Groups_Ouminus__class_Ouminus(_965307), _965311)), _965309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965307), hAPP(c_Groups_Ouminus__class_Ouminus(_965307), _965309)), _965311)))], (10601 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965307), hAPP(c_Groups_Ouminus__class_Ouminus(_965307), _965309)), _965311)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965307), hAPP(c_Groups_Ouminus__class_Ouminus(_965307), _965311)), _965309)))]]], (47423 ^ _780478) ^ [_1734780, _1734782, _1734784, _1734786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1734780), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734782)), c_List_OdropWhile(_1734782, _1734784, _1734786)))), -(hAPP(hAPP(c_List_Onth(_1734782), c_List_OdropWhile(_1734782, _1734784, _1734786)), _1734780) = hAPP(hAPP(c_List_Onth(_1734782), _1734786), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1734780), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734782)), c_List_OtakeWhile(_1734782, _1734784, _1734786)))))], (10639 ^ _780478) ^ [_966052, _966054, _966056, _966058] : [class_Orderings_Olinorder(_966052), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966052), _966054), hAPP(hAPP(c_Orderings_Oord__class_Omin(_966052), _966056), _966058))), 10646 ^ _780478 : [(10649 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966052), _966054), _966058)))], (10647 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966052), _966054), _966056)))]]], (12075 ^ _780478) ^ [_992579, _992581, _992583] : [class_Orderings_Olinorder(_992579), hBOOL(hAPP(c_Finite__Set_Ofinite(_992579), _992581)), -(hBOOL(hAPP(hAPP(c_member(_992579), _992583), _992581))), -(_992581 = c_Orderings_Obot__class_Obot(tc_fun(_992579, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_992579, c_Orderings_Oord__class_Omax(_992579), hAPP(hAPP(c_Set_Oinsert(_992579), _992583), _992581)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_992579), _992583), c_Big__Operators_Olattice_OSup__fin(_992579, c_Orderings_Oord__class_Omax(_992579), _992581)))], (13502 ^ _780478) ^ [_1021239] : [class_Lattices_Oboolean__algebra(_1021239), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1021239), c_Orderings_Obot__class_Obot(_1021239)) = c_Orderings_Otop__class_Otop(_1021239))], (34685 ^ _780478) ^ [_1434379, _1434381, _1434383] : [class_Int_Onumber__ring(_1434379), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1434379), _1434381), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1434383))) = hAPP(hAPP(c_HOL_OLet(_1434379, _1434379), hAPP(hAPP(c_Power_Opower__class_Opower(_1434379), _1434381), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434383))), hAPP(hAPP(c_COMBS(_1434379, _1434379, _1434379), c_Groups_Otimes__class_Otimes(_1434379)), c_COMBI(_1434379))))], (4868 ^ _780478) ^ [_854711, _854713, _854715, _854717] : [-(c_List_Olexord(_854717, _854713) = c_List_Olexord(_854715, _854711)), _854717 = _854715, _854713 = _854711], (44069 ^ _780478) ^ [_1662816, _1662818, _1662820] : [-(hAPP(c_List_Ohd(_1662816), hAPP(hAPP(c_List_Olist_OCons(_1662816), _1662818), _1662820)) = _1662818)], (38480 ^ _780478) ^ [] : [-(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))))], (32010 ^ _780478) ^ [_1385220, _1385222] : [class_Int_Onumber__ring(_1385220), 32013 ^ _780478 : [(32020 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1385222)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1385220), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1385222)) = hAPP(c_Int_Onumber__class_Onumber__of(_1385220), _1385222))], (32014 ^ _780478) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1385222))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1385220), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1385222)) = c_Groups_Ozero__class_Ozero(_1385220))]]], (6700 ^ _780478) ^ [_890983, _890985, _890987, _890989, _890991] : [class_Groups_Ominus(_890983), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890985, _890983)), _890987), _890989), _890991) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_890983), hAPP(_890987, _890991)), hAPP(_890989, _890991)))], (230 ^ _780478) ^ [_784125, _784127] : [-(class_Fields_Olinordered__field__inverse__zero(_784125)), _784127 = _784125, class_Fields_Olinordered__field__inverse__zero(_784127)], (42119 ^ _780478) ^ [_1615805, _1615807, _1615809] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615805)), _1615807), c_Wellfounded_Oacc(tc_List_Olist(_1615805), c_List_Olistrel1(_1615805, _1615809)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615805)), _1615807), c_List_Olists(_1615805, c_Wellfounded_Oacc(_1615805, _1615809)))))], (24171 ^ _780478) ^ [_1230495, _1230497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230497)), -(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), _1230495), _1230497))))], (44596 ^ _780478) ^ [_1672862, _1672864, _1672866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672862), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672864)), _1672866))), -(c_List_Olast(_1672864, hAPP(hAPP(c_List_Odrop(_1672864), _1672862), _1672866)) = c_List_Olast(_1672864, _1672866))], (43463 ^ _780478) ^ [_1648012, _1648014, _1648016, _1648018] : [hAPP(hAPP(c_List_Oappend(_1648012), _1648014), _1648016) = hAPP(hAPP(c_List_Oappend(_1648012), _1648014), _1648018), -(_1648016 = _1648018)], (51007 ^ _780478) ^ [_1814128, _1814130, _1814132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1814128)), 51010 ^ _780478 : [(51017 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814130), _1814132)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1814128), _1814130)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1814128), _1814132))))], (51011 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1814128), _1814130)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1814128), _1814132))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814130), _1814132)))]]], (17482 ^ _780478) ^ [_1105098, _1105100] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105098, tc_fun(_1105098, tc_HOL_Obool)), _1105100), hAPP(hAPP(c_COMBC(_1105098, tc_fun(_1105098, tc_HOL_Obool), tc_fun(_1105098, tc_HOL_Obool)), c_Set_Oinsert(_1105098)), c_Orderings_Obot__class_Obot(tc_fun(_1105098, tc_HOL_Obool)))) = _1105100)], (30117 ^ _780478) ^ [_1339363, _1339365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1339363)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1339363), _1339365)), _1339363) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (25982 ^ _780478) ^ [_1262119, _1262121, _1262123] : [class_Fields_Ofield(_1262119), -(_1262121 = c_Groups_Oone__class_Oone(_1262119)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1262119), hAPP(c_Power_Opower__class_Opower(_1262119), _1262121)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1262123)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1262119), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1262119), hAPP(hAPP(c_Power_Opower__class_Opower(_1262119), _1262121), _1262123)), c_Groups_Oone__class_Oone(_1262119))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1262119), _1262121), c_Groups_Oone__class_Oone(_1262119))))], (46455 ^ _780478) ^ [_1715633, _1715635, _1715637] : [class_Orderings_Olinorder(_1715633), c_List_Olinorder__class_Osorted(_1715633, _1715635), -(c_List_Olinorder__class_Osorted(_1715633, c_List_Olinorder__class_Oinsort__insert__key(_1715633, _1715633, c_COMBI(_1715633), _1715637, _1715635)))], (14947 ^ _780478) ^ [_1049072, _1049074, _1049076, _1049078, _1049080] : [-(hBOOL(hAPP(hAPP(c_member(_1049072), _1049074), c_SetInterval_Oord_OatLeastAtMost(_1049072, _1049076, _1049078, _1049080)))), hBOOL(hAPP(hAPP(_1049076, _1049078), _1049074)), hBOOL(hAPP(hAPP(_1049076, _1049074), _1049080))], (48393 ^ _780478) ^ [_1755884, _1755886, _1755888, _1755890, _1755892] : [_1755884 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1755886, _1755888, _1755890, _1755892), _1755884) = c_Lazy__Sequence_Oempty(_1755888))], (30859 ^ _780478) ^ [_1353675, _1353677, _1353679, _1353681] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1353675, tc_HOL_Obool), tc_fun(_1353677, tc_HOL_Obool)), _1353679), hAPP(hAPP(c_COMBC(tc_fun(_1353675, tc_HOL_Obool), tc_fun(_1353675, tc_fun(_1353677, tc_HOL_Obool)), tc_fun(_1353677, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1353675, tc_fun(_1353677, tc_HOL_Obool))), _1353681)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1353675, tc_fun(_1353677, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353675, tc_HOL_Obool), _1353679)), _1353681))], (22487 ^ _780478) ^ [_1199112, _1199114, _1199116] : [hAPP(c_Finite__Set_Ocard(_1199112), _1199114) = hAPP(c_Nat_OSuc, _1199116), 22492 ^ _780478 : [(22495 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1199112), 22490 ^ [_1199112, _1199114, _1199116]), 22491 ^ [_1199112, _1199114, _1199116]))], (22497 ^ _780478) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1199112), 22491 ^ [_1199112, _1199114, _1199116]) = _1199116)], (22499 ^ _780478) ^ [] : [_1199116 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(22491 ^ [_1199112, _1199114, _1199116] = c_Orderings_Obot__class_Obot(tc_fun(_1199112, tc_HOL_Obool)))], (22493 ^ _780478) ^ [] : [-(_1199114 = hAPP(hAPP(c_Set_Oinsert(_1199112), 22490 ^ [_1199112, _1199114, _1199116]), 22491 ^ [_1199112, _1199114, _1199116]))]]], (32190 ^ _780478) ^ [_1388586, _1388588, _1388590] : [class_Int_Onumber__ring(_1388586), class_Rings_Olinordered__idom(_1388586), 32197 ^ _780478 : [(32204 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1388588), _1388590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388586), hAPP(c_Int_Onumber__class_Onumber__of(_1388586), _1388588)), hAPP(c_Int_Onumber__class_Onumber__of(_1388586), _1388590))))], (32198 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1388586), hAPP(c_Int_Onumber__class_Onumber__of(_1388586), _1388588)), hAPP(c_Int_Onumber__class_Onumber__of(_1388586), _1388590))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1388588), _1388590)))]]], (23291 ^ _780478) ^ [_1213880, _1213882] : [23292 ^ _780478 : [(23295 ^ _780478) ^ [] : [_1213880 = _1213882], (23293 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213880), _1213882))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213880), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1213882), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (52245 ^ _780478) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (7403 ^ _780478) ^ [_904483, _904485, _904487, _904489] : [c_Fun_Oinj__on(_904483, _904485, _904487, _904489), -(c_Fun_Oinj__on(_904485, _904483, c_Fun_Othe__inv__into(_904483, _904485, _904489, _904487), hAPP(c_Set_Oimage(_904483, _904485, _904487), _904489)))], (46141 ^ _780478) ^ [_1708155, _1708157, _1708159] : [hBOOL(hAPP(c_List_Odistinct(_1708155), _1708157)), -(hAPP(c_List_Ofilter(_1708155, hAPP(hAPP(c_COMBC(_1708155, tc_fun(_1708155, tc_HOL_Obool), tc_HOL_Obool), c_member(_1708155)), hAPP(c_List_Oset(_1708155), c_List_Osublist(_1708155, _1708157, _1708159)))), _1708157) = c_List_Osublist(_1708155, _1708157, _1708159))], (9532 ^ _780478) ^ [_944270, _944272, _944274, _944276, _944278] : [class_Groups_Oordered__cancel__ab__semigroup__add(_944270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944270), _944272), _944274)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944270), _944276), _944278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944270), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944270), _944272), _944276)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944270), _944274), _944278))))], (6031 ^ _780478) ^ [_876373, _876375] : [_876375 = c_Orderings_Obot__class_Obot(tc_fun(_876373, tc_HOL_Obool)), 6034 ^ _780478 : [(6035 ^ _780478) ^ [_876453] : [hBOOL(hAPP(hAPP(c_member(_876373), _876453), _876375))]]], (20554 ^ _780478) ^ [_1163788, _1163790, _1163792] : [class_Groups_Oordered__ab__group__add(_1163788), 20557 ^ _780478 : [(20564 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163788), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163788), _1163790), _1163792)), c_Groups_Ozero__class_Ozero(_1163788))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163788), _1163790), _1163792)))], (20558 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163788), _1163790), _1163792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1163788), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1163788), _1163790), _1163792)), c_Groups_Ozero__class_Ozero(_1163788))))]]], (30013 ^ _780478) ^ [_1337333, _1337335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1337333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337335, _1337333)), _1337333)))], (46364 ^ _780478) ^ [_1713602, _1713604] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1713602, _1713604)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1713602), hAPP(c_Nat_OSuc, _1713604)))], (20312 ^ _780478) ^ [_1159290, _1159292, _1159294, _1159296] : [class_Rings_Olinordered__ring__strict(_1159290), 20315 ^ _780478 : [(20330 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159290), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159290), _1159292), _1159294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159290), _1159292), _1159296)))), 20331 ^ _780478 : [(20338 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159290), _1159292), c_Groups_Ozero__class_Ozero(_1159290))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159290), _1159296), _1159294))], (20332 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159290), c_Groups_Ozero__class_Ozero(_1159290)), _1159292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159290), _1159294), _1159296))]]], (20316 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159290), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159290), _1159292), _1159294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159290), _1159292), _1159296))), 20321 ^ _780478 : [(20324 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159290), _1159294), _1159296)))], (20322 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159290), c_Groups_Ozero__class_Ozero(_1159290)), _1159292)))]], 20325 ^ _780478 : [(20328 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159290), _1159296), _1159294)))], (20326 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159290), _1159292), c_Groups_Ozero__class_Ozero(_1159290))))]]]]], (52301 ^ _780478) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (16106 ^ _780478) ^ [_1072082, _1072084, _1072086, _1072088] : [-(hBOOL(hAPP(hAPP(c_member(_1072082), _1072084), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072082, tc_HOL_Obool)), _1072086), _1072088)))), hBOOL(hAPP(hAPP(c_member(_1072082), _1072084), _1072086)), hBOOL(hAPP(hAPP(c_member(_1072082), _1072084), _1072088))], (16516 ^ _780478) ^ [_1082147, _1082149, _1082151] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1082147, tc_HOL_Obool)), _1082149), _1082151) = c_Orderings_Obot__class_Obot(tc_fun(_1082147, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1082147, tc_HOL_Obool)), _1082149), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1082147, tc_HOL_Obool)), _1082151))))], (19067 ^ _780478) ^ [_1138718, _1138720, _1138722, _1138724, _1138726] : [19069 ^ _780478 : [(19072 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1138724, 19068 ^ [_1138718, _1138720, _1138722, _1138724, _1138726]), _1138726))], (19070 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1138718), 19068 ^ [_1138718, _1138720, _1138722, _1138724, _1138726]), _1138722)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1138718, tc_fun(_1138720, tc_HOL_Obool)), _1138722), _1138724), _1138726)))], (50495 ^ _780478) ^ [_1802084, _1802086, _1802088, _1802090, _1802092] : [c_Fun_Obij__betw(_1802084, _1802086, _1802088, _1802090, _1802092), -(hAPP(c_Finite__Set_Ocard(_1802084), _1802090) = hAPP(c_Finite__Set_Ocard(_1802086), _1802092))], (3984 ^ _780478) ^ [_840565, _840567, _840569, _840571, _840573, _840575, _840577, _840579] : [-(c_Lazy__Sequence_Ohb__bind(_840579, _840575, _840571, _840567) = c_Lazy__Sequence_Ohb__bind(_840577, _840573, _840569, _840565)), _840579 = _840577, _840575 = _840573, _840571 = _840569, _840567 = _840565], (45761 ^ _780478) ^ [_1699388, _1699390] : [c_List_Oremdups(_1699388, _1699390) = c_List_Olist_ONil(_1699388), -(_1699390 = c_List_Olist_ONil(_1699388))], (35247 ^ _780478) ^ [] : [-(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))], (9520 ^ _780478) ^ [_943748, _943750, _943752, _943754, _943756] : [class_Rings_Osemiring__0(_943748), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943748), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943750, _943748), _943752), _943754)), _943756) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943750, _943748), hAPP(hAPP(c_COMBC(_943750, _943748, _943748), hAPP(hAPP(c_COMBB(_943748, tc_fun(_943748, _943748), _943750), c_Groups_Otimes__class_Otimes(_943748)), _943752)), _943756)), _943754))], (30442 ^ _780478) ^ [_1345571, _1345573] : [class_Groups_Oordered__ab__group__add__abs(_1345571), 30445 ^ _780478 : [(30452 ^ _780478) ^ [] : [_1345573 = c_Groups_Ozero__class_Ozero(_1345571), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345571), hAPP(c_Groups_Oabs__class_Oabs(_1345571), _1345573)), c_Groups_Ozero__class_Ozero(_1345571))))], (30446 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345571), hAPP(c_Groups_Oabs__class_Oabs(_1345571), _1345573)), c_Groups_Ozero__class_Ozero(_1345571))), -(_1345573 = c_Groups_Ozero__class_Ozero(_1345571))]]], (14695 ^ _780478) ^ [_1043368, _1043370] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043368), _1043370)), _1043368)))], (41724 ^ _780478) ^ [_1603769, _1603771, _1603773, _1603775, _1603777] : [hAPP(hAPP(c_List_Olist_OCons(_1603769), _1603771), _1603773) = hAPP(hAPP(c_List_Olist_OCons(_1603769), _1603775), _1603777), 41727 ^ _780478 : [(41730 ^ _780478) ^ [] : [-(_1603773 = _1603777)], (41728 ^ _780478) ^ [] : [-(_1603771 = _1603775)]]], (48449 ^ _780478) ^ [_1757413, _1757415] : [c_Wellfounded_Oacyclic(_1757413, hAPP(c_Set_OCollect(tc_prod(_1757413, _1757413)), hAPP(c_Product__Type_Oprod_Oprod__case(_1757413, _1757413, tc_HOL_Obool), _1757415))), -(c_Wellfounded_Oacyclic(_1757413, hAPP(c_Set_OCollect(tc_prod(_1757413, _1757413)), hAPP(c_Product__Type_Oprod_Oprod__case(_1757413, _1757413, tc_HOL_Obool), c_Predicate_Oconversep(_1757413, _1757413, _1757415)))))], (35736 ^ _780478) ^ [_1457805, _1457807, _1457809, _1457811, _1457813, _1457815] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1457805, _1457807), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1457809), _1457811))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1457805, _1457807), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1457813), _1457815))), -(_1457807 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1457811 = _1457815)], (37957 ^ _780478) ^ [_1507654, _1507656, _1507658, _1507660, _1507662, _1507664] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507654, _1507656, _1507658), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507654, _1507656), tc_HOL_Obool)), _1507660), _1507662)), _1507664) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507654, _1507658), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507654, _1507656, _1507658), _1507660), _1507664)), hAPP(hAPP(c_Relation_Orel__comp(_1507654, _1507656, _1507658), _1507662), _1507664)))], (42326 ^ _780478) ^ [_1621319, _1621321, _1621323] : [-(hAPP(c_List_Oset(_1621319), hAPP(hAPP(c_List_Olist_OCons(_1621319), _1621321), _1621323)) = hAPP(hAPP(c_Set_Oinsert(_1621319), _1621321), hAPP(c_List_Oset(_1621319), _1621323)))], (19542 ^ _780478) ^ [_1145726] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145726)))], (9754 ^ _780478) ^ [_949002, _949004, _949006, _949008, _949010] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_949002), 9757 ^ _780478 : [(9758 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949002), _949004), _949008)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949002), _949006), _949010)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949002), _949004), _949010)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949002), _949006), _949008)), -(_949004 = _949006), -(_949008 = _949010)], (9768 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949002), _949004), _949008)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949002), _949006), _949010)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949002), _949004), _949010)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949002), _949006), _949008))), 9771 ^ _780478 : [(9774 ^ _780478) ^ [] : [_949008 = _949010], (9772 ^ _780478) ^ [] : [_949004 = _949006]]]]], (28372 ^ _780478) ^ [_1305545, _1305547, _1305549] : [class_Orderings_Oorder(_1305545), 28375 ^ _780478 : [(28382 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305545), _1305547), _1305549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305545, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1305545), _1305547)), hAPP(c_SetInterval_Oord__class_OatMost(_1305545), _1305549))))], (28376 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305545, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1305545), _1305547)), hAPP(c_SetInterval_Oord__class_OatMost(_1305545), _1305549))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305545), _1305547), _1305549)))]]], (18858 ^ _780478) ^ [_1134416, _1134418, _1134420, _1134422, _1134424] : [class_Complete__Lattice_Ocomplete__lattice(_1134416), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134418), _1134420)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1134416), _1134422), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1134418, _1134416), _1134420), _1134424)) = hAPP(hAPP(c_Finite__Set_Ofold(_1134418, _1134416, hAPP(hAPP(c_COMBB(_1134416, tc_fun(_1134416, _1134416), _1134418), c_Lattices_Osemilattice__inf__class_Oinf(_1134416)), _1134424)), _1134422), _1134420))], (5386 ^ _780478) ^ [_862864, _862866, _862868, _862870, _862872, _862874, _862876, _862878] : [-(c_Lazy__Sequence_Omap(_862878, _862874, _862870, _862866) = c_Lazy__Sequence_Omap(_862876, _862872, _862868, _862864)), _862878 = _862876, _862874 = _862872, _862870 = _862868, _862866 = _862864], (17414 ^ _780478) ^ [_1102576, _1102578, _1102580, _1102582, _1102584, _1102586] : [-(hAPP(c_Set_Oimage(_1102576, _1102578, _1102580), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102582, tc_fun(_1102576, tc_HOL_Obool)), _1102584), _1102586)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102582, tc_fun(_1102578, tc_HOL_Obool)), _1102584), hAPP(hAPP(c_COMBB(tc_fun(_1102576, tc_HOL_Obool), tc_fun(_1102578, tc_HOL_Obool), _1102582), c_Set_Oimage(_1102576, _1102578, _1102580)), _1102586)))], (3630 ^ _780478) ^ [_834780, _834782, _834784, _834786] : [-(c_List_Olist__update(_834786, _834782) = c_List_Olist__update(_834784, _834780)), _834786 = _834784, _834782 = _834780], (41196 ^ _780478) ^ [_1589332, _1589334, _1589336, _1589338] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1589332, _1589334), tc_fun(_1589332, _1589334)), _1589336), c_Fun_Ocomp(_1589334, _1589334, _1589332, _1589338)) = c_Fun_Ocomp(_1589334, _1589334, _1589332, hAPP(hAPP(c_Nat_Ocompow(_1589334, _1589334), _1589336), _1589338)))], (17941 ^ _780478) ^ [_1114620, _1114622] : [17942 ^ _780478 : [(17945 ^ _780478) ^ [] : [_1114620 = _1114622], (17943 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114620), _1114622))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114620), hAPP(c_Nat_OSuc, _1114622))))], (3048 ^ _780478) ^ [_825725, _825727, _825729, _825731] : [-(c_List_Olexn(_825731, _825727) = c_List_Olexn(_825729, _825725)), _825731 = _825729, _825727 = _825725], (50137 ^ _780478) ^ [_1794295, _1794297, _1794299, _1794301, _1794303] : [c_Fun_Oinj__on(_1794295, _1794297, _1794299, _1794301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794295, tc_HOL_Obool)), _1794303), _1794301)), -(hAPP(c_Set_Oimage(_1794297, _1794295, c_Hilbert__Choice_Oinv__into(_1794295, _1794297, _1794301, _1794299)), hAPP(c_Set_Oimage(_1794295, _1794297, _1794299), _1794303)) = _1794303)], (802 ^ _780478) ^ [_792517, _792519, _792521, _792523] : [-(c_Relation_Osym(_792521, _792517)), c_Relation_Osym(_792523, _792519), _792523 = _792521, _792519 = _792517], (12057 ^ _780478) ^ [_992330, _992332, _992334] : [class_Orderings_Olinorder(_992330), hBOOL(hAPP(c_Finite__Set_Ofinite(_992330), _992332)), -(hBOOL(hAPP(hAPP(c_member(_992330), _992334), _992332))), -(_992332 = c_Orderings_Obot__class_Obot(tc_fun(_992330, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_992330, c_Orderings_Oord__class_Omin(_992330), hAPP(hAPP(c_Set_Oinsert(_992330), _992334), _992332)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_992330), _992334), c_Big__Operators_Olattice_OInf__fin(_992330, c_Orderings_Oord__class_Omin(_992330), _992332)))], (24725 ^ _780478) ^ [_1239899, _1239901] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1239899, _1239901)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1239901)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (41071 ^ _780478) ^ [_1586245] : [-(c_Transitive__Closure_Ortrancl(_1586245, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1586245, _1586245), tc_HOL_Obool))) = c_Relation_OId(_1586245))], (21071 ^ _780478) ^ [_1172306, _1172308] : [class_Rings_Ocomm__semiring__1(_1172306), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1172306), _1172308), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1172306))], (9418 ^ _780478) ^ [_941869, _941871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_941869, tc_HOL_Obool)), _941871), c_Orderings_Obot__class_Obot(tc_fun(_941869, tc_HOL_Obool))))], (4628 ^ _780478) ^ [_850883, _850885] : [_850885 = _850883, -(c_Nat_Osize__class_Osize(_850885) = c_Nat_Osize__class_Osize(_850883))], (43423 ^ _780478) ^ [_1647119, _1647121, _1647123, _1647125] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1647119)), hAPP(hAPP(c_List_Oappend(_1647119), _1647121), _1647123)), c_List_Olists(_1647119, _1647125))), 43426 ^ _780478 : [(43429 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1647119)), _1647123), c_List_Olists(_1647119, _1647125))))], (43427 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1647119)), _1647121), c_List_Olists(_1647119, _1647125))))]]], (44690 ^ _780478) ^ [_1674785, _1674787, _1674789, _1674791, _1674793, _1674795, _1674797, _1674799] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674785, _1674787), _1674789), _1674791), hAPP(hAPP(c_List_Ozip(_1674785, _1674787), _1674793), hAPP(hAPP(c_List_Omap(_1674795, _1674787), _1674797), _1674799))) = hAPP(hAPP(c_List_Omap(tc_prod(_1674785, _1674795), _1674789), hAPP(c_Product__Type_Oprod_Oprod__case(_1674785, _1674795, _1674789), hAPP(hAPP(c_COMBB(tc_fun(_1674795, tc_prod(_1674785, _1674787)), tc_fun(_1674795, _1674789), _1674785), hAPP(c_COMBB(tc_prod(_1674785, _1674787), _1674789, _1674795), _1674791)), hAPP(hAPP(c_COMBC(_1674785, tc_fun(_1674795, _1674787), tc_fun(_1674795, tc_prod(_1674785, _1674787))), hAPP(hAPP(c_COMBB(tc_fun(_1674787, tc_prod(_1674785, _1674787)), tc_fun(tc_fun(_1674795, _1674787), tc_fun(_1674795, tc_prod(_1674785, _1674787))), _1674785), c_COMBB(_1674787, tc_prod(_1674785, _1674787), _1674795)), c_Product__Type_OPair(_1674785, _1674787))), _1674797)))), hAPP(hAPP(c_List_Ozip(_1674785, _1674795), _1674793), _1674799)))], (638 ^ _780478) ^ [_790107, _790109, _790111, _790113, _790115, _790117, _790119, _790121] : [-(c_Nat__Transfer_Otransfer__morphism(_790119, _790115, _790111, _790107)), c_Nat__Transfer_Otransfer__morphism(_790121, _790117, _790113, _790109), _790121 = _790119, _790117 = _790115, _790113 = _790111, _790109 = _790107], (52315 ^ _780478) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (44366 ^ _780478) ^ [_1668738, _1668740, _1668742] : [44367 ^ _780478 : [(44368 ^ _780478) ^ [_1668827, _1668829] : [_1668740 = hAPP(hAPP(c_List_Olist_OCons(_1668738), _1668829), _1668827)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668738), tc_List_Olist(_1668738))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668738), tc_List_Olist(_1668738)), c_List_Olist_ONil(_1668738)), _1668740)), c_List_Olexord(_1668738, _1668742))))], (44083 ^ _780478) ^ [_1663035, _1663037, _1663039] : [-(_1663035 = c_List_Olist_ONil(_1663037)), -(hAPP(c_List_Ohd(_1663037), hAPP(hAPP(c_List_Oappend(_1663037), _1663035), _1663039)) = hAPP(c_List_Ohd(_1663037), _1663035))], (38261 ^ _780478) ^ [_1515457, _1515459, _1515461] : [c_Wellfounded_Owf(_1515457, _1515459), -(c_Wellfounded_Owf(_1515457, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1515457, _1515457), tc_HOL_Obool)), _1515461), _1515459)))], (42069 ^ _780478) ^ [_1614627, _1614629, _1614631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1614627, _1614627), tc_HOL_Obool)), _1614629), hAPP(hAPP(c_Product__Type_OSigma(_1614627, _1614627), _1614631), hAPP(c_COMBK(tc_fun(_1614627, tc_HOL_Obool), _1614627), _1614631)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1614627), tc_List_Olist(_1614627)), tc_HOL_Obool)), c_List_Olistrel(_1614627, _1614629)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1614627), tc_List_Olist(_1614627)), c_List_Olists(_1614627, _1614631)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1614627), tc_HOL_Obool), tc_List_Olist(_1614627)), c_List_Olists(_1614627, _1614631))))))], (45993 ^ _780478) ^ [_1704542, _1704544, _1704546, _1704548] : [-(c_List_Oconcat(_1704542, hAPP(hAPP(c_List_Omap(_1704544, tc_List_Olist(_1704542)), hAPP(hAPP(c_COMBC(_1704544, tc_List_Olist(_1704542), tc_List_Olist(_1704542)), hAPP(hAPP(c_COMBB(_1704542, tc_fun(tc_List_Olist(_1704542), tc_List_Olist(_1704542)), _1704544), c_List_Olist_OCons(_1704542)), _1704546)), c_List_Olist_ONil(_1704542))), _1704548)) = hAPP(hAPP(c_List_Omap(_1704544, _1704542), _1704546), _1704548))], (29229 ^ _780478) ^ [_1323057, _1323059, _1323061] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1323057), _1323059), _1323061) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1323057), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323059, _1323061)), _1323061))], (9993 ^ _780478) ^ [_954250, _954252, _954254] : [class_Groups_Oab__semigroup__mult(_954250), hBOOL(hAPP(c_Finite__Set_Ofinite(_954250), _954252)), -(hBOOL(hAPP(hAPP(c_member(_954250), _954254), _954252))), -(hAPP(c_Finite__Set_Ofold1(_954250, c_Groups_Otimes__class_Otimes(_954250)), hAPP(hAPP(c_Set_Oinsert(_954250), _954254), _954252)) = hAPP(hAPP(c_Finite__Set_Ofold(_954250, _954250, c_Groups_Otimes__class_Otimes(_954250)), _954254), _954252))], (8828 ^ _780478) ^ [_933008, _933010, _933012] : [class_Orderings_Oorder(_933008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933008), _933010), _933012)), _933012 = _933010], (15049 ^ _780478) ^ [_1051296, _1051298, _1051300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051296), _1051298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051300), _1051298))))], (38198 ^ _780478) ^ [_1514333, _1514335, _1514337, _1514339] : [c_Wellfounded_Owf(_1514333, _1514335), c_Wellfounded_Owf(_1514337, _1514339), -(c_Wellfounded_Owf(tc_prod(_1514333, _1514337), c_Wellfounded_Olex__prod(_1514333, _1514337, _1514335, _1514339)))], (17434 ^ _780478) ^ [_1103638, _1103640, _1103642, _1103644, _1103646, _1103648] : [class_Complete__Lattice_Ocomplete__lattice(_1103638), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103640, _1103638), _1103642), hAPP(hAPP(c_COMBB(tc_fun(_1103644, _1103638), _1103638, _1103640), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103644, _1103638), _1103646)), _1103648)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103644, _1103638), _1103646), hAPP(hAPP(c_COMBB(tc_fun(_1103640, _1103638), _1103638, _1103644), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103640, _1103638), _1103642)), hAPP(c_COMBC(_1103640, _1103644, _1103638), _1103648))))], (22985 ^ _780478) ^ [_1208250, _1208252, _1208254, _1208256] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208250), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1208252, tc_Nat_Onat), _1208254), _1208256)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1208252, _1208250), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1208250, _1208252), c_Nat_Osemiring__1__class_Oof__nat(_1208250)), _1208254)), _1208256)), class_Groups_Ocomm__monoid__mult(_1208250), class_Rings_Osemiring__1(_1208250)], (36476 ^ _780478) ^ [_1474548] : [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), _1474548))), 36479 ^ _780478 : [(36486 ^ _780478) ^ [] : [-(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), _1474548)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474548)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474548)), 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), _1474548)))))], (36480 ^ _780478) ^ [] : [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), _1474548))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1474548)) = 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)))]]], (31690 ^ _780478) ^ [_1378699, _1378701, _1378703] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378699), hAPP(hAPP(c_Set_Oinsert(_1378699), _1378701), c_Orderings_Obot__class_Obot(tc_fun(_1378699, tc_HOL_Obool)))), _1378703) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1378699, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1378699, _1378699, _1378703), hAPP(hAPP(c_Set_Oinsert(_1378699), _1378701), c_Orderings_Obot__class_Obot(tc_fun(_1378699, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1378699, tc_HOL_Obool), tc_HOL_Obool))))], (28258 ^ _780478) ^ [_1303594, _1303596, _1303598] : [class_Orderings_Olinorder(_1303594), 28261 ^ _780478 : [(28268 ^ _780478) ^ [] : [_1303596 = _1303598, -(hAPP(c_SetInterval_Oord__class_OatMost(_1303594), _1303596) = hAPP(c_SetInterval_Oord__class_OatMost(_1303594), _1303598))], (28262 ^ _780478) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1303594), _1303596) = hAPP(c_SetInterval_Oord__class_OatMost(_1303594), _1303598), -(_1303596 = _1303598)]]], (40704 ^ _780478) ^ [_1577365, _1577367, _1577369, _1577371] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577365, _1577365)), hAPP(hAPP(c_Product__Type_OPair(_1577365, _1577365), _1577367), _1577369)), c_Transitive__Closure_Ortrancl(_1577365, _1577371))), hBOOL(hAPP(hAPP(c_member(_1577365), _1577369), c_Wellfounded_Oacc(_1577365, _1577371))), -(hBOOL(hAPP(hAPP(c_member(_1577365), _1577367), c_Wellfounded_Oacc(_1577365, _1577371))))], (50076 ^ _780478) ^ [_1792734, _1792736, _1792738, _1792740] : [hAPP(c_Set_Oimage(_1792734, _1792736, _1792738), c_Orderings_Otop__class_Otop(tc_fun(_1792734, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792736, tc_HOL_Obool)), -(hAPP(_1792738, hAPP(c_Hilbert__Choice_Oinv__into(_1792734, _1792736, c_Orderings_Otop__class_Otop(tc_fun(_1792734, tc_HOL_Obool)), _1792738), _1792740)) = _1792740)], (37229 ^ _780478) ^ [_1488766, _1488768] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1488766), _1488768) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1488766, _1488768)))], (47177 ^ _780478) ^ [_1729677, _1729679] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729677), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1729677))), _1729679))), -(c_List_Otranspose(_1729677, c_List_Otranspose(_1729677, _1729679)) = c_List_OtakeWhile(tc_List_Olist(_1729677), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1729677)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1729677), tc_List_Olist(_1729677), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1729677))), _1729679))], (30434 ^ _780478) ^ [_1345407, _1345409, _1345411, _1345413] : [-(hAPP(c_Set_Ovimage(_1345407, _1345409, _1345411), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1345409, tc_HOL_Obool), _1345413)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1345409, tc_HOL_Obool), tc_fun(_1345407, tc_HOL_Obool)), _1345413), c_Set_Ovimage(_1345407, _1345409, _1345411)))], (38746 ^ _780478) ^ [_1527643, _1527645, _1527647, _1527649, _1527651, _1527653] : [class_Groups_Ocomm__monoid__add(_1527643), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527645, _1527643), hAPP(hAPP(c_COMBC(_1527645, tc_fun(_1527647, tc_HOL_Obool), _1527643), hAPP(hAPP(c_COMBB(tc_fun(_1527647, _1527643), tc_fun(tc_fun(_1527647, tc_HOL_Obool), _1527643), _1527645), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1527647, _1527643)), _1527649)), _1527651)), _1527653) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1527645, _1527647), _1527643), hAPP(c_Product__Type_Oprod_Oprod__case(_1527645, _1527647, _1527643), _1527649)), hAPP(hAPP(c_Product__Type_OSigma(_1527645, _1527647), _1527653), hAPP(c_COMBK(tc_fun(_1527647, tc_HOL_Obool), _1527645), _1527651))))], (7018 ^ _780478) ^ [_897669, _897671, _897673, _897675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897669, tc_HOL_Obool)), _897671), _897673)), hBOOL(hAPP(hAPP(c_member(_897669), _897675), _897671)), -(hBOOL(hAPP(hAPP(c_member(_897669), _897675), _897673)))], (30380 ^ _780478) ^ [_1344333, _1344335, _1344337, _1344339] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1344333, tc_HOL_Obool), tc_fun(_1344335, tc_HOL_Obool)), _1344337), hAPP(hAPP(c_COMBC(tc_fun(_1344333, tc_HOL_Obool), tc_fun(_1344333, tc_fun(_1344335, tc_HOL_Obool)), tc_fun(_1344335, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1344333, tc_fun(_1344335, tc_HOL_Obool))), _1344339)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1344333, tc_fun(_1344335, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1344333, tc_HOL_Obool), _1344337)), _1344339))], (24727 ^ _780478) ^ [_1239946, _1239948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239946)), -(c_SMT_Oz3div(_1239948, _1239946) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1239948), _1239946))], (13218 ^ _780478) ^ [_1015119] : [class_Lattices_Osemilattice__sup(_1015119), -(c_Finite__Set_Ofun__left__comm__idem(_1015119, _1015119, c_Lattices_Osemilattice__sup__class_Osup(_1015119)))], (13384 ^ _780478) ^ [_1018865, _1018867] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018865), _1018867)), 13387 ^ _780478 : [(13394 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018865), c_Orderings_Otop__class_Otop(tc_fun(_1018865, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1018865), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018865, tc_HOL_Obool)), _1018867))))], (13388 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018865), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018865, tc_HOL_Obool)), _1018867))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1018865), c_Orderings_Otop__class_Otop(tc_fun(_1018865, tc_HOL_Obool)))))]]], (48865 ^ _780478) ^ [_1766415, _1766417, _1766419] : [hBOOL(hAPP(hAPP(c_List_Omember(_1766415), _1766419), _1766417)), -(hBOOL(hAPP(hAPP(c_member(_1766415), _1766417), hAPP(c_List_Oset(_1766415), _1766419))))], (42572 ^ _780478) ^ [_1628836] : [42574 ^ _780478 : [(42577 ^ _780478) ^ [] : [42573 ^ [_1628836] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42575 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42573 ^ [_1628836]), hAPP(c_List_Oset(tc_Nat_Onat), _1628836))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1628836) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4160 ^ _780478) ^ [_843441, _843443] : [_843443 = _843441, -(c_New__Random__Sequence_Opos__single(_843443) = c_New__Random__Sequence_Opos__single(_843441))], (52351 ^ _780478) ^ [] : [-(hBOOL(c_fTrue))], (23575 ^ _780478) ^ [_1218654] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218654), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (37259 ^ _780478) ^ [_1489431] : [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), _1489431))), -(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), _1489431)) = 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), _1489431))))], (49442 ^ _780478) ^ [_1780877, _1780879, _1780881, _1780883, _1780885] : [c_Predicate_Otransp(_1780877, _1780879), hBOOL(hAPP(hAPP(_1780879, _1780881), _1780883)), hBOOL(hAPP(hAPP(_1780879, _1780883), _1780885)), -(hBOOL(hAPP(hAPP(_1780879, _1780881), _1780885)))], (33644 ^ _780478) ^ [_1414955] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1414955)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414955) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4062 ^ _780478) ^ [_841854, _841856, _841858, _841860, _841862, _841864, _841866, _841868] : [-(c_New__Random__Sequence_Oneg__bind(_841868, _841864, _841860, _841856) = c_New__Random__Sequence_Oneg__bind(_841866, _841862, _841858, _841854)), _841868 = _841866, _841864 = _841862, _841860 = _841858, _841856 = _841854], (9638 ^ _780478) ^ [_946113, _946115] : [class_Orderings_Olinorder(_946113), hBOOL(hAPP(c_Finite__Set_Ofinite(_946113), _946115)), -(_946115 = c_Orderings_Obot__class_Obot(tc_fun(_946113, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_946113), c_Big__Operators_Olinorder__class_OMax(_946113, _946115)), _946115)))], (27972 ^ _780478) ^ [_1297706, _1297708, _1297710, _1297712] : [class_Groups_Ocomm__monoid__add(_1297706), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1297706), _1297708), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1297710), hAPP(c_Nat_OSuc, _1297712))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1297706), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1297706, tc_Nat_Onat), _1297708), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1297710, _1297712)))], (41524 ^ _780478) ^ [_1598240, _1598242] : [-(c_Wellfounded_Owf(_1598240, _1598242)), 41527 ^ _780478 : [(41530 ^ _780478) ^ [_1598460] : [hBOOL(hAPP(hAPP(c_member(_1598240), _1598460), 41525 ^ [_1598240, _1598242])), 41534 ^ _780478 : [(41537 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1598240), 41533 ^ [_1598240, _1598242, _1598460]), 41525 ^ [_1598240, _1598242])))], (41535 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1598240, _1598240)), hAPP(hAPP(c_Product__Type_OPair(_1598240, _1598240), 41533 ^ [_1598240, _1598242, _1598460]), _1598460)), _1598242)))]]], (41528 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1598240), 41526 ^ [_1598240, _1598242]), 41525 ^ [_1598240, _1598242])))]]], (48525 ^ _780478) ^ [_1759549, _1759551, _1759553, _1759555] : [-(c_Lazy__Sequence_Oproduct(_1759549, _1759551, _1759553, _1759555) = hAPP(c_Lazy__Sequence_Obind(_1759549, tc_prod(_1759549, _1759551), _1759553), hAPP(hAPP(c_COMBB(tc_fun(_1759551, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1759549, _1759551))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1759549, _1759551)), _1759549), c_Lazy__Sequence_Obind(_1759551, tc_prod(_1759549, _1759551), _1759555)), hAPP(hAPP(c_COMBB(tc_fun(_1759551, tc_prod(_1759549, _1759551)), tc_fun(_1759551, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1759549, _1759551))), _1759549), hAPP(c_COMBB(tc_prod(_1759549, _1759551), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1759549, _1759551)), _1759551), c_Lazy__Sequence_Osingle(tc_prod(_1759549, _1759551)))), c_Product__Type_OPair(_1759549, _1759551)))))], (8694 ^ _780478) ^ [_930960, _930962] : [class_Lattices_Oab__semigroup__idem__mult(_930960), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930960), _930962), _930962) = _930962)], (42540 ^ _780478) ^ [_1628127, _1628129, _1628131, _1628133, _1628135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628127), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628129)), _1628131))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1628127), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628133)), _1628135))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1628129, _1628133)), hAPP(hAPP(c_List_Ozip(_1628129, _1628133), _1628131), _1628135)), _1628127) = hAPP(hAPP(c_Product__Type_OPair(_1628129, _1628133), hAPP(hAPP(c_List_Onth(_1628129), _1628131), _1628127)), hAPP(hAPP(c_List_Onth(_1628133), _1628135), _1628127)))], (8398 ^ _780478) ^ [_924640, _924642, _924644, _924646, _924648] : [class_Groups_Ocomm__monoid__add(_924640), hBOOL(hAPP(c_Finite__Set_Ofinite(_924642), _924644)), -(hBOOL(hAPP(hAPP(c_member(_924642), _924646), _924644))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_924642, _924640), _924648), hAPP(hAPP(c_Set_Oinsert(_924642), _924646), _924644)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924640), hAPP(_924648, _924646)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_924642, _924640), _924648), _924644)))], (43193 ^ _780478) ^ [_1641793, _1641795, _1641797] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1641793)), -(c_List_Osublist(_1641795, hAPP(hAPP(c_List_Olist_OCons(_1641795), _1641797), c_List_Olist_ONil(_1641795)), _1641793) = hAPP(hAPP(c_List_Olist_OCons(_1641795), _1641797), c_List_Olist_ONil(_1641795)))], (50125 ^ _780478) ^ [_1794005, _1794007, _1794009, _1794011] : [c_Fun_Oinj__on(_1794005, _1794007, _1794009, c_Orderings_Otop__class_Otop(tc_fun(_1794005, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1794007, _1794005, c_Hilbert__Choice_Oinv__into(_1794005, _1794007, c_Orderings_Otop__class_Otop(tc_fun(_1794005, tc_HOL_Obool)), _1794009)), hAPP(c_Set_Oimage(_1794005, _1794007, _1794009), _1794011)) = _1794011)], (37036 ^ _780478) ^ [_1484945, _1484947] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1484945, _1484945)), hAPP(hAPP(c_Product__Type_OPair(_1484945, _1484945), 37037 ^ [_1484945, _1484947]), 37037 ^ [_1484945, _1484947])), _1484947))), -(c_Relation_Oirrefl(_1484945, _1484947))], (42784 ^ _780478) ^ [_1633665, _1633667] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1633665, _1633667))))], (6037 ^ _780478) ^ [_876489, _876491, _876493] : [hBOOL(hAPP(hAPP(c_member(_876489), _876491), _876493)), -(hAPP(hAPP(c_Set_Oinsert(_876489), _876491), _876493) = _876493)], (37513 ^ _780478) ^ [_1496285, _1496287, _1496289, _1496291, _1496293, _1496295] : [hAPP(_1496291, hAPP(c_Product__Type_Ofst(_1496285, _1496289), _1496293)) = hAPP(_1496295, hAPP(c_Product__Type_Ofst(_1496285, _1496289), _1496293)), -(hAPP(c_Product__Type_Oapfst(_1496285, _1496287, _1496289, _1496291), _1496293) = hAPP(c_Product__Type_Oapfst(_1496285, _1496287, _1496289, _1496295), _1496293))], (44582 ^ _780478) ^ [_1672654, _1672656, _1672658] : [_1672654 = c_List_Olist_ONil(_1672656), -(c_List_Olast(_1672656, hAPP(hAPP(c_List_Oappend(_1672656), _1672658), _1672654)) = c_List_Olast(_1672656, _1672658))], (37375 ^ _780478) ^ [_1491840, _1491842, _1491844, _1491846, _1491848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1491840, _1491842)), hAPP(_1491840, _1491844))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1491846, _1491846)), hAPP(hAPP(c_Product__Type_OPair(_1491846, _1491846), _1491842), _1491844)), _1491848)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491846, _1491846)), hAPP(hAPP(c_Product__Type_OPair(_1491846, _1491846), _1491842), _1491844)), c_Wellfounded_Omlex__prod(_1491846, _1491840, _1491848))))], (24507 ^ _780478) ^ [_1235810, _1235812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235810)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1235812)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235810), _1235812)), _1235810)))], (43550 ^ _780478) ^ [_1650009, _1650011, _1650013] : [_1650009 = hAPP(hAPP(c_List_Oappend(_1650011), _1650009), _1650013), -(_1650013 = c_List_Olist_ONil(_1650011))], (30853 ^ _780478) ^ [_1353494, _1353496] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1353494), _1353496))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1353494))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1353496))))], (39215 ^ _780478) ^ [_1541820, _1541822, _1541824] : [-(c_Relation_Orefl__on(_1541820, _1541822, _1541824)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541820, _1541820), tc_HOL_Obool)), _1541824), hAPP(hAPP(c_Product__Type_OSigma(_1541820, _1541820), _1541822), hAPP(c_COMBK(tc_fun(_1541820, tc_HOL_Obool), _1541820), _1541822)))), 39221 ^ _780478 : [(39224 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1541820, _1541820)), hAPP(hAPP(c_Product__Type_OPair(_1541820, _1541820), 39220 ^ [_1541820, _1541822, _1541824]), 39220 ^ [_1541820, _1541822, _1541824])), _1541824))], (39222 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1541820), 39220 ^ [_1541820, _1541822, _1541824]), _1541822)))]]], (51499 ^ _780478) ^ [_1823243, _1823245] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823243), _1823245))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823243, _1823245) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (2832 ^ _780478) ^ [_822399, _822401, _822403, _822405] : [-(c_Random_Oinc__shift(_822405, _822401) = c_Random_Oinc__shift(_822403, _822399)), _822405 = _822403, _822401 = _822399], (46198 ^ _780478) ^ [_1710316, _1710318, _1710320, _1710322] : [-(c_List_Ofoldr(_1710316, _1710318, _1710320, c_List_Olist_ONil(_1710316), _1710322) = _1710322)], (42828 ^ _780478) ^ [_1634530, _1634532] : [hAPP(c_Finite__Set_Ocard(_1634530), hAPP(c_List_Oset(_1634530), _1634532)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634530)), _1634532), -(hBOOL(hAPP(c_List_Odistinct(_1634530), _1634532)))], (2268 ^ _780478) ^ [_813635, _813637] : [_813637 = _813635, -(c_Int_Oring__1__class_OInts(_813637) = c_Int_Oring__1__class_OInts(_813635))], (32562 ^ _780478) ^ [_1395458, _1395460, _1395462, _1395464] : [class_Fields_Olinordered__field__inverse__zero(_1395458), class_Int_Onumber(_1395458), 32569 ^ _780478 : [(32570 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1395458), _1395460), _1395462)), hAPP(c_Int_Onumber__class_Onumber__of(_1395458), _1395464))), 32573 ^ _780478 : [(32580 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), c_Groups_Ozero__class_Ozero(_1395458)), _1395462))), 32583 ^ _780478 : [(32590 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), _1395462), c_Groups_Ozero__class_Ozero(_1395458)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), c_Groups_Ozero__class_Ozero(_1395458)), hAPP(c_Int_Onumber__class_Onumber__of(_1395458), _1395464))))], (32584 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), _1395462), c_Groups_Ozero__class_Ozero(_1395458))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395458), hAPP(c_Int_Onumber__class_Onumber__of(_1395458), _1395464)), _1395462)), _1395460)))]]], (32574 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), c_Groups_Ozero__class_Ozero(_1395458)), _1395462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), _1395460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395458), hAPP(c_Int_Onumber__class_Onumber__of(_1395458), _1395464)), _1395462))))]]], (32596 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1395458), _1395460), _1395462)), hAPP(c_Int_Onumber__class_Onumber__of(_1395458), _1395464)))), 32599 ^ _780478 : [(32602 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), _1395460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395458), hAPP(c_Int_Onumber__class_Onumber__of(_1395458), _1395464)), _1395462)))], (32600 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), c_Groups_Ozero__class_Ozero(_1395458)), _1395462)))]], 32603 ^ _780478 : [(32606 ^ _780478) ^ [] : [32607 ^ _780478 : [(32610 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395458), hAPP(c_Int_Onumber__class_Onumber__of(_1395458), _1395464)), _1395462)), _1395460))], (32608 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), _1395462), c_Groups_Ozero__class_Ozero(_1395458))))]], 32611 ^ _780478 : [(32614 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), c_Groups_Ozero__class_Ozero(_1395458)), hAPP(c_Int_Onumber__class_Onumber__of(_1395458), _1395464)))], (32612 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), _1395462), c_Groups_Ozero__class_Ozero(_1395458)))]]], (32604 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395458), c_Groups_Ozero__class_Ozero(_1395458)), _1395462))]]]]], (24517 ^ _780478) ^ [_1235969, _1235971, _1235973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235969)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235973), _1235969)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235971), _1235973)), _1235969))], (39959 ^ _780478) ^ [_1559301, _1559303, _1559305, _1559307, _1559309, _1559311] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1559301, _1559303), _1559301, tc_prod(_1559305, _1559307), c_Product__Type_Ofst(_1559301, _1559303)), c_Product__Type_Omap__pair(_1559305, _1559301, _1559307, _1559303, _1559309, _1559311)) = hAPP(c_Fun_Ocomp(_1559305, _1559301, tc_prod(_1559305, _1559307), _1559309), c_Product__Type_Ofst(_1559305, _1559307)))], (36916 ^ _780478) ^ [_1482678] : [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), _1482678))), -(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), _1482678)) = 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), _1482678))))], (2400 ^ _780478) ^ [_815633, _815635] : [_815635 = _815633, -(c_Nat_Onat_Onat__size(_815635) = c_Nat_Onat_Onat__size(_815633))], (31061 ^ _780478) ^ [_1358225, _1358227, _1358229] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1358225), _1358227)), 31067 ^ _780478 : [(31070 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1358229, 31066 ^ [_1358225, _1358227, _1358229])))], (31068 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358225), 31066 ^ [_1358225, _1358227, _1358229]), _1358227)))]], -(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(_1358225, tc_Nat_Onat), _1358229), _1358227))))], (35792 ^ _780478) ^ [_1459390, _1459392, _1459394, _1459396, _1459398, _1459400] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1459390, tc_fun(_1459392, tc_fun(_1459394, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1459390, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1459392, _1459394), tc_HOL_Obool), tc_fun(_1459392, tc_fun(_1459394, tc_HOL_Obool)), _1459390), hAPP(c_COMBC(_1459392, tc_fun(tc_prod(_1459392, _1459394), tc_HOL_Obool), tc_fun(_1459394, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459394, tc_fun(tc_fun(tc_prod(_1459392, _1459394), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1459392, _1459394), tc_HOL_Obool), tc_fun(_1459394, tc_HOL_Obool)), _1459392), c_COMBC(_1459394, tc_fun(tc_prod(_1459392, _1459394), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459394, tc_prod(_1459392, _1459394)), tc_fun(_1459394, tc_fun(tc_fun(tc_prod(_1459392, _1459394), tc_HOL_Obool), tc_HOL_Obool)), _1459392), hAPP(c_COMBB(tc_prod(_1459392, _1459394), tc_fun(tc_fun(tc_prod(_1459392, _1459394), tc_HOL_Obool), tc_HOL_Obool), _1459394), c_member(tc_prod(_1459392, _1459394)))), c_Product__Type_OPair(_1459392, _1459394))))), _1459396)), _1459398), _1459400)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1459392, _1459394)), hAPP(hAPP(c_Product__Type_OPair(_1459392, _1459394), _1459398), _1459400)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1459390, tc_fun(tc_prod(_1459392, _1459394), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1459390, tc_HOL_Obool))), _1459396))))], (33736 ^ _780478) ^ [_1417048] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1417048)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417048)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1417048)))], (36680 ^ _780478) ^ [_1477886, _1477888] : [_1477886 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1477888, _1477886) = 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), _1477888)))], (34393 ^ _780478) ^ [_1429169, _1429171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1429169)), c_Int_OBit0(_1429171))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429169), _1429171)))], (40484 ^ _780478) ^ [_1571992, _1571994, _1571996, _1571998, _1572000] : [_1571992 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1571994, _1571996, _1571992, _1571998), _1572000) = hAPP(c_Product__Type_OPair(_1571994, _1571996), _1572000))], (31132 ^ _780478) ^ [_1359771, _1359773, _1359775] : [31133 ^ _780478 : [(31136 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1359771), hAPP(c_Set_OCollect(_1359771), _1359775)))], (31134 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1359771), hAPP(c_Set_OCollect(_1359771), _1359773)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1359771), hAPP(c_Set_OCollect(_1359771), hAPP(hAPP(c_COMBS(_1359771, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1359771), c_fconj), _1359773)), _1359775)))))], (43831 ^ _780478) ^ [_1656970, _1656972, _1656974] : [-(hAPP(hAPP(c_List_Oappend(_1656970), hAPP(hAPP(c_List_Otake(_1656970), _1656972), _1656974)), hAPP(hAPP(c_List_Odrop(_1656970), _1656972), _1656974)) = _1656974)], (32276 ^ _780478) ^ [_1390201, _1390203, _1390205] : [class_Int_Onumber__ring(_1390201), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1390201), hAPP(c_Int_Onumber__class_Onumber__of(_1390201), _1390203)), hAPP(c_Int_Onumber__class_Onumber__of(_1390201), _1390205)) = hAPP(c_Int_Onumber__class_Onumber__of(_1390201), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1390203), _1390205)))], (41864 ^ _780478) ^ [_1608053, _1608055, _1608057, _1608059, _1608061] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608053), tc_List_Olist(_1608053))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608053), tc_List_Olist(_1608053)), _1608055), _1608057)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1608053), c_List_Olistrel1(_1608053, _1608059)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608053), tc_List_Olist(_1608053))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608053), tc_List_Olist(_1608053)), hAPP(hAPP(c_List_Olist_OCons(_1608053), _1608061), _1608055)), hAPP(hAPP(c_List_Olist_OCons(_1608053), _1608061), _1608057))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1608053), c_List_Olistrel1(_1608053, _1608059)))))], (30169 ^ _780478) ^ [_1340220] : [_1340220 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1340220) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44412 ^ _780478) ^ [_1669790, _1669792, _1669794, _1669796] : [class_Orderings_Olinorder(_1669790), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669790, _1669790, c_COMBI(_1669790)), _1669792), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669790, _1669790, c_COMBI(_1669790)), _1669794), _1669796)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669790, _1669790, c_COMBI(_1669790)), _1669794), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669790, _1669790, c_COMBI(_1669790)), _1669792), _1669796)))], (29704 ^ _780478) ^ [_1331973, _1331975, _1331977] : [hBOOL(hAPP(_1331973, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331975, _1331977))), 29707 ^ _780478 : [(29732 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331977), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29735 ^ _780478 : [(29736 ^ _780478) ^ [_1332595, _1332597] : [-(hBOOL(hAPP(_1331973, _1332595))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331977), _1332595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1332595), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1331975 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1331977), _1332597)), _1332595)]]], (29714 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331977)), 29717 ^ _780478 : [(29718 ^ _780478) ^ [_1332303, _1332305] : [-(hBOOL(hAPP(_1331973, _1332303))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1332303), _1331977)), _1331975 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1331977), _1332305)), _1332303)]]], (29708 ^ _780478) ^ [] : [_1331977 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1331973, _1331975)))]]], (4986 ^ _780478) ^ [_856566, _856568, _856570, _856572] : [-(c_Relation_Oconverse(_856572, _856568) = c_Relation_Oconverse(_856570, _856566)), _856572 = _856570, _856568 = _856566], (38134 ^ _780478) ^ [_1513077, _1513079, _1513081, _1513083] : [c_Wellfounded_Omax__extp(_1513077, _1513079, _1513081, _1513083), 38137 ^ _780478 : [(38140 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1513077), _1513083)))], (38142 ^ _780478) ^ [] : [_1513083 = c_Orderings_Obot__class_Obot(tc_fun(_1513077, tc_HOL_Obool))], (38144 ^ _780478) ^ [_1513293] : [hBOOL(hAPP(hAPP(c_member(_1513077), _1513293), _1513081)), 38148 ^ _780478 : [(38151 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1513079, _1513293), 38147 ^ [_1513077, _1513079, _1513081, _1513083, _1513293])))], (38149 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513077), 38147 ^ [_1513077, _1513079, _1513081, _1513083, _1513293]), _1513083)))]]], (38138 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1513077), _1513081)))]]], (18079 ^ _780478) ^ [_1116977, _1116979, _1116981] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1116977, tc_HOL_Obool)), _1116979), _1116981) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116977, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1116977, tc_HOL_Obool)), _1116979), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1116977, tc_HOL_Obool)), _1116981), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1116977, tc_HOL_Obool), tc_HOL_Obool))))))], (2586 ^ _780478) ^ [_818550, _818552, _818554, _818556, _818558, _818560, _818562, _818564] : [-(c_Recdef_Osame__fst(_818564, _818560, _818556, _818552) = c_Recdef_Osame__fst(_818562, _818558, _818554, _818550)), _818564 = _818562, _818560 = _818558, _818556 = _818554, _818552 = _818550], (13048 ^ _780478) ^ [_1011645, _1011647, _1011649, _1011651] : [hBOOL(hAPP(hAPP(c_member(_1011645), _1011647), _1011649)), -(hBOOL(hAPP(hAPP(c_member(_1011645), _1011647), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011645, tc_HOL_Obool)), _1011649), _1011651))))], (29968 ^ _780478) ^ [_1336581, _1336583] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336581, _1336583) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1336581 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1336583), 29971 ^ [_1336581, _1336583]))], (36804 ^ _780478) ^ [_1480515, _1480517] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480515, _1480517), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1480515), _1480517)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1480515, _1480517)))))], (52387 ^ _780478) ^ [_1834299, _1834301] : [hBOOL(_1834299), -(hBOOL(hAPP(hAPP(c_fdisj, _1834299), _1834301)))], (5690 ^ _780478) ^ [_867568, _867570, _867572, _867574, _867576, _867578] : [-(c_COMBS(_867578, _867574, _867570) = c_COMBS(_867576, _867572, _867568)), _867578 = _867576, _867574 = _867572, _867570 = _867568], (12379 ^ _780478) ^ [_998972, _998974, _998976, _998978, _998980] : [class_Groups_Ocomm__monoid__add(_998972), class_Groups_Oordered__ab__semigroup__add(_998972), 12389 ^ _780478 : [(12392 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998972), hAPP(_998978, 12388 ^ [_998972, _998974, _998976, _998978, _998980])), hAPP(_998980, 12388 ^ [_998972, _998974, _998976, _998978, _998980])))], (12390 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_998974), 12388 ^ [_998972, _998974, _998976, _998978, _998980]), _998976)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998972), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_998974, _998972), _998978), _998976)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_998974, _998972), _998980), _998976))))], (37195 ^ _780478) ^ [_1488088, _1488090, _1488092, _1488094] : [_1488088 = _1488090, 37198 ^ _780478 : [(37201 ^ _780478) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1488092, _1488094), _1488088) = hAPP(c_Product__Type_Osnd(_1488092, _1488094), _1488090))], (37199 ^ _780478) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1488092, _1488094), _1488088) = hAPP(c_Product__Type_Ofst(_1488092, _1488094), _1488090))]]], (35750 ^ _780478) ^ [_1458009, _1458011, _1458013, _1458015, _1458017, _1458019] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1458009, _1458011), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1458013), _1458015))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1458009, _1458011), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1458017), _1458019))), -(_1458011 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1458013 = _1458017)], (42270 ^ _780478) ^ [_1620051, _1620053, _1620055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620051)), _1620053)), _1620055)), -(hAPP(hAPP(c_List_Otake(_1620051), _1620055), _1620053) = _1620053)], (19057 ^ _780478) ^ [_1138500, _1138502, _1138504, _1138506, _1138508] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1138500, tc_fun(_1138502, tc_HOL_Obool)), _1138504), _1138506), _1138508)), 19060 ^ _780478 : [(19061 ^ _780478) ^ [_1138609] : [hBOOL(hAPP(hAPP(c_member(_1138500), _1138609), _1138504)), -(hBOOL(hAPP(hAPP(_1138506, _1138609), _1138508)))]]], (46475 ^ _780478) ^ [_1715927, _1715929] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1715927, _1715929)))], (23741 ^ _780478) ^ [_1221905, _1221907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1221905), _1221907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221905)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221907))))], (17809 ^ _780478) ^ [_1112379, _1112381, _1112383, _1112385, _1112387, _1112389] : [class_Complete__Lattice_Ocomplete__lattice(_1112379), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112381, tc_fun(_1112383, _1112379)), _1112385), _1112387), _1112389) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112381, _1112379), _1112385), hAPP(hAPP(c_COMBC(_1112381, _1112383, _1112379), _1112387), _1112389)))], (33955 ^ _780478) ^ [_1421818, _1421820] : [class_Rings_Osemiring__1(_1421818), 33958 ^ _780478 : [(33965 ^ _780478) ^ [] : [_1421820 = c_Groups_Ozero__class_Ozero(_1421818), -(c_Int_Oiszero(_1421818, _1421820))], (33959 ^ _780478) ^ [] : [c_Int_Oiszero(_1421818, _1421820), -(_1421820 = c_Groups_Ozero__class_Ozero(_1421818))]]], (15301 ^ _780478) ^ [_1055920, _1055922, _1055924] : [class_Rings_Oring__1(_1055920), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1055920), hAPP(c_Groups_Ouminus__class_Ouminus(_1055920), _1055922)), _1055924) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1055920), hAPP(hAPP(c_Power_Opower__class_Opower(_1055920), hAPP(c_Groups_Ouminus__class_Ouminus(_1055920), c_Groups_Oone__class_Oone(_1055920))), _1055924)), hAPP(hAPP(c_Power_Opower__class_Opower(_1055920), _1055922), _1055924)))], (40195 ^ _780478) ^ [_1564854, _1564856, _1564858, _1564860, _1564862, _1564864] : [c_Finite__Set_Ofolding__idem(_1564854, _1564856, _1564858, _1564860), hBOOL(hAPP(c_Finite__Set_Ofinite(_1564854), _1564862)), hBOOL(hAPP(hAPP(c_member(_1564854), _1564864), _1564862)), -(hAPP(c_Fun_Ocomp(_1564856, _1564856, _1564856, hAPP(_1564860, _1564862)), hAPP(_1564858, _1564864)) = hAPP(_1564860, _1564862))], (19346 ^ _780478) ^ [_1142916, _1142918] : [class_Groups_Olinordered__ab__group__add(_1142916), 19349 ^ _780478 : [(19356 ^ _780478) ^ [] : [_1142918 = c_Groups_Ozero__class_Ozero(_1142916), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1142916), _1142918) = _1142918)], (19350 ^ _780478) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1142916), _1142918) = _1142918, -(_1142918 = c_Groups_Ozero__class_Ozero(_1142916))]]], (14653 ^ _780478) ^ [_1042489, _1042491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042489), _1042491)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042491), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042491), _1042489)) = _1042489)], (39528 ^ _780478) ^ [_1548509, _1548511, _1548513] : [39530 ^ _780478 : [(39533 ^ _780478) ^ [] : [hBOOL(hAPP(_1548511, 39529 ^ [_1548509, _1548511, _1548513]))], (39531 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1548509), 39529 ^ [_1548509, _1548511, _1548513]), _1548513)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1548509, _1548511), _1548513)))], (6254 ^ _780478) ^ [_880737, _880739, _880741, _880743, _880745] : [6257 ^ _780478 : [(6260 ^ _780478) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_880739, _880741, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_880739)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_880739), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _880739), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 6256 ^ [_880737, _880739, _880741, _880743, _880745]))), _880743), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _880739), hAPP(_880745, 6255 ^ [_880737, _880739, _880741, _880743, _880745])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_880739), tc_HOL_Obool))))], (6258 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_880737, 6255 ^ [_880737, _880739, _880741, _880743, _880745]), 6256 ^ [_880737, _880739, _880741, _880743, _880745])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_880739, _880741, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_880739)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_880739), _880737), _880743), _880745)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_880739), tc_HOL_Obool)))))], (44229 ^ _780478) ^ [_1665723, _1665725, _1665727, _1665729] : [class_Groups_Osemigroup__add(_1665723), -(hAPP(c_List_Ofoldl(_1665723, _1665723, c_Groups_Oplus__class_Oplus(_1665723), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1665723), _1665725), _1665727)), _1665729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1665723), _1665725), hAPP(c_List_Ofoldl(_1665723, _1665723, c_Groups_Oplus__class_Oplus(_1665723), _1665727), _1665729)))], (46621 ^ _780478) ^ [_1718156, _1718158, _1718160, _1718162, _1718164] : [class_Orderings_Olinorder(_1718156), c_List_Olinorder__class_Osorted(_1718156, hAPP(hAPP(c_List_Omap(_1718158, _1718156), _1718160), _1718162)), -(c_List_Olinorder__class_Osorted(_1718156, hAPP(hAPP(c_List_Omap(_1718158, _1718156), _1718160), c_List_Olinorder__class_Oinsort__insert__key(_1718158, _1718156, _1718160, _1718164, _1718162))))], (40925 ^ _780478) ^ [_1582219, _1582221, _1582223] : [c_Equiv__Relations_Oequiv(_1582219, _1582221, _1582223), -(hAPP(hAPP(c_Relation_Orel__comp(_1582219, _1582219, _1582219), hAPP(c_Relation_Oconverse(_1582219, _1582219), _1582223)), _1582223) = _1582223)], (37101 ^ _780478) ^ [_1486269, _1486271, _1486273, _1486275] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1486269, _1486271), _1486273)), hBOOL(hAPP(hAPP(_1486271, _1486275), _1486273)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1486269, _1486271), _1486275)))], (32114 ^ _780478) ^ [_1386850, _1386852, _1386854, _1386856, _1386858] : [c_Com_Ocom_OWhile(_1386850, _1386852) = c_Com_Ocom_OLocal(_1386854, _1386856, _1386858)], (41683 ^ _780478) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39422 ^ _780478) ^ [_1546081, _1546083] : [c_Nitpick_Owf_H(_1546081, _1546083), 39425 ^ _780478 : [(39428 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1546081, _1546081)), _1546083))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (39426 ^ _780478) ^ [] : [-(c_Wellfounded_Oacyclic(_1546081, _1546083))]]], (25345 ^ _780478) ^ [_1251517, _1251519, _1251521] : [class_Rings_Odivision__ring(_1251517), -(_1251519 = c_Groups_Ozero__class_Ozero(_1251517)), 25352 ^ _780478 : [(25359 ^ _780478) ^ [] : [_1251521 = _1251519, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251517), _1251521), _1251519) = c_Groups_Oone__class_Oone(_1251517))], (25353 ^ _780478) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251517), _1251521), _1251519) = c_Groups_Oone__class_Oone(_1251517), -(_1251521 = _1251519)]]], (12133 ^ _780478) ^ [_993804, _993806, _993808] : [class_Orderings_Olinorder(_993804), hBOOL(hAPP(c_Finite__Set_Ofinite(_993804), _993806)), -(hBOOL(hAPP(hAPP(c_member(_993804), _993808), _993806))), -(c_Big__Operators_Olattice_OInf__fin(_993804, c_Orderings_Oord__class_Omin(_993804), hAPP(hAPP(c_Set_Oinsert(_993804), _993808), _993806)) = hAPP(hAPP(c_Finite__Set_Ofold(_993804, _993804, c_Orderings_Oord__class_Omin(_993804)), _993808), _993806))], (30037 ^ _780478) ^ [_1337753, _1337755] : [class_Rings_Olinordered__idom(_1337753), 30040 ^ _780478 : [(30047 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337753), _1337755), c_Groups_Ozero__class_Ozero(_1337753))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337753), c_Groups_Osgn__class_Osgn(_1337753, _1337755)), c_Groups_Ozero__class_Ozero(_1337753))))], (30041 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337753), c_Groups_Osgn__class_Osgn(_1337753, _1337755)), c_Groups_Ozero__class_Ozero(_1337753))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337753), _1337755), c_Groups_Ozero__class_Ozero(_1337753))))]]], (47657 ^ _780478) ^ [_1740188, _1740190, _1740192, _1740194, _1740196, _1740198, _1740200, _1740202] : [47659 ^ _780478 : [(47662 ^ _780478) ^ [] : [hAPP(c_Fun_Ocomp(_1740192, _1740192, _1740194, hAPP(_1740196, 47658 ^ [_1740188, _1740190, _1740192, _1740194, _1740196, _1740198, _1740200, _1740202])), _1740198) = hAPP(c_Fun_Ocomp(_1740194, _1740192, _1740194, _1740198), hAPP(_1740200, 47658 ^ [_1740188, _1740190, _1740192, _1740194, _1740196, _1740198, _1740200, _1740202]))], (47660 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740188), 47658 ^ [_1740188, _1740190, _1740192, _1740194, _1740196, _1740198, _1740200, _1740202]), hAPP(c_List_Oset(_1740188), _1740190))))]], -(hAPP(c_List_Ofoldl(_1740192, _1740188, hAPP(c_COMBC(_1740188, _1740192, _1740192), _1740196), hAPP(_1740198, _1740202)), _1740190) = hAPP(_1740198, hAPP(c_List_Ofoldl(_1740194, _1740188, hAPP(c_COMBC(_1740188, _1740194, _1740194), _1740200), _1740202), _1740190)))], (470 ^ _780478) ^ [_787565, _787567] : [-(c_Nat__Transfer_Onat__set(_787565)), _787567 = _787565, c_Nat__Transfer_Onat__set(_787567)], (10755 ^ _780478) ^ [_968104, _968106, _968108] : [class_Orderings_Olinorder(_968104), 10758 ^ _780478 : [(10765 ^ _780478) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_968104), _968106), _968108) = _968106, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968104), _968106), _968108)))], (10759 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968104), _968106), _968108)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_968104), _968106), _968108) = _968106)]]], (37239 ^ _780478) ^ [_1489103, _1489105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489103), 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)), _1489105)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1489103), _1489105) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1489103, _1489105)))], (8597 ^ _780478) ^ [_929184, _929186, _929188, _929190] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929184, tc_HOL_Obool)), _929186), hAPP(hAPP(c_Set_Oinsert(_929184), _929188), _929190)))), 8600 ^ _780478 : [(8603 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929184, tc_HOL_Obool)), _929186), _929190))], (8601 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929184), _929188), _929190)))]], 8604 ^ _780478 : [(8607 ^ _780478) ^ [] : [8608 ^ _780478 : [(8611 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929184, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_929184, tc_HOL_Obool)), _929186), hAPP(hAPP(c_Set_Oinsert(_929184), _929188), c_Orderings_Obot__class_Obot(tc_fun(_929184, tc_HOL_Obool))))), _929190))], (8609 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929184), _929188), _929186)))]], 8612 ^ _780478 : [(8615 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929184, tc_HOL_Obool)), _929186), _929190))], (8613 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929184), _929188), _929186))]]], (8605 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_929184), _929188), _929190))]]], (2314 ^ _780478) ^ [_814332, _814334, _814336, _814338, _814340, _814342, _814344, _814346] : [-(c_Nitpick_Oprod(_814346, _814342, _814338, _814334) = c_Nitpick_Oprod(_814344, _814340, _814336, _814332)), _814346 = _814344, _814342 = _814340, _814338 = _814336, _814334 = _814332], (25227 ^ _780478) ^ [_1249306] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249306)) = _1249306)], (4956 ^ _780478) ^ [_856119, _856121, _856123, _856125] : [-(c_Relation_OId__on(_856125, _856121) = c_Relation_OId__on(_856123, _856119)), _856125 = _856123, _856121 = _856119], (9466 ^ _780478) ^ [_942795, _942797, _942799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942795, tc_HOL_Obool)), _942797), _942799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942795, tc_HOL_Obool)), _942797), _942799))), -(_942797 = _942799)], (13008 ^ _780478) ^ [_1010958, _1010960, _1010962] : [class_Lattices_Obounded__lattice__bot(_1010958), 13011 ^ _780478 : [(13020 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010958), _1010960), _1010962) = c_Orderings_Obot__class_Obot(_1010958)), _1010960 = c_Orderings_Obot__class_Obot(_1010958), _1010962 = c_Orderings_Obot__class_Obot(_1010958)], (13012 ^ _780478) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010958), _1010960), _1010962) = c_Orderings_Obot__class_Obot(_1010958), 13015 ^ _780478 : [(13018 ^ _780478) ^ [] : [-(_1010962 = c_Orderings_Obot__class_Obot(_1010958))], (13016 ^ _780478) ^ [] : [-(_1010960 = c_Orderings_Obot__class_Obot(_1010958))]]]]], (42125 ^ _780478) ^ [_1615969, _1615971, _1615973, _1615975] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615969), tc_List_Olist(_1615969))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615969), tc_List_Olist(_1615969)), _1615971), _1615973)), c_List_Olistrel(_1615969, _1615975))), 42128 ^ _780478 : [(42131 ^ _780478) ^ [_1616198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1616198), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615969)), _1615971))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1615969, _1615969)), hAPP(hAPP(c_Product__Type_OPair(_1615969, _1615969), hAPP(hAPP(c_List_Onth(_1615969), _1615971), _1616198)), hAPP(hAPP(c_List_Onth(_1615969), _1615973), _1616198))), _1615975)))], (42129 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615969)), _1615971) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615969)), _1615973))]]], (24777 ^ _780478) ^ [_1240840, _1240842] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1240840, _1240842))))], (44288 ^ _780478) ^ [_1666946, _1666948] : [class_Complete__Lattice_Ocomplete__lattice(_1666946), -(c_Complete__Lattice_OInf__class_OInf(_1666946, hAPP(c_List_Oset(_1666946), _1666948)) = hAPP(c_List_Ofoldl(_1666946, _1666946, c_Lattices_Osemilattice__inf__class_Oinf(_1666946), c_Orderings_Otop__class_Otop(_1666946)), _1666948))], (20950 ^ _780478) ^ [_1170494] : [_1170494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170494), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (33120 ^ _780478) ^ [_1406359, _1406361] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406359) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406361), 33123 ^ _780478 : [(33130 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406359)))), 33133 ^ _780478 : [(33140 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406361)))), -(_1406359 = _1406361)], (33134 ^ _780478) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406361))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406359) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (33124 ^ _780478) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406361)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (43516 ^ _780478) ^ [_1649241, _1649243, _1649245, _1649247, _1649249, _1649251] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649241)), _1649243) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649245)), _1649247), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649241)), _1649249) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649245)), _1649251), -(hAPP(hAPP(c_List_Ozip(_1649241, _1649245), hAPP(hAPP(c_List_Oappend(_1649241), _1649243), _1649249)), hAPP(hAPP(c_List_Oappend(_1649245), _1649247), _1649251)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1649241, _1649245)), hAPP(hAPP(c_List_Ozip(_1649241, _1649245), _1649243), _1649247)), hAPP(hAPP(c_List_Ozip(_1649241, _1649245), _1649249), _1649251)))], (41720 ^ _780478) ^ [_1603660, _1603662, _1603664] : [_1603660 = hAPP(hAPP(c_List_Olist_OCons(_1603662), _1603664), _1603660)], (50743 ^ _780478) ^ [_1806909, _1806911, _1806913, _1806915] : [c_Equiv__Relations_Oequivp(_1806909, _1806911), 50749 ^ _780478 : [(50752 ^ _780478) ^ [] : [hBOOL(hAPP(_1806915, 50748 ^ [_1806909, _1806911, _1806913, _1806915]))], (50750 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1806913, 50748 ^ [_1806909, _1806911, _1806913, _1806915])))]], 50755 ^ _780478 : [(50756 ^ _780478) ^ [_1807168] : [hBOOL(hAPP(_1806913, _1807168))]], 50758 ^ _780478 : [(50761 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1806915, 50757 ^ [_1806909, _1806911, _1806913, _1806915])))], (50759 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806909), 50757 ^ [_1806909, _1806911, _1806913, _1806915]), c_Quotient_ORespects(_1806909, _1806911))))]]], (52027 ^ _780478) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (35515 ^ _780478) ^ [] : [-(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))], (39781 ^ _780478) ^ [_1555115, _1555117, _1555119, _1555121, _1555123, _1555125] : [c_Fun_Oinj__on(_1555115, _1555117, hAPP(c_Fun_Ocomp(_1555119, _1555117, _1555115, _1555121), _1555123), _1555125), -(c_Fun_Oinj__on(_1555119, _1555117, _1555121, hAPP(c_Set_Oimage(_1555115, _1555119, _1555123), _1555125)))], (25559 ^ _780478) ^ [_1254989, _1254991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1254989)), hAPP(c_Int_Onat, _1254991))), 25562 ^ _780478 : [(25565 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1254989), _1254991)))], (25563 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254991)))]]], (14683 ^ _780478) ^ [_1043106, _1043108, _1043110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043106), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043110), _1043108))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043106), _1043108)), _1043110)))], (36184 ^ _780478) ^ [_1468340, _1468342, _1468344] : [-(hAPP(c_Divides_Oadjust(_1468340), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1468342), _1468344)) = 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), _1468344), _1468340)), 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)))), _1468342)), 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)))), _1468342)), _1468344))))], (38496 ^ _780478) ^ [_1520714, _1520716] : [-(hAPP(c_List_Olexn(_1520714, _1520716), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1520714), tc_List_Olist(_1520714)), tc_HOL_Obool)))], (24765 ^ _780478) ^ [_1240660, _1240662, _1240664, _1240666] : [24766 ^ _780478 : [(24769 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1240664), _1240666)))], (24767 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1240660), _1240662)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1240660, _1240664)), c_Sum__Type_OPlus(_1240660, _1240664, _1240662, _1240666)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29920 ^ _780478) ^ [_1335833, _1335835] : [class_Rings_Olinordered__idom(_1335833), 29923 ^ _780478 : [(29930 ^ _780478) ^ [] : [_1335835 = c_Groups_Ozero__class_Ozero(_1335833), -(c_Groups_Osgn__class_Osgn(_1335833, _1335835) = c_Groups_Ozero__class_Ozero(_1335833))], (29924 ^ _780478) ^ [] : [c_Groups_Osgn__class_Osgn(_1335833, _1335835) = c_Groups_Ozero__class_Ozero(_1335833), -(_1335835 = c_Groups_Ozero__class_Ozero(_1335833))]]], (35445 ^ _780478) ^ [_1448178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1448178)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448178), c_Int_OMin)))], (13884 ^ _780478) ^ [_1028680, _1028682, _1028684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028680), _1028682)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028680), _1028684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028682), _1028684)))], (1584 ^ _780478) ^ [_803142, _803144] : [-(class_Rings_Oordered__comm__semiring(_803142)), _803144 = _803142, class_Rings_Oordered__comm__semiring(_803144)], (16877 ^ _780478) ^ [_1090351, _1090353, _1090355] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1090351), _1090353)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090351), _1090355)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090351, tc_HOL_Obool)), _1090353), _1090355) = c_Orderings_Obot__class_Obot(tc_fun(_1090351, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1090351), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1090351, tc_HOL_Obool)), _1090353), _1090355)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1090351), _1090353)), hAPP(c_Finite__Set_Ocard(_1090351), _1090355)))], (43469 ^ _780478) ^ [_1648121, _1648123, _1648125, _1648127] : [_1648125 = _1648127, -(hAPP(hAPP(c_List_Oappend(_1648121), _1648123), _1648125) = hAPP(hAPP(c_List_Oappend(_1648121), _1648123), _1648127))], (10181 ^ _780478) ^ [_957382, _957384] : [class_Groups_Ogroup__add(_957382), -(hAPP(c_Groups_Ouminus__class_Ouminus(_957382), hAPP(c_Groups_Ouminus__class_Ouminus(_957382), _957384)) = _957384)], (42682 ^ _780478) ^ [_1631232, _1631234, _1631236, _1631238, _1631240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1631232, tc_HOL_Obool)), hAPP(c_List_Oset(_1631232), _1631234)), _1631236)), hBOOL(hAPP(hAPP(c_member(_1631232), _1631238), _1631236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1631232, tc_HOL_Obool)), hAPP(c_List_Oset(_1631232), hAPP(hAPP(c_List_Olist__update(_1631232, _1631234), _1631240), _1631238))), _1631236)))], (37503 ^ _780478) ^ [_1495969, _1495971, _1495973, _1495975, _1495977, _1495979, _1495981] : [-(hAPP(c_Product__Type_Oapsnd(_1495969, _1495971, _1495973, _1495975), hAPP(c_Product__Type_Oapfst(_1495977, _1495973, _1495969, _1495979), _1495981)) = hAPP(hAPP(c_Product__Type_OPair(_1495973, _1495971), hAPP(_1495979, hAPP(c_Product__Type_Ofst(_1495977, _1495969), _1495981))), hAPP(_1495975, hAPP(c_Product__Type_Osnd(_1495977, _1495969), _1495981))))], (37519 ^ _780478) ^ [_1496440, _1496442, _1496444, _1496446, _1496448] : [-(hAPP(c_Product__Type_Ofst(_1496440, _1496442), hAPP(c_Product__Type_Oapfst(_1496444, _1496440, _1496442, _1496446), _1496448)) = hAPP(_1496446, hAPP(c_Product__Type_Ofst(_1496444, _1496442), _1496448)))], (45947 ^ _780478) ^ [_1703027, _1703029] : [class_Orderings_Olinorder(_1703027), -(c_List_Olinorder__class_Osort__key(_1703027, _1703027, c_COMBI(_1703027), _1703029) = hAPP(c_List_Ofoldl(tc_List_Olist(_1703027), _1703027, hAPP(c_COMBC(_1703027, tc_List_Olist(_1703027), tc_List_Olist(_1703027)), c_List_Olinorder__class_Oinsort__key(_1703027, _1703027, c_COMBI(_1703027))), c_List_Olist_ONil(_1703027)), _1703029))], (39145 ^ _780478) ^ [_1539910, _1539912, _1539914, _1539916, _1539918, _1539920, _1539922, _1539924] : [-(hAPP(c_Product__Type_Omap__pair(_1539910, _1539912, _1539914, _1539916, _1539918, _1539920), hAPP(hAPP(c_Product__Type_OPair(_1539910, _1539914), _1539922), _1539924)) = hAPP(hAPP(c_Product__Type_OPair(_1539912, _1539916), hAPP(_1539918, _1539922)), hAPP(_1539920, _1539924)))], (33450 ^ _780478) ^ [_1411738, _1411740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411738)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411740))), 33453 ^ _780478 : [(33454 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411738), _1411740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1411740)))], (33460 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411738), _1411740)))]]], (42320 ^ _780478) ^ [_1621141, _1621143, _1621145, _1621147] : [-(hAPP(hAPP(c_List_Otake(_1621141), hAPP(c_Nat_OSuc, _1621143)), hAPP(hAPP(c_List_Olist_OCons(_1621141), _1621145), _1621147)) = hAPP(hAPP(c_List_Olist_OCons(_1621141), _1621145), hAPP(hAPP(c_List_Otake(_1621141), _1621143), _1621147)))], (16144 ^ _780478) ^ [_1072830, _1072832, _1072834] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072830, tc_HOL_Obool)), _1072832), _1072834) = c_Orderings_Obot__class_Obot(tc_fun(_1072830, tc_HOL_Obool)), 16147 ^ _780478 : [(16148 ^ _780478) ^ [_1072954] : [hBOOL(hAPP(hAPP(c_member(_1072830), _1072954), _1072832)), 16151 ^ _780478 : [(16152 ^ _780478) ^ [_1073044] : [hBOOL(hAPP(hAPP(c_member(_1072830), _1073044), _1072834)), _1072954 = _1073044]]]]], (30584 ^ _780478) ^ [_1348190, _1348192] : [class_Groups_Oordered__ab__group__add__abs(_1348190), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348190), hAPP(c_Groups_Ouminus__class_Ouminus(_1348190), _1348192)), hAPP(c_Groups_Oabs__class_Oabs(_1348190), _1348192))))], (29191 ^ _780478) ^ [_1322208, _1322210, _1322212] : [-(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, _1322208, _1322210)), _1322212), _1322210) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1322208), _1322212), _1322210))], (32450 ^ _780478) ^ [_1393279, _1393281, _1393283, _1393285] : [class_Fields_Ofield__inverse__zero(_1393279), class_Int_Onumber(_1393279), 32457 ^ _780478 : [(32458 ^ _780478) ^ [] : [_1393281 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1393279), _1393283), hAPP(c_Int_Onumber__class_Onumber__of(_1393279), _1393285)), 32461 ^ _780478 : [(32468 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1393279), _1393285) = c_Groups_Ozero__class_Ozero(_1393279), -(_1393281 = c_Groups_Ozero__class_Ozero(_1393279))], (32462 ^ _780478) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1393279), _1393285) = c_Groups_Ozero__class_Ozero(_1393279)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393279), _1393281), hAPP(c_Int_Onumber__class_Onumber__of(_1393279), _1393285)) = _1393283)]]], (32474 ^ _780478) ^ [] : [-(_1393281 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1393279), _1393283), hAPP(c_Int_Onumber__class_Onumber__of(_1393279), _1393285))), 32477 ^ _780478 : [(32480 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393279), _1393281), hAPP(c_Int_Onumber__class_Onumber__of(_1393279), _1393285)) = _1393283], (32478 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1393279), _1393285) = c_Groups_Ozero__class_Ozero(_1393279)]], 32481 ^ _780478 : [(32484 ^ _780478) ^ [] : [_1393281 = c_Groups_Ozero__class_Ozero(_1393279)], (32482 ^ _780478) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1393279), _1393285) = c_Groups_Ozero__class_Ozero(_1393279))]]]]], (45787 ^ _780478) ^ [_1699798] : [-(c_List_Oremdups(_1699798, c_List_Olist_ONil(_1699798)) = c_List_Olist_ONil(_1699798))], (45181 ^ _780478) ^ [_1686074] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1686074)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1686074))], (4810 ^ _780478) ^ [_853806, _853808, _853810, _853812] : [-(c_Product__Type_Osnd(_853812, _853808) = c_Product__Type_Osnd(_853810, _853806)), _853812 = _853810, _853808 = _853806], (39975 ^ _780478) ^ [_1559781, _1559783, _1559785, _1559787, _1559789, _1559791] : [c_Finite__Set_Ofolding(_1559781, _1559783, _1559785, _1559787), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559781), _1559789)), -(hAPP(c_Fun_Ocomp(_1559783, _1559783, _1559783, hAPP(_1559785, _1559791)), hAPP(_1559787, _1559789)) = hAPP(c_Fun_Ocomp(_1559783, _1559783, _1559783, hAPP(_1559787, _1559789)), hAPP(_1559785, _1559791)))], (32750 ^ _780478) ^ [_1399062, _1399064, _1399066, _1399068] : [class_Int_Onumber__ring(_1399062), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1399062), hAPP(c_Int_Onumber__class_Onumber__of(_1399062), _1399064)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1399062), _1399066), hAPP(c_Int_Onumber__class_Onumber__of(_1399062), _1399068))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1399062), hAPP(c_Int_Onumber__class_Onumber__of(_1399062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1399064), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1399068)))), _1399066))], (47107 ^ _780478) ^ [_1728208, _1728210, _1728212, _1728214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728208), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728210)), _1728212))), -(hAPP(c_List_Orev(_1728210), hAPP(hAPP(c_List_Olist__update(_1728210, _1728212), _1728208), _1728214)) = hAPP(hAPP(c_List_Olist__update(_1728210, hAPP(c_List_Orev(_1728210), _1728212)), 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(_1728210)), _1728212)), _1728208)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1728214))], (23011 ^ _780478) ^ [_1208773, _1208775, _1208777, _1208779] : [class_Rings_Osemiring__1(_1208773), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1208775, _1208773), hAPP(c_COMBK(_1208773, _1208775), _1208777)), _1208779) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208773), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208773), hAPP(c_Finite__Set_Ocard(_1208775), _1208779))), _1208777))], (4700 ^ _780478) ^ [_852041, _852043, _852045, _852047, _852049, _852051, _852053, _852055] : [-(c_Random__Sequence_ORandom(_852055, _852051, _852047, _852043) = c_Random__Sequence_ORandom(_852053, _852049, _852045, _852041)), _852055 = _852053, _852051 = _852049, _852047 = _852045, _852043 = _852041], (22823 ^ _780478) ^ [_1205323, _1205325, _1205327] : [class_Rings_Olinordered__semidom(_1205323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205323), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205323), _1205325)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205323), _1205327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205325), _1205327)))], (4260 ^ _780478) ^ [_844925, _844927] : [_844927 = _844925, -(c_List_Onth(_844927) = c_List_Onth(_844925))], (13410 ^ _780478) ^ [_1019415, _1019417, _1019419, _1019421] : [c_Fun_Oinj__on(_1019415, _1019417, _1019419, c_Orderings_Otop__class_Otop(tc_fun(_1019415, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1019415, _1019417, c_Orderings_Otop__class_Otop(tc_fun(_1019415, tc_HOL_Obool)), _1019419), hAPP(_1019419, _1019421)) = _1019421)], (7655 ^ _780478) ^ [_909439, _909441, _909443] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909439, tc_HOL_Obool)), _909441), hAPP(hAPP(c_Set_Oinsert(_909439), _909443), _909441))))], (37929 ^ _780478) ^ [_1506135, _1506137, _1506139] : [hBOOL(hAPP(hAPP(c_member(_1506135), _1506139), c_Wellfounded_Oacc(_1506135, _1506137))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1506135, hAPP(hAPP(c_COMBC(_1506135, tc_fun(tc_prod(_1506135, _1506135), tc_HOL_Obool), tc_fun(_1506135, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506135, tc_fun(tc_fun(tc_prod(_1506135, _1506135), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1506135, _1506135), tc_HOL_Obool), tc_fun(_1506135, tc_HOL_Obool)), _1506135), c_COMBC(_1506135, tc_fun(tc_prod(_1506135, _1506135), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506135, tc_prod(_1506135, _1506135)), tc_fun(_1506135, tc_fun(tc_fun(tc_prod(_1506135, _1506135), tc_HOL_Obool), tc_HOL_Obool)), _1506135), hAPP(c_COMBB(tc_prod(_1506135, _1506135), tc_fun(tc_fun(tc_prod(_1506135, _1506135), tc_HOL_Obool), tc_HOL_Obool), _1506135), c_member(tc_prod(_1506135, _1506135)))), c_Product__Type_OPair(_1506135, _1506135)))), _1506137)), _1506139)))], (30891 ^ _780478) ^ [_1354489, _1354491, _1354493] : [class_Complete__Lattice_Ocomplete__lattice(_1354489), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354489), _1354491)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1354489), _1354493), c_Complete__Lattice_OSup__class_OSup(_1354489, _1354491)) = hAPP(hAPP(c_Finite__Set_Ofold(_1354489, _1354489, c_Lattices_Osemilattice__sup__class_Osup(_1354489)), _1354493), _1354491))], (50427 ^ _780478) ^ [_1800815, _1800817, _1800819, _1800821, _1800823, _1800825, _1800827] : [c_Fun_Obij__betw(_1800815, _1800817, _1800819, _1800821, _1800823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1800815, tc_HOL_Obool)), _1800825), _1800821)), hAPP(c_Set_Oimage(_1800815, _1800817, _1800819), _1800825) = _1800827, -(c_Fun_Obij__betw(_1800815, _1800817, _1800819, _1800825, _1800827))], (52069 ^ _780478) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (44221 ^ _780478) ^ [_1665569, _1665571, _1665573, _1665575] : [-(hAPP(c_List_Ofoldl(_1665569, _1665571, _1665573, _1665575), c_List_Olist_ONil(_1665571)) = _1665575)], (23459 ^ _780478) ^ [_1216604, _1216606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216604), _1216606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216604), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216606), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (40390 ^ _780478) ^ [_1569605, _1569607] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569605, _1569605), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1569605, _1569607)), hAPP(hAPP(c_Product__Type_OSigma(_1569605, _1569605), hAPP(c_Relation_OField(_1569605), _1569607)), hAPP(c_COMBK(tc_fun(_1569605, tc_HOL_Obool), _1569605), hAPP(c_Relation_OField(_1569605), _1569607))))))], (41860 ^ _780478) ^ [_1607950, _1607952] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1607950), tc_List_Olist(_1607950)), tc_HOL_Obool)), c_List_Olistrel1(_1607950, c_Transitive__Closure_Ortrancl(_1607950, _1607952))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1607950), c_List_Olistrel1(_1607950, _1607952)))))], (45781 ^ _780478) ^ [_1699705, _1699707] : [_1699707 = c_List_Olist_ONil(_1699705), -(c_List_Olist_ONil(_1699705) = c_List_Oremdups(_1699705, _1699707))], (4804 ^ _780478) ^ [_853721, _853723] : [_853723 = _853721, -(c_Random__Sequence_Osingle(_853723) = c_Random__Sequence_Osingle(_853721))], (48507 ^ _780478) ^ [_1758560, _1758562, _1758564, _1758566, _1758568] : [-(c_Predicate_Oconversep(_1758560, _1758562, c_Predicate_Opred__comp(_1758560, _1758564, _1758562, _1758566, _1758568)) = c_Predicate_Opred__comp(_1758562, _1758564, _1758560, c_Predicate_Oconversep(_1758564, _1758562, _1758568), c_Predicate_Oconversep(_1758560, _1758564, _1758566)))], (48095 ^ _780478) ^ [_1749870, _1749872, _1749874, _1749876] : [c_List_Olist__ex(_1749870, _1749872, hAPP(hAPP(c_List_Olist_OCons(_1749870), _1749874), _1749876)), -(hBOOL(hAPP(_1749872, _1749874))), -(c_List_Olist__ex(_1749870, _1749872, _1749876))], (52017 ^ _780478) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (44418 ^ _780478) ^ [_1669965, _1669967, _1669969, _1669971, _1669973, _1669975] : [class_Orderings_Olinorder(_1669965), -(hAPP(_1669967, _1669969) = hAPP(_1669967, _1669971)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669973, _1669965, _1669967), _1669971), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669973, _1669965, _1669967), _1669969), _1669975)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669973, _1669965, _1669967), _1669969), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669973, _1669965, _1669967), _1669971), _1669975)))], (45999 ^ _780478) ^ [_1704975, _1704977] : [-(c_List_Oconcat(_1704975, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704975), tc_List_Olist(_1704975)), c_List_Olist_Olist__case(tc_List_Olist(_1704975), _1704975, c_List_Olist_ONil(_1704975), hAPP(hAPP(c_COMBB(tc_List_Olist(_1704975), tc_fun(tc_List_Olist(_1704975), tc_List_Olist(_1704975)), _1704975), c_COMBK(tc_List_Olist(_1704975), tc_List_Olist(_1704975))), hAPP(hAPP(c_COMBC(_1704975, tc_List_Olist(_1704975), tc_List_Olist(_1704975)), c_List_Olist_OCons(_1704975)), c_List_Olist_ONil(_1704975))))), _1704977)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704975), _1704975), c_List_Ohd(_1704975)), hAPP(c_List_Ofilter(tc_List_Olist(_1704975), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1704975)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704975), tc_List_Olist(_1704975), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1704975)))), _1704977)))], (10869 ^ _780478) ^ [_970010, _970012, _970014] : [class_Groups_Oordered__ab__group__add(_970010), 10872 ^ _780478 : [(10879 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970010), _970014), _970012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970010), hAPP(c_Groups_Ouminus__class_Ouminus(_970010), _970012)), hAPP(c_Groups_Ouminus__class_Ouminus(_970010), _970014))))], (10873 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970010), hAPP(c_Groups_Ouminus__class_Ouminus(_970010), _970012)), hAPP(c_Groups_Ouminus__class_Ouminus(_970010), _970014))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970010), _970014), _970012)))]]], (34665 ^ _780478) ^ [_1434016, _1434018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1434016)), c_Int_OBit1(_1434018))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434016), _1434018)))], (5344 ^ _780478) ^ [_862169, _862171, _862173, _862175, _862177, _862179] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_862179, _862175, _862171) = c_Lazy__Sequence_Olazy__sequence_OInsert(_862177, _862173, _862169)), _862179 = _862177, _862175 = _862173, _862171 = _862169], (13176 ^ _780478) ^ [_1014329, _1014331, _1014333] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014329, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014329, tc_HOL_Obool)), _1014331), _1014333)), _1014333) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014329, tc_HOL_Obool)), _1014331), _1014333))], (17131 ^ _780478) ^ [_1095554, _1095556, _1095558] : [class_Orderings_Olinorder(_1095554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095554), _1095556)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095554), _1095558)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095554, tc_HOL_Obool)), _1095556), _1095558) = c_Orderings_Obot__class_Obot(tc_fun(_1095554, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095554), c_Big__Operators_Olattice_OSup__fin(_1095554, c_Orderings_Oord__class_Omax(_1095554), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1095554, tc_HOL_Obool)), _1095556), _1095558))), c_Big__Operators_Olattice_OSup__fin(_1095554, c_Orderings_Oord__class_Omax(_1095554), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095554, tc_HOL_Obool)), _1095556), _1095558))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095554), c_Big__Operators_Olattice_OSup__fin(_1095554, c_Orderings_Oord__class_Omax(_1095554), _1095556)), c_Big__Operators_Olattice_OSup__fin(_1095554, c_Orderings_Oord__class_Omax(_1095554), _1095558)))], (41607 ^ _780478) ^ [_1600391, _1600393, _1600395, _1600397] : [class_Rings_Olinordered__semidom(_1600391), 41613 ^ _780478 : [(41616 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1600391), c_Groups_Ozero__class_Ozero(_1600391)), hAPP(_1600397, 41612 ^ [_1600391, _1600393, _1600395, _1600397])))], (41614 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1600393), 41612 ^ [_1600391, _1600393, _1600395, _1600397]), _1600395)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1600391), c_Groups_Ozero__class_Ozero(_1600391)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1600393, _1600391), _1600397), _1600395))))], (9914 ^ _780478) ^ [_952548, _952550, _952552, _952554] : [class_Rings_Ocomm__semiring__1(_952548), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952548), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952548), _952550), _952552)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952548), _952554), _952552)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952548), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952548), _952550), _952554)), _952552))], (42552 ^ _780478) ^ [_1628453, _1628455] : [class_Groups_Ocomm__monoid__add(_1628453), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1628453), _1628455) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1628453), hAPP(c_List_Onth(_1628453), _1628455)), 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(_1628453)), _1628455))))], (45357 ^ _780478) ^ [_1689697, _1689699, _1689701, _1689703, _1689705] : [c_List_Opartition(_1689697, _1689699, _1689701) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1689697), tc_List_Olist(_1689697)), _1689703), _1689705), 45360 ^ _780478 : [(45367 ^ _780478) ^ [_1689959] : [hBOOL(hAPP(hAPP(c_member(_1689697), _1689959), hAPP(c_List_Oset(_1689697), _1689705))), hBOOL(hAPP(_1689699, _1689959))], (45361 ^ _780478) ^ [_1689850] : [hBOOL(hAPP(hAPP(c_member(_1689697), _1689850), hAPP(c_List_Oset(_1689697), _1689703))), -(hBOOL(hAPP(_1689699, _1689850)))]]], (39787 ^ _780478) ^ [_1555238, _1555240, _1555242, _1555244, _1555246, _1555248] : [-(hAPP(c_Set_Oimage(_1555238, _1555240, hAPP(c_Fun_Ocomp(_1555242, _1555240, _1555238, _1555244), _1555246)), _1555248) = hAPP(c_Set_Oimage(_1555242, _1555240, _1555244), hAPP(c_Set_Oimage(_1555238, _1555242, _1555246), _1555248)))], (26264 ^ _780478) ^ [_1267411, _1267413, _1267415] : [class_Fields_Olinordered__field__inverse__zero(_1267411), 26267 ^ _780478 : [(26282 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267411), c_Groups_Ozero__class_Ozero(_1267411)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267411), _1267413), _1267415)))), 26283 ^ _780478 : [(26290 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267411), _1267413), c_Groups_Ozero__class_Ozero(_1267411))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267411), _1267415), c_Groups_Ozero__class_Ozero(_1267411)))], (26284 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267411), c_Groups_Ozero__class_Ozero(_1267411)), _1267413)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267411), c_Groups_Ozero__class_Ozero(_1267411)), _1267415))]]], (26268 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267411), c_Groups_Ozero__class_Ozero(_1267411)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267411), _1267413), _1267415))), 26273 ^ _780478 : [(26276 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267411), c_Groups_Ozero__class_Ozero(_1267411)), _1267415)))], (26274 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267411), c_Groups_Ozero__class_Ozero(_1267411)), _1267413)))]], 26277 ^ _780478 : [(26280 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267411), _1267415), c_Groups_Ozero__class_Ozero(_1267411))))], (26278 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1267411), _1267413), c_Groups_Ozero__class_Ozero(_1267411))))]]]]], (13857 ^ _780478) ^ [_1028254] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028254), _1028254)))], (24563 ^ _780478) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23683 ^ _780478) ^ [_1220689, _1220691, _1220693, _1220695] : [class_Orderings_Oorder(_1220689), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1220689, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220689, _1220691), _1220693)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220689, _1220693), _1220695)) = c_Orderings_Obot__class_Obot(tc_fun(_1220689, tc_HOL_Obool)))], (9204 ^ _780478) ^ [_938360, _938362, _938364] : [class_Orderings_Olinorder(_938360), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938360), _938362), _938364))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938360), _938364), _938362)))], (25952 ^ _780478) ^ [_1261569, _1261571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261569)), 25955 ^ _780478 : [(25962 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261569), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1261571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1261569)), _1261571)))], (25956 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1261569)), _1261571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1261569), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1261571))))]]], (660 ^ _780478) ^ [_790460, _790462] : [-(class_Fields_Olinordered__field(_790460)), _790462 = _790460, class_Fields_Olinordered__field(_790462)], (35165 ^ _780478) ^ [_1443288, _1443290] : [class_Rings_Osemiring__1(_1443288), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1443290)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1443288), 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)))), _1443290))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1443288), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1443288), hAPP(c_Int_Onat, _1443290))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1443288), hAPP(c_Int_Onat, _1443290))))], (31933 ^ _780478) ^ [_1383613, _1383615, _1383617, _1383619, _1383621, _1383623] : [class_Groups_Oab__semigroup__mult(_1383613), hBOOL(hAPP(c_Finite__Set_Ofinite(_1383615), _1383617)), 31943 ^ _780478 : [(31946 ^ _780478) ^ [] : [hAPP(_1383619, 31942 ^ [_1383613, _1383615, _1383617, _1383619, _1383621, _1383623]) = hAPP(_1383621, 31942 ^ [_1383613, _1383615, _1383617, _1383619, _1383621, _1383623])], (31944 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1383615), 31942 ^ [_1383613, _1383615, _1383617, _1383619, _1383621, _1383623]), _1383617)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1383613, _1383615, c_Groups_Otimes__class_Otimes(_1383613)), _1383619), _1383623), _1383617) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1383613, _1383615, c_Groups_Otimes__class_Otimes(_1383613)), _1383621), _1383623), _1383617))], (3662 ^ _780478) ^ [_835318, _835320] : [_835320 = _835318, -(c_Orderings_Oord__class_Omax(_835320) = c_Orderings_Oord__class_Omax(_835318))], (29598 ^ _780478) ^ [_1329984, _1329986, _1329988] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1329984), _1329986)), _1329988) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1329984), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1329986), _1329988))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1329984), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329986, _1329988))), _1329988)))], (52285 ^ _780478) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (8503 ^ _780478) ^ [_927081, _927083, _927085, _927087, _927089] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_927081, _927083, hAPP(hAPP(c_Set_Oinsert(_927081), _927085), _927087)), _927089)), 8508 ^ _780478 : [(8513 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_927081), 8506 ^ [_927081, _927083, _927085, _927087, _927089]), 8507 ^ [_927081, _927083, _927085, _927087, _927089]))], (8511 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_927081, _927081, _927083, 8506 ^ [_927081, _927083, _927085, _927087, _927089], 8507 ^ [_927081, _927083, _927085, _927087, _927089]), _927089)))], (8509 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_927081), _927085), _927087) = hAPP(hAPP(c_Set_Oinsert(_927081), 8506 ^ [_927081, _927083, _927085, _927087, _927089]), 8507 ^ [_927081, _927083, _927085, _927087, _927089]))]]], (6698 ^ _780478) ^ [_890948, _890950, _890952, _890954] : [c_Com_Ocom_OWhile(_890948, _890950) = c_Com_Ocom_OSemi(_890952, _890954)], (42520 ^ _780478) ^ [_1627530, _1627532, _1627534, _1627536, _1627538, _1627540] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627530, _1627532)), hAPP(hAPP(c_Product__Type_OPair(_1627530, _1627532), _1627534), _1627536)), hAPP(c_List_Oset(tc_prod(_1627530, _1627532)), hAPP(hAPP(c_List_Ozip(_1627530, _1627532), _1627538), _1627540)))), -(hBOOL(hAPP(hAPP(c_member(_1627530), _1627534), hAPP(c_List_Oset(_1627530), _1627538))))], (2780 ^ _780478) ^ [_821579, _821581, _821583, _821585] : [-(c_Wellfounded_Omax__ext(_821585, _821581) = c_Wellfounded_Omax__ext(_821583, _821579)), _821585 = _821583, _821581 = _821579], (15087 ^ _780478) ^ [_1052061, _1052063, _1052065, _1052067] : [class_Rings_Ocomm__semiring__1(_1052061), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1052061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052061), _1052063), _1052065)), _1052067) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052061), hAPP(hAPP(c_Power_Opower__class_Opower(_1052061), _1052063), _1052067)), hAPP(hAPP(c_Power_Opower__class_Opower(_1052061), _1052065), _1052067)))], (46368 ^ _780478) ^ [_1713680] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1713680) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1713680)))], (48926 ^ _780478) ^ [_1767690, _1767692, _1767694] : [-(c_List_Olist__ex1(_1767690, _1767692, _1767694)), 48927 ^ _780478 : [(48928 ^ _780478) ^ [_1767784] : [hBOOL(hAPP(hAPP(c_member(_1767690), _1767784), hAPP(c_List_Oset(_1767690), _1767694))), hBOOL(hAPP(_1767692, _1767784)), 48936 ^ _780478 : [(48941 ^ _780478) ^ [] : [48935 ^ [_1767690, _1767692, _1767694, _1767784] = _1767784], (48939 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1767692, 48935 ^ [_1767690, _1767692, _1767694, _1767784])))], (48937 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767690), 48935 ^ [_1767690, _1767692, _1767694, _1767784]), hAPP(c_List_Oset(_1767690), _1767694))))]]]]], (52275 ^ _780478) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (52317 ^ _780478) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (43528 ^ _780478) ^ [_1649611, _1649613] : [-(hAPP(hAPP(c_List_Oappend(_1649611), c_List_Olist_ONil(_1649611)), _1649613) = _1649613)], (26842 ^ _780478) ^ [_1277786, _1277788, _1277790, _1277792] : [class_Fields_Olinordered__field(_1277786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277786), _1277788), c_Groups_Ozero__class_Ozero(_1277786))), 26849 ^ _780478 : [(26856 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277786), _1277792), _1277788)), _1277790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277786), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277786), _1277790), _1277788)), _1277792)))], (26850 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277786), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277786), _1277790), _1277788)), _1277792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277786), _1277792), _1277788)), _1277790)))]]], (38774 ^ _780478) ^ [_1528414, _1528416, _1528418] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1528414, _1528416), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528414, _1528416), c_Orderings_Otop__class_Otop(tc_fun(_1528414, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1528416, tc_HOL_Obool), _1528414), _1528418))) = hAPP(hAPP(c_Product__Type_OSigma(_1528414, _1528416), c_Orderings_Otop__class_Otop(tc_fun(_1528414, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1528416, tc_HOL_Obool), _1528414), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1528416, tc_HOL_Obool)), _1528418))))], (30737 ^ _780478) ^ [_1351577, _1351579] : [class_Groups_Oordered__ab__group__add__abs(_1351577), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351577), _1351579), c_Groups_Ozero__class_Ozero(_1351577))), -(hAPP(c_Groups_Oabs__class_Oabs(_1351577), _1351579) = hAPP(c_Groups_Ouminus__class_Ouminus(_1351577), _1351579))], (16372 ^ _780478) ^ [_1078384, _1078386, _1078388] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078384, tc_HOL_Obool)), _1078386), _1078388) = c_Orderings_Obot__class_Obot(tc_fun(_1078384, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078384, tc_HOL_Obool)), _1078386), _1078388) = _1078386)], (7746 ^ _780478) ^ [_911377, _911379, _911381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911377, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_911377, tc_fun(_911377, tc_HOL_Obool), tc_HOL_Obool), c_member(_911377)), _911379)), hAPP(hAPP(c_COMBC(_911377, tc_fun(_911377, tc_HOL_Obool), tc_HOL_Obool), c_member(_911377)), _911381))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911377, tc_HOL_Obool)), _911379), _911381)))], (29045 ^ _780478) ^ [_1318946, _1318948, _1318950, _1318952] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1318946, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318948, tc_fun(tc_fun(_1318946, tc_HOL_Obool), tc_HOL_Obool)), _1318950), hAPP(hAPP(c_COMBB(tc_fun(_1318946, tc_HOL_Obool), tc_fun(tc_fun(_1318946, tc_HOL_Obool), tc_HOL_Obool), _1318948), c_Set_OPow(_1318946)), _1318952))), hAPP(c_Set_OPow(_1318946), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1318948, tc_fun(_1318946, tc_HOL_Obool)), _1318950), _1318952)))))], (34079 ^ _780478) ^ [_1423814] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1423814), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1423814)), c_Int_OPls)))], (11871 ^ _780478) ^ [_989130, _989132] : [class_Orderings_Olinorder(_989130), hBOOL(hAPP(c_Finite__Set_Ofinite(_989130), _989132)), -(_989132 = c_Orderings_Obot__class_Obot(tc_fun(_989130, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_989130), c_Big__Operators_Olattice_OInf__fin(_989130, c_Orderings_Oord__class_Omin(_989130), _989132)), c_Big__Operators_Olattice_OSup__fin(_989130, c_Orderings_Oord__class_Omax(_989130), _989132))))], (16378 ^ _780478) ^ [_1078517, _1078519, _1078521] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078517, tc_HOL_Obool)), _1078519), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078517, tc_HOL_Obool)), _1078521), _1078519)) = c_Orderings_Obot__class_Obot(tc_fun(_1078517, tc_HOL_Obool)))], (38693 ^ _780478) ^ [_1526021, _1526023, _1526025, _1526027] : [hBOOL(hAPP(hAPP(c_member(_1526021), _1526027), hAPP(c_Relation_ODomain(_1526021, _1526023), _1526025))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1526021, _1526023, hAPP(hAPP(c_COMBC(_1526021, tc_fun(tc_prod(_1526021, _1526023), tc_HOL_Obool), tc_fun(_1526023, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526023, tc_fun(tc_fun(tc_prod(_1526021, _1526023), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526021, _1526023), tc_HOL_Obool), tc_fun(_1526023, tc_HOL_Obool)), _1526021), c_COMBC(_1526023, tc_fun(tc_prod(_1526021, _1526023), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526023, tc_prod(_1526021, _1526023)), tc_fun(_1526023, tc_fun(tc_fun(tc_prod(_1526021, _1526023), tc_HOL_Obool), tc_HOL_Obool)), _1526021), hAPP(c_COMBB(tc_prod(_1526021, _1526023), tc_fun(tc_fun(tc_prod(_1526021, _1526023), tc_HOL_Obool), tc_HOL_Obool), _1526023), c_member(tc_prod(_1526021, _1526023)))), c_Product__Type_OPair(_1526021, _1526023)))), _1526025)), _1526027)))], (8376 ^ _780478) ^ [_924200, _924202, _924204, _924206, _924208, _924210] : [c_Finite__Set_Ofun__left__comm(_924200, _924202, _924204), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_924200, _924202, _924204, _924206, _924208), _924210)), -(hAPP(hAPP(c_Finite__Set_Ofold(_924200, _924202, _924204), _924206), _924208) = _924210)], (38240 ^ _780478) ^ [_1514989] : [-(c_Wellfounded_Owf(tc_fun(_1514989, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1514989)))], (39343 ^ _780478) ^ [_1544687, _1544689] : [c_Predicate_Oreflp(_1544687, _1544689), -(c_Relation_Orefl__on(_1544687, c_Orderings_Otop__class_Otop(tc_fun(_1544687, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1544687, _1544687)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544687, _1544687, tc_HOL_Obool), _1544689))))], (20610 ^ _780478) ^ [_1164787] : [class_Rings_Olinordered__semidom(_1164787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164787), c_Groups_Oone__class_Oone(_1164787)), c_Groups_Ozero__class_Ozero(_1164787)))], (37073 ^ _780478) ^ [_1485693, _1485695, _1485697] : [37075 ^ _780478 : [(37078 ^ _780478) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1485693, _1485695), 37074 ^ [_1485693, _1485695, _1485697]))], (37076 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1485695, 37074 ^ [_1485693, _1485695, _1485697]), _1485697)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1485693, _1485695), _1485697)))], (19318 ^ _780478) ^ [_1142511, _1142513, _1142515] : [class_Groups_Ogroup__add(_1142511), 19321 ^ _780478 : [(19328 ^ _780478) ^ [] : [_1142513 = _1142515, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142511), _1142513), _1142515) = c_Groups_Ozero__class_Ozero(_1142511))], (19322 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142511), _1142513), _1142515) = c_Groups_Ozero__class_Ozero(_1142511), -(_1142513 = _1142515)]]], (21251 ^ _780478) ^ [_1175318, _1175320] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1175318), _1175320) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1175318), _1175320)))], (7387 ^ _780478) ^ [_904179, _904181, _904183, _904185, _904187] : [c_Fun_Oinj__on(_904179, _904181, _904183, _904185), hBOOL(hAPP(hAPP(c_member(_904179), _904187), _904185)), -(hAPP(c_Fun_Othe__inv__into(_904179, _904181, _904185, _904183), hAPP(_904183, _904187)) = _904187)], (46101 ^ _780478) ^ [_1707114, _1707116, _1707118] : [-(c_List_Oremdups(_1707114, hAPP(c_List_Ofilter(_1707114, _1707116), _1707118)) = hAPP(c_List_Ofilter(_1707114, _1707116), c_List_Oremdups(_1707114, _1707118)))], (20956 ^ _780478) ^ [_1170596, _1170598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170596), hAPP(c_Nat_OSuc, _1170598))), -(_1170596 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20964 ^ _780478 : [(20967 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20963 ^ [_1170596, _1170598]), _1170598)))], (20965 ^ _780478) ^ [] : [-(_1170596 = hAPP(c_Nat_OSuc, 20963 ^ [_1170596, _1170598]))]]], (52255 ^ _780478) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (18502 ^ _780478) ^ [_1127099, _1127101, _1127103] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127099, tc_fun(_1127101, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1127099, tc_HOL_Obool))), _1127103) = c_Orderings_Otop__class_Otop(tc_fun(_1127101, tc_HOL_Obool)))], (1484 ^ _780478) ^ [_801892, _801894] : [-(class_Enum_Oenum(_801892)), _801894 = _801892, class_Enum_Oenum(_801894)], (51829 ^ _780478) ^ [_1828473, _1828475] : [class_Orderings_Otop(_1828473), -(class_Orderings_Otop(tc_fun(_1828475, _1828473)))], (50513 ^ _780478) ^ [_1802407, _1802409, _1802411, _1802413] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1802407), _1802409)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1802411), _1802413)), 50520 ^ _780478 : [(50527 ^ _780478) ^ [] : [hAPP(c_Finite__Set_Ocard(_1802407), _1802409) = hAPP(c_Finite__Set_Ocard(_1802411), _1802413), -(c_Fun_Obij__betw(_1802407, _1802411, 50530 ^ [_1802407, _1802409, _1802411, _1802413], _1802409, _1802413))], (50521 ^ _780478) ^ [] : [50522 ^ _780478 : [(50523 ^ _780478) ^ [_1802596] : [c_Fun_Obij__betw(_1802407, _1802411, _1802596, _1802409, _1802413)]], -(hAPP(c_Finite__Set_Ocard(_1802407), _1802409) = hAPP(c_Finite__Set_Ocard(_1802411), _1802413))]]], (40426 ^ _780478) ^ [_1570427, _1570429, _1570431, _1570433, _1570435] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570427, _1570427)), hAPP(hAPP(c_Product__Type_OPair(_1570427, _1570427), _1570429), _1570431)), c_Transitive__Closure_Otrancl(_1570427, _1570433))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570427, _1570427)), hAPP(hAPP(c_Product__Type_OPair(_1570427, _1570427), _1570431), _1570435)), c_Transitive__Closure_Otrancl(_1570427, _1570433))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570427, _1570427)), hAPP(hAPP(c_Product__Type_OPair(_1570427, _1570427), _1570429), _1570435)), c_Transitive__Closure_Otrancl(_1570427, _1570433))))], (25375 ^ _780478) ^ [_1251933, _1251935] : [class_Rings_Odivision__ring__inverse__zero(_1251933), 25378 ^ _780478 : [(25385 ^ _780478) ^ [] : [-(_1251935 = c_Groups_Ozero__class_Ozero(_1251933)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251933), _1251935), _1251935) = c_Groups_Oone__class_Oone(_1251933))], (25379 ^ _780478) ^ [] : [_1251935 = c_Groups_Ozero__class_Ozero(_1251933), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251933), _1251935), _1251935) = c_Groups_Ozero__class_Ozero(_1251933))]]], (5282 ^ _780478) ^ [_861200, _861202, _861204, _861206] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_861206, _861202) = c_SetInterval_Oord__class_OatLeastLessThan(_861204, _861200)), _861206 = _861204, _861202 = _861200], (22618 ^ _780478) ^ [_1201694, _1201696, _1201698] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1201694), _1201696)), _1201698) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201694), _1201698)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201696), _1201698)))], (38638 ^ _780478) ^ [_1524347, _1524349, _1524351] : [_1524351 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524347, _1524349), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1524347, _1524349), _1524351) = c_Orderings_Obot__class_Obot(tc_fun(_1524347, tc_HOL_Obool)))], (44406 ^ _780478) ^ [_1669699] : [class_Orderings_Olinorder(_1669699), -(c_Finite__Set_Ofun__left__comm(_1669699, tc_List_Olist(_1669699), c_List_Olinorder__class_Oinsort__key(_1669699, _1669699, c_COMBI(_1669699))))], (28985 ^ _780478) ^ [_1317561, _1317563] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1317561, tc_HOL_Obool)), hAPP(c_Set_OPow(_1317561), _1317563))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1317561), _1317563)))], (17983 ^ _780478) ^ [_1115279, _1115281] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115279), _1115281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115279), hAPP(c_Nat_OSuc, _1115281))))], (49820 ^ _780478) ^ [_1787707, _1787709] : [c_Predicate_Osymp(_1787707, _1787709), -(c_Relation_Osym(_1787707, hAPP(c_Set_OCollect(tc_prod(_1787707, _1787707)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787707, _1787707, tc_HOL_Obool), _1787709))))], (31166 ^ _780478) ^ [_1360525, _1360527, _1360529] : [hBOOL(hAPP(_1360529, _1360527)), -(hBOOL(hAPP(hAPP(c_member(_1360525), _1360527), hAPP(c_Set_OCollect(_1360525), _1360529))))], (6366 ^ _780478) ^ [_883367, _883369, _883371, _883373, _883375, _883377] : [c_Hoare__Mirabelle_Ohoare__derivs(_883367, _883369, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883367)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883367), _883371), _883373), _883375)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883367), tc_HOL_Obool)))), 6373 ^ _780478 : [(6376 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_883377, 6371 ^ [_883367, _883369, _883371, _883373, _883375, _883377]), 6372 ^ [_883367, _883369, _883371, _883373, _883375, _883377]))], (6374 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_883375, 6371 ^ [_883367, _883369, _883371, _883373, _883375, _883377]), 6372 ^ [_883367, _883369, _883371, _883373, _883375, _883377])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_883367, _883369, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_883367)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_883367), _883371), _883373), _883377)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_883367), tc_HOL_Obool)))))], (38772 ^ _780478) ^ [_1528322, _1528324, _1528326] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1528322, _1528324), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528322, _1528324), _1528326), hAPP(c_COMBK(tc_fun(_1528324, tc_HOL_Obool), _1528322), c_Orderings_Otop__class_Otop(tc_fun(_1528324, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1528322, _1528324), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1528322, tc_HOL_Obool)), _1528326)), hAPP(c_COMBK(tc_fun(_1528324, tc_HOL_Obool), _1528322), c_Orderings_Otop__class_Otop(tc_fun(_1528324, tc_HOL_Obool)))))], (49480 ^ _780478) ^ [_1781418, _1781420, _1781422, _1781424] : [c_Predicate_Osymp(_1781418, _1781420), hBOOL(hAPP(hAPP(_1781420, _1781422), _1781424)), -(hBOOL(hAPP(hAPP(_1781420, _1781424), _1781422)))], (7204 ^ _780478) ^ [_900651, _900653, _900655] : [class_Orderings_Opreorder(_900651), _900653 = _900655, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900651), _900653), _900655)))], (38818 ^ _780478) ^ [_1529948, _1529950, _1529952, _1529954, _1529956] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529948, _1529950), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529948, tc_HOL_Obool)), _1529952), _1529954)), hAPP(c_COMBK(tc_fun(_1529950, tc_HOL_Obool), _1529948), _1529956)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1529948, _1529950), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529948, _1529950), _1529952), hAPP(c_COMBK(tc_fun(_1529950, tc_HOL_Obool), _1529948), _1529956))), hAPP(hAPP(c_Product__Type_OSigma(_1529948, _1529950), _1529954), hAPP(c_COMBK(tc_fun(_1529950, tc_HOL_Obool), _1529948), _1529956))))], (45795 ^ _780478) ^ [_1699958, _1699960, _1699962, _1699964] : [-(_1699958 = _1699960), -(hAPP(c_List_OremoveAll(_1699962, _1699958), hAPP(hAPP(c_List_Olist_OCons(_1699962), _1699960), _1699964)) = hAPP(hAPP(c_List_Olist_OCons(_1699962), _1699960), hAPP(c_List_OremoveAll(_1699962, _1699958), _1699964)))], (42328 ^ _780478) ^ [_1621372, _1621374, _1621376] : [-(c_List_Osublist(_1621372, _1621374, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1621376)) = hAPP(hAPP(c_List_Otake(_1621372), _1621376), _1621374))], (2468 ^ _780478) ^ [_816703, _816705, _816707, _816709] : [-(c_Divides_Odivmod__nat(_816709, _816705) = c_Divides_Odivmod__nat(_816707, _816703)), _816709 = _816707, _816705 = _816703], (15141 ^ _780478) ^ [_1053146, _1053148] : [class_Lattices_Olattice(_1053146), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053146), _1053148)), -(c_Big__Operators_Olattice__class_OSup__fin(_1053146, _1053148) = hAPP(c_Finite__Set_Ofold1(_1053146, c_Lattices_Osemilattice__sup__class_Osup(_1053146)), _1053148))], (3246 ^ _780478) ^ [_828802, _828804, _828806, _828808, _828810, _828812, _828814, _828816] : [-(c_Nitpick_Osetsum_H(_828816, _828812, _828808, _828804) = c_Nitpick_Osetsum_H(_828814, _828810, _828806, _828802)), _828816 = _828814, _828812 = _828810, _828808 = _828806, _828804 = _828802], (46987 ^ _780478) ^ [_1725570, _1725572, _1725574] : [-(hAPP(c_List_Orev(_1725570), hAPP(hAPP(c_List_Oappend(_1725570), _1725572), _1725574)) = hAPP(hAPP(c_List_Oappend(_1725570), hAPP(c_List_Orev(_1725570), _1725574)), hAPP(c_List_Orev(_1725570), _1725572)))], (41814 ^ _780478) ^ [_1606599, _1606601, _1606603, _1606605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606599), tc_List_Olist(_1606599))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606599), tc_List_Olist(_1606599)), _1606601), _1606603)), c_List_Olex(_1606599, _1606605))), 41817 ^ _780478 : [(41820 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606599)), _1606601) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1606599)), _1606603))], (41818 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606599), tc_List_Olist(_1606599))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606599), tc_List_Olist(_1606599)), _1606601), _1606603)), c_List_Olexord(_1606599, _1606605))))]]], (18912 ^ _780478) ^ [_1135531, _1135533, _1135535] : [class_Lattices_Olattice(_1135531), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135531), _1135533)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135531), _1135535)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1135531, tc_HOL_Obool)), _1135533), _1135535) = c_Orderings_Obot__class_Obot(tc_fun(_1135531, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1135531), c_Big__Operators_Olattice__class_OInf__fin(_1135531, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1135531, tc_HOL_Obool)), _1135533), _1135535))), c_Big__Operators_Olattice__class_OInf__fin(_1135531, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1135531, tc_HOL_Obool)), _1135533), _1135535))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1135531), c_Big__Operators_Olattice__class_OInf__fin(_1135531, _1135533)), c_Big__Operators_Olattice__class_OInf__fin(_1135531, _1135535)))], (20862 ^ _780478) ^ [_1169056, _1169058, _1169060, _1169062] : [class_Groups_Ocomm__monoid__add(_1169056), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1169058), _1169060))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1169058, _1169056), _1169062), _1169060) = c_Groups_Ozero__class_Ozero(_1169056))], (22747 ^ _780478) ^ [_1203957, _1203959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1203957), _1203959)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203957)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203959))))], (22799 ^ _780478) ^ [_1204900, _1204902] : [class_Rings_Olinordered__semidom(_1204900), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204900), c_Groups_Ozero__class_Ozero(_1204900)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1204900), _1204902))))], (43768 ^ _780478) ^ [_1655081, _1655083, _1655085, _1655087, _1655089, _1655091] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655081), tc_List_Olist(_1655081))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655081), tc_List_Olist(_1655081)), hAPP(hAPP(c_List_Oappend(_1655081), _1655083), hAPP(hAPP(c_List_Olist_OCons(_1655081), _1655085), c_List_Olist_ONil(_1655081)))), hAPP(hAPP(c_List_Oappend(_1655081), _1655087), hAPP(hAPP(c_List_Olist_OCons(_1655081), _1655089), c_List_Olist_ONil(_1655081))))), c_List_Olistrel1(_1655081, _1655091))), 43773 ^ _780478 : [(43776 ^ _780478) ^ [] : [-(_1655085 = _1655089)], (43774 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655081), tc_List_Olist(_1655081))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655081), tc_List_Olist(_1655081)), _1655083), _1655087)), c_List_Olistrel1(_1655081, _1655091))))]], 43777 ^ _780478 : [(43780 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1655081, _1655081)), hAPP(hAPP(c_Product__Type_OPair(_1655081, _1655081), _1655085), _1655089)), _1655091)))], (43778 ^ _780478) ^ [] : [-(_1655083 = _1655087)]]], (52179 ^ _780478) ^ [_1831892, _1831894] : [-(class_Nat_Osize(tc_sum(_1831892, _1831894)))], (47994 ^ _780478) ^ [_1747902, _1747904, _1747906] : [class_Orderings_Olinorder(_1747902), 48000 ^ _780478 : [(48003 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1747902), _1747906), 47999 ^ [_1747902, _1747904, _1747906]))], (48001 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747902), 47999 ^ [_1747902, _1747904, _1747906]), hAPP(c_List_Oset(_1747902), _1747904))))]], c_List_Olinorder__class_Osorted(_1747902, _1747904), -(c_List_Olinorder__class_Osorted(_1747902, hAPP(hAPP(c_List_Olist_OCons(_1747902), _1747906), _1747904)))], (51929 ^ _780478) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (8868 ^ _780478) ^ [_933620, _933622, _933624] : [class_Orderings_Oorder(_933620), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933620), _933622), _933624)), _933622 = _933624], (39242 ^ _780478) ^ [_1542434, _1542436] : [-(c_Relation_Orefl__on(_1542434, _1542436, c_Relation_OId__on(_1542434, _1542436)))], (1744 ^ _780478) ^ [_805142, _805144] : [-(class_Orderings_Opreorder(_805142)), _805144 = _805142, class_Orderings_Opreorder(_805144)], (40552 ^ _780478) ^ [_1573667, _1573669, _1573671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573667, _1573667), tc_HOL_Obool)), _1573669), _1573671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573667, _1573667), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573667, _1573669)), c_Transitive__Closure_Ortrancl(_1573667, _1573671))))], (48995 ^ _780478) ^ [_1769113, _1769115, _1769117, _1769119] : [class_Groups_Ocomm__monoid__add(_1769113), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1769115, tc_HOL_Obool)), _1769117)), 49005 ^ _780478 : [(49008 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1769115), 49004 ^ [_1769113, _1769115, _1769117, _1769119]))], (49006 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1769115, tc_HOL_Obool)), 49004 ^ [_1769113, _1769115, _1769117, _1769119]), _1769117)))]], 49012 ^ _780478 : [(49016 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1769115, tc_HOL_Obool)), 49014 ^ [_1769113, _1769115, _1769117, _1769119]), _1769117)))], (49013 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1769115, tc_HOL_Obool)), 49011 ^ [_1769113, _1769115, _1769117, _1769119]), _1769117)))], (49025 ^ _780478) ^ [] : [hAPP(_1769119, 49019 ^ [_1769113, _1769115, _1769117, _1769119]) = c_Groups_Ozero__class_Ozero(_1769113)], (49021 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769115), 49019 ^ [_1769113, _1769115, _1769117, _1769119]), 49011 ^ [_1769113, _1769115, _1769117, _1769119])))], (49023 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769115), 49019 ^ [_1769113, _1769115, _1769117, _1769119]), 49014 ^ [_1769113, _1769115, _1769117, _1769119])))], (49018 ^ _780478) ^ [] : [49011 ^ [_1769113, _1769115, _1769117, _1769119] = 49014 ^ [_1769113, _1769115, _1769117, _1769119]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1769115, _1769113), _1769119), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1769115, tc_HOL_Obool), _1769117)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1769115, tc_HOL_Obool), _1769113), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1769115, _1769113), _1769119)), _1769117))], (5658 ^ _780478) ^ [_867092, _867094] : [_867094 = _867092, -(c_member(_867094) = c_member(_867092))], (18550 ^ _780478) ^ [_1128414] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1128414) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1128414)))], (16522 ^ _780478) ^ [_1082290, _1082292, _1082294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1082290, tc_HOL_Obool)), _1082292), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1082290, tc_HOL_Obool)), _1082294))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1082290, tc_HOL_Obool)), _1082292), _1082294) = c_Orderings_Obot__class_Obot(tc_fun(_1082290, tc_HOL_Obool)))], (24523 ^ _780478) ^ [_1236100, _1236102, _1236104, _1236106] : [class_Divides_Osemiring__div(_1236100), -(_1236102 = c_Groups_Ozero__class_Ozero(_1236100)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236100), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236100), _1236104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1236100), _1236102), _1236106))), _1236102) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236100), _1236106), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236100), _1236104), _1236102)))], (22765 ^ _780478) ^ [_1204282, _1204284, _1204286] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1204282, tc_Nat_Onat), _1204284), _1204286)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1204282, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1204282), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1204284)), _1204286))], (2700 ^ _780478) ^ [_820301, _820303] : [_820303 = _820301, -(c_HOL_OAll(_820303) = c_HOL_OAll(_820301))], (41947 ^ _780478) ^ [_1610771, _1610773, _1610775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1610771, _1610771), tc_HOL_Obool)), _1610773), _1610775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1610771), tc_List_Olist(_1610771)), tc_HOL_Obool)), c_List_Olistrel(_1610771, _1610773)), c_List_Olistrel(_1610771, _1610775))))], (25817 ^ _780478) ^ [_1259125, _1259127] : [25818 ^ _780478 : [(25821 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259127))], (25819 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259125))]], 25822 ^ _780478 : [(25829 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1259125), _1259127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1259125)), hAPP(c_Int_Onat, _1259127))))], (25823 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1259125)), hAPP(c_Int_Onat, _1259127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1259125), _1259127)))]]], (7002 ^ _780478) ^ [_897407, _897409] : [class_Orderings_Opreorder(_897407), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897407), _897409), _897409)))], (5744 ^ _780478) ^ [_868389, _868391] : [_868391 = _868389, -(c_Hoare__Mirabelle_Otriple_Otriple(_868391) = c_Hoare__Mirabelle_Otriple_Otriple(_868389))], (45843 ^ _780478) ^ [_1700840, _1700842, _1700844] : [-(hAPP(c_List_Oset(_1700840), hAPP(c_List_OremoveAll(_1700840, _1700842), _1700844)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1700840, tc_HOL_Obool)), hAPP(c_List_Oset(_1700840), _1700844)), hAPP(hAPP(c_Set_Oinsert(_1700840), _1700842), c_Orderings_Obot__class_Obot(tc_fun(_1700840, tc_HOL_Obool)))))], (45244 ^ _780478) ^ [_1687258, _1687260] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1687258), _1687260) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1687258, 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)))), _1687260))))], (9546 ^ _780478) ^ [_944541, _944543, _944545, _944547, _944549] : [class_Groups_Oordered__cancel__ab__semigroup__add(_944541), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944541), _944543), _944545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944541), _944547), _944549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_944541), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944541), _944543), _944547)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_944541), _944545), _944549))))], (37237 ^ _780478) ^ [_1489022, _1489024, _1489026] : [-(c_HOL_OThe(tc_prod(_1489022, _1489024), hAPP(c_Product__Type_Oprod_Oprod__case(_1489022, _1489024, tc_HOL_Obool), _1489026)) = c_HOL_OThe(tc_prod(_1489022, _1489024), hAPP(hAPP(c_COMBS(tc_prod(_1489022, _1489024), _1489024, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1489022, tc_fun(_1489024, tc_HOL_Obool), tc_prod(_1489022, _1489024)), _1489026), c_Product__Type_Ofst(_1489022, _1489024))), c_Product__Type_Osnd(_1489022, _1489024))))], (48764 ^ _780478) ^ [_1764163, _1764165, _1764167, _1764169, _1764171, _1764173] : [-(c_New__Random__Sequence_Opos__union(_1764163, _1764165, _1764167, _1764169, _1764171, _1764173) = c_New__DSequence_Opos__union(_1764163, hAPP(hAPP(hAPP(_1764165, _1764169), _1764171), _1764173), hAPP(hAPP(hAPP(_1764167, _1764169), _1764171), _1764173)))], (14455 ^ _780478) ^ [_1038388] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1038388)), 14459 ^ _780478 : [(14460 ^ _780478) ^ [_1038468] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1038468), _1038388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038468), 14458 ^ [_1038388])))]]], (30368 ^ _780478) ^ [_1343973, _1343975, _1343977, _1343979] : [class_Fields_Olinordered__field(_1343973), -(hAPP(c_Groups_Oabs__class_Oabs(_1343973), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343975, _1343973), _1343977), _1343979)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1343975, _1343973), hAPP(hAPP(c_COMBB(_1343973, _1343973, _1343975), c_Groups_Oabs__class_Oabs(_1343973)), _1343977)), _1343979))], (6392 ^ _780478) ^ [_884195, _884197, _884199, _884201, _884203] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_884195, _884197, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_884195)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_884195), hAPP(hAPP(c_COMBC(_884195, 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)), _884195), 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)), _884195), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _884199))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _884201))), c_Com_Ocom_OWhile(_884201, _884203)), _884199)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_884195), tc_HOL_Obool)))))], (35970 ^ _780478) ^ [_1463551, _1463553, _1463555, _1463557, _1463559] : [hAPP(c_Relation_OImage(_1463551, _1463551, _1463553), hAPP(hAPP(c_Set_Oinsert(_1463551), _1463555), c_Orderings_Obot__class_Obot(tc_fun(_1463551, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1463551, _1463551, _1463553), hAPP(hAPP(c_Set_Oinsert(_1463551), _1463557), c_Orderings_Obot__class_Obot(tc_fun(_1463551, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1463551, _1463559, _1463553), hBOOL(hAPP(hAPP(c_member(_1463551), _1463557), _1463559)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1463551, _1463551)), hAPP(hAPP(c_Product__Type_OPair(_1463551, _1463551), _1463555), _1463557)), _1463553)))], (19572 ^ _780478) ^ [_1146186, _1146188, _1146190] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146186), _1146188) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146186), _1146190), -(_1146186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1146188 = _1146190)], (45663 ^ _780478) ^ [_1697336, _1697338] : [-(_1697336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1697338, _1697336, c_List_Olist_ONil(_1697338)) = c_List_Olist_ONil(tc_List_Olist(_1697338)))], (16480 ^ _780478) ^ [_1081307, _1081309, _1081311, _1081313] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1081307), _1081309)), c_Fun_Oinj__on(_1081311, _1081307, _1081313, c_Orderings_Otop__class_Otop(tc_fun(_1081311, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1081311), hAPP(c_Set_Ovimage(_1081311, _1081307, _1081313), _1081309))))], (31658 ^ _780478) ^ [_1377649, _1377651, _1377653] : [_1377651 = c_Orderings_Obot__class_Obot(tc_fun(_1377649, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377649), _1377651), _1377653) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377649, tc_HOL_Obool), tc_HOL_Obool)))], (40230 ^ _780478) ^ [_1565627, _1565629, _1565631, _1565633, _1565635, _1565637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1565627, tc_HOL_Obool)), _1565629), _1565631)), 40236 ^ _780478 : [(40239 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1565633, tc_HOL_Obool)), hAPP(_1565635, 40235 ^ [_1565627, _1565629, _1565631, _1565633, _1565635, _1565637])), hAPP(_1565637, 40235 ^ [_1565627, _1565629, _1565631, _1565633, _1565635, _1565637])))], (40237 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565627), 40235 ^ [_1565627, _1565629, _1565631, _1565633, _1565635, _1565637]), _1565629)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565627, _1565633), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1565627, _1565633), _1565629), _1565635)), hAPP(hAPP(c_Product__Type_OSigma(_1565627, _1565633), _1565631), _1565637))))], (24357 ^ _780478) ^ [_1233309, _1233311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233309)), 24360 ^ _780478 : [(24367 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233309), _1233311)), -(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), _1233311), _1233309))))], (24361 ^ _780478) ^ [] : [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), _1233311), _1233309))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233309), _1233311)))]]], (48613 ^ _780478) ^ [_1761287, _1761289, _1761291, _1761293, _1761295] : [c_List_Oreplicate(_1761287, _1761289, _1761291) = c_List_Oreplicate(_1761287, _1761293, _1761295), 48616 ^ _780478 : [(48619 ^ _780478) ^ [] : [-(_1761289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1761291 = _1761295)], (48617 ^ _780478) ^ [] : [-(_1761289 = _1761293)]]], (51877 ^ _780478) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (49686 ^ _780478) ^ [_1785560, _1785562] : [49689 ^ _780478 : [(49692 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785560, _1785560)), hAPP(hAPP(c_Product__Type_OPair(_1785560, _1785560), 49688 ^ [_1785560, _1785562]), 49687 ^ [_1785560, _1785562])), _1785562))], (49690 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785560, _1785560)), hAPP(hAPP(c_Product__Type_OPair(_1785560, _1785560), 49687 ^ [_1785560, _1785562]), 49688 ^ [_1785560, _1785562])), _1785562)))]], -(c_Relation_Osym(_1785560, _1785562))], (51145 ^ _780478) ^ [_1816961, _1816963, _1816965] : [class_Divides_Osemiring__div(_1816961), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816961), _1816963), _1816965)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1816961), _1816963), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1816961), _1816965), _1816963)) = _1816965)], (28979 ^ _780478) ^ [_1317417, _1317419, _1317421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1317417, tc_HOL_Obool)), _1317419), _1317421)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1317417, tc_HOL_Obool)), _1317419), hAPP(c_Set_OPow(_1317417), _1317421))))], (6946 ^ _780478) ^ [_896154, _896156, _896158, _896160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896154, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896154, tc_HOL_Obool)), _896156), hAPP(hAPP(c_Set_Oinsert(_896154), _896158), c_Orderings_Obot__class_Obot(tc_fun(_896154, tc_HOL_Obool))))), _896160)), hBOOL(hAPP(hAPP(c_member(_896154), _896158), _896156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896154, tc_HOL_Obool)), _896156), hAPP(hAPP(c_Set_Oinsert(_896154), _896158), _896160))))], (44508 ^ _780478) ^ [_1671567, _1671569, _1671571, _1671573, _1671575] : [class_Orderings_Olinorder(_1671567), hBOOL(hAPP(hAPP(c_member(_1671567), hAPP(_1671569, _1671571)), hAPP(c_Set_Oimage(_1671573, _1671567, _1671569), hAPP(c_List_Oset(_1671573), _1671575)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1671573, _1671567, _1671569, _1671571, _1671575) = _1671575)], (47625 ^ _780478) ^ [_1739294, _1739296] : [-(c_List_Omeasures(_1739294, _1739296) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1739294), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1739294, tc_List_Olist(tc_fun(_1739294, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1739294, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1739294, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1739294), c_List_Omap(tc_fun(_1739294, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1739294, tc_Nat_Onat), _1739294, tc_Nat_Onat), c_COMBI(tc_fun(_1739294, tc_Nat_Onat))))), _1739296)))], (34815 ^ _780478) ^ [] : [-(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))))], (23069 ^ _780478) ^ [_1209813, _1209815, _1209817] : [hBOOL(hAPP(_1209813, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1209815), _1209817)))), 23072 ^ _780478 : [(23079 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1209815), _1209817)), -(hBOOL(hAPP(_1209813, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23073 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1209817), _1209815)), -(hBOOL(hAPP(_1209813, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1209815)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1209817)))))]]], (34727 ^ _780478) ^ [_1435322] : [class_Int_Onumber__ring(_1435322), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1435322), c_Groups_Oone__class_Oone(_1435322)), c_Groups_Oone__class_Oone(_1435322)) = hAPP(c_Int_Onumber__class_Onumber__of(_1435322), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (44602 ^ _780478) ^ [_1672989, _1672991] : [-(_1672989 = c_List_Olist_ONil(_1672991)), -(hAPP(hAPP(c_List_Oappend(_1672991), c_List_Obutlast(_1672991, _1672989)), hAPP(hAPP(c_List_Olist_OCons(_1672991), c_List_Olast(_1672991, _1672989)), c_List_Olist_ONil(_1672991))) = _1672989)], (41253 ^ _780478) ^ [_1590698, _1590700, _1590702, _1590704] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590698, _1590698)), hAPP(hAPP(c_Product__Type_OPair(_1590698, _1590698), _1590700), _1590702)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590698, _1590698), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590704))), -(_1590700 = _1590702)], (46186 ^ _780478) ^ [_1709860, _1709862] : [-(c_Random_Opick(_1709860, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1709860), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1709860, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1709860, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1709860)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1709862)) = c_Random_Opick(_1709860, _1709862))], (43187 ^ _780478) ^ [_1641735, _1641737] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1641735), _1641737))), -(c_List_Oupto(_1641735, _1641737) = c_List_Olist_ONil(tc_Int_Oint))], (1942 ^ _780478) ^ [_808438, _808440, _808442, _808444, _808446, _808448, _808450, _808452] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_808452, _808448, _808444, _808440) = c_Hoare__Mirabelle_Otriple_Otriple__case(_808450, _808446, _808442, _808438)), _808452 = _808450, _808448 = _808446, _808444 = _808442, _808440 = _808438], (36343 ^ _780478) ^ [_1471827, _1471829, _1471831, _1471833, _1471835, _1471837] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471827, _1471829, _1471831), _1471833), hAPP(hAPP(c_Product__Type_OPair(_1471827, _1471829), _1471835), _1471837)) = hAPP(hAPP(_1471833, _1471835), _1471837))], (42560 ^ _780478) ^ [_1628621, _1628623] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1628621, _1628623)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1628621, _1628623))], (34313 ^ _780478) ^ [_1427673] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427673)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427673)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427673)), 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)))))], (37953 ^ _780478) ^ [_1507508, _1507510, _1507512, _1507514] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507508, _1507510, _1507512), _1507514), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507510, _1507512), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507508, _1507512), tc_HOL_Obool)))], (44223 ^ _780478) ^ [_1665608, _1665610, _1665612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1665608), _1665610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1665608), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1665610), _1665612))))], (41714 ^ _780478) ^ [_1603509, _1603511, _1603513, _1603515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603509)), _1603511)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603509)), _1603513))), _1603511 = hAPP(hAPP(c_List_Olist_OCons(_1603509), _1603515), _1603513)], (27330 ^ _780478) ^ [_1286350, _1286352] : [class_Rings_Oring__1(_1286350), 27333 ^ _780478 : [(27340 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1286352), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1286350), _1286352) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1286350), hAPP(c_Int_Onat, _1286352)))], (27334 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1286352), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1286350), _1286352) = hAPP(c_Groups_Ouminus__class_Ouminus(_1286350), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1286350), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1286352)))))]]], (13950 ^ _780478) ^ [_1029859, _1029861, _1029863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029859), _1029861)), _1029863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029861), _1029863)))], (37919 ^ _780478) ^ [_1505726, _1505728, _1505730] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1505726, _1505728, _1505730, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1505728)], (13674 ^ _780478) ^ [_1024721, _1024723, _1024725, _1024727, _1024729, _1024731] : [c_Fun_Oinj__on(_1024721, _1024723, _1024725, _1024727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024723, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1024721, _1024723, _1024725), _1024727)), _1024729)), c_Fun_Oinj__on(_1024723, _1024721, _1024731, _1024729), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024721, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1024723, _1024721, _1024731), _1024729)), _1024727)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024721), _1024727)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024723), _1024729)), -(hAPP(c_Finite__Set_Ocard(_1024721), _1024727) = hAPP(c_Finite__Set_Ocard(_1024723), _1024729))], (16689 ^ _780478) ^ [_1085859, _1085861, _1085863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1085859), _1085861)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085859), _1085863)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1085859), _1085861)), hAPP(c_Finite__Set_Ocard(_1085859), _1085863)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1085859), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1085859, tc_HOL_Obool)), _1085861), _1085863))), hAPP(c_Finite__Set_Ocard(_1085859), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1085859, tc_HOL_Obool)), _1085861), _1085863))))], (50646 ^ _780478) ^ [_1805069, _1805071] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805069), _1805071)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1805069, 50649 ^ [_1805069, _1805071], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1805069), _1805071)), _1805071))], (40694 ^ _780478) ^ [_1577144, _1577146, _1577148, _1577150] : [hBOOL(hAPP(hAPP(c_member(_1577144), _1577146), c_Wellfounded_Oacc(_1577144, _1577148))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1577144, _1577144)), hAPP(hAPP(c_Product__Type_OPair(_1577144, _1577144), _1577150), _1577146)), c_Transitive__Closure_Ortrancl(_1577144, _1577148))), -(hBOOL(hAPP(hAPP(c_member(_1577144), _1577150), c_Wellfounded_Oacc(_1577144, _1577148))))], (13440 ^ _780478) ^ [_1020032, _1020034, _1020036, _1020038] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1020032), _1020034)), 13443 ^ _780478 : [(13450 ^ _780478) ^ [] : [hAPP(c_Finite__Set_Ocard(_1020036), hAPP(c_Set_Oimage(_1020032, _1020036, _1020038), _1020034)) = hAPP(c_Finite__Set_Ocard(_1020032), _1020034), -(c_Fun_Oinj__on(_1020032, _1020036, _1020038, _1020034))], (13444 ^ _780478) ^ [] : [c_Fun_Oinj__on(_1020032, _1020036, _1020038, _1020034), -(hAPP(c_Finite__Set_Ocard(_1020036), hAPP(c_Set_Oimage(_1020032, _1020036, _1020038), _1020034)) = hAPP(c_Finite__Set_Ocard(_1020032), _1020034))]]], (31899 ^ _780478) ^ [_1382905, _1382907, _1382909, _1382911, _1382913] : [c_Com_Ocom_OSemi(_1382905, _1382907) = c_Com_Ocom_OCond(_1382909, _1382911, _1382913)], (5961 ^ _780478) ^ [_875258, _875260, _875262] : [hBOOL(hAPP(_875262, _875260)), -(hBOOL(hAPP(hAPP(c_member(_875258), _875260), _875262)))], (17967 ^ _780478) ^ [_1115052, _1115054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115052)), _1115054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115052), _1115054)))], (38917 ^ _780478) ^ [_1532677, _1532679, _1532681, _1532683] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1532677, _1532679)), hAPP(hAPP(c_Product__Type_OSigma(_1532677, _1532679), _1532681), hAPP(c_COMBK(tc_fun(_1532679, tc_HOL_Obool), _1532677), _1532683)))), -(_1532681 = c_Orderings_Obot__class_Obot(tc_fun(_1532677, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1532679), _1532683)))], (11647 ^ _780478) ^ [_984552, _984554, _984556] : [class_Orderings_Olinorder(_984552), hBOOL(hAPP(c_Finite__Set_Ofinite(_984552), _984554)), 11654 ^ _780478 : [(11661 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984552, tc_HOL_Obool)), _984554), hAPP(hAPP(c_Set_Oinsert(_984552), _984556), c_Orderings_Obot__class_Obot(tc_fun(_984552, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_984552, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_984552, hAPP(hAPP(c_Set_Oinsert(_984552), _984556), _984554)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_984552), _984556), c_Big__Operators_Olinorder__class_OMax(_984552, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984552, tc_HOL_Obool)), _984554), hAPP(hAPP(c_Set_Oinsert(_984552), _984556), c_Orderings_Obot__class_Obot(tc_fun(_984552, tc_HOL_Obool)))))))], (11655 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_984552, tc_HOL_Obool)), _984554), hAPP(hAPP(c_Set_Oinsert(_984552), _984556), c_Orderings_Obot__class_Obot(tc_fun(_984552, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_984552, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_984552, hAPP(hAPP(c_Set_Oinsert(_984552), _984556), _984554)) = _984556)]]], (8752 ^ _780478) ^ [_931812, _931814, _931816, _931818] : [class_Orderings_Oorder(_931812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931812), _931814), _931816)), _931814 = _931818, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931812), _931818), _931816)))], (51873 ^ _780478) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (22628 ^ _780478) ^ [_1201920, _1201922, _1201924] : [class_Nat_Osemiring__char__0(_1201920), 22631 ^ _780478 : [(22638 ^ _780478) ^ [] : [_1201922 = _1201924, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201920), _1201922) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201920), _1201924))], (22632 ^ _780478) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201920), _1201922) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201920), _1201924), -(_1201922 = _1201924)]]], (10095 ^ _780478) ^ [_956042, _956044] : [class_Groups_Olinordered__ab__group__add(_956042), hBOOL(hAPP(c_Finite__Set_Ofinite(_956042), _956044)), -(_956044 = c_Orderings_Obot__class_Obot(tc_fun(_956042, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_956042), c_Big__Operators_Olinorder__class_OMin(_956042, _956044)) = c_Big__Operators_Olinorder__class_OMax(_956042, hAPP(c_Set_Oimage(_956042, _956042, c_Groups_Ouminus__class_Ouminus(_956042)), _956044)))], (17280 ^ _780478) ^ [_1099161, _1099163, _1099165, _1099167, _1099169, _1099171] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099161, tc_fun(_1099163, tc_HOL_Obool)), _1099165), hAPP(hAPP(c_COMBC(_1099161, tc_fun(_1099167, tc_fun(_1099163, tc_HOL_Obool)), tc_fun(_1099163, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1099167, tc_HOL_Obool), tc_fun(tc_fun(_1099167, tc_fun(_1099163, tc_HOL_Obool)), tc_fun(_1099163, tc_HOL_Obool)), _1099161), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099167, tc_fun(_1099163, tc_HOL_Obool))), _1099169)), _1099171)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099167, tc_fun(_1099163, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099161, tc_fun(_1099167, tc_HOL_Obool)), _1099165), _1099169)), _1099171))], (40456 ^ _780478) ^ [_1571234, _1571236, _1571238, _1571240, _1571242] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571234, _1571234)), hAPP(hAPP(c_Product__Type_OPair(_1571234, _1571234), _1571236), _1571238)), _1571240)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571234, _1571234)), hAPP(hAPP(c_Product__Type_OPair(_1571234, _1571234), _1571238), _1571242)), _1571240)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571234, _1571234)), hAPP(hAPP(c_Product__Type_OPair(_1571234, _1571234), _1571236), _1571242)), c_Transitive__Closure_Otrancl(_1571234, _1571240))))], (24875 ^ _780478) ^ [_1242479, _1242481, _1242483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242479)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1242479), _1242481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242483), _1242481)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242483), _1242479))))], (33364 ^ _780478) ^ [_1410461] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410461), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410461)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (42332 ^ _780478) ^ [_1621479, _1621481, _1621483] : [42334 ^ _780478 : [(42337 ^ _780478) ^ [] : [hBOOL(hAPP(_1621483, 42333 ^ [_1621479, _1621481, _1621483]))], (42335 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621479), 42333 ^ [_1621479, _1621481, _1621483]), hAPP(c_List_Oset(_1621479), _1621481))))]], 42338 ^ _780478 : [(42339 ^ _780478) ^ [_1621663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1621663), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621479)), _1621481))), -(hBOOL(hAPP(_1621483, hAPP(hAPP(c_List_Onth(_1621479), _1621481), _1621663))))]]], (43865 ^ _780478) ^ [_1657679, _1657681, _1657683, _1657685] : [-(hAPP(hAPP(c_List_Odrop(_1657679), _1657681), hAPP(hAPP(c_List_Otake(_1657679), _1657683), _1657685)) = hAPP(hAPP(c_List_Otake(_1657679), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1657683), _1657681)), hAPP(hAPP(c_List_Odrop(_1657679), _1657681), _1657685)))], (44706 ^ _780478) ^ [_1675572, _1675574, _1675576, _1675578] : [_1675578 = c_List_Olist_ONil(_1675572), -(hAPP(hAPP(c_List_Omap(_1675572, _1675574), _1675576), _1675578) = c_List_Olist_ONil(_1675574))], (39709 ^ _780478) ^ [_1553644, _1553646] : [-(c_Hilbert__Choice_OEps(_1553644, hAPP(c_fequal, _1553646)) = _1553646)], (41190 ^ _780478) ^ [_1589225, _1589227, _1589229] : [c_Relation_Osingle__valued(_1589225, _1589225, _1589227), -(c_Relation_Osingle__valued(_1589225, _1589225, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589225, _1589225), tc_HOL_Obool), _1589229), _1589227)))], (44843 ^ _780478) ^ [_1679035, _1679037, _1679039, _1679041, _1679043] : [-(c_List_Olist_Olist__size(_1679035, _1679037, hAPP(hAPP(c_List_Omap(_1679039, _1679035), _1679041), _1679043)) = c_List_Olist_Olist__size(_1679039, hAPP(c_Fun_Ocomp(_1679035, tc_Nat_Onat, _1679039, _1679037), _1679041), _1679043))], (14177 ^ _780478) ^ [_1033842, _1033844, _1033846] : [class_Rings_Olinordered__semidom(_1033842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033842), c_Groups_Oone__class_Oone(_1033842)), _1033844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033842), c_Groups_Oone__class_Oone(_1033842)), _1033846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033842), c_Groups_Oone__class_Oone(_1033842)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033842), _1033844), _1033846))))], (37726 ^ _780478) ^ [_1500525] : [-(hAPP(c_Relation_OField(_1500525), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1500525, _1500525), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1500525, tc_HOL_Obool)))], (7423 ^ _780478) ^ [_904883, _904885, _904887, _904889] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_904883), _904885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904883, tc_HOL_Obool)), _904885), _904887)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_904883, tc_Nat_Onat), _904889), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_904883, tc_HOL_Obool)), _904887), _904885)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_904883, tc_Nat_Onat), _904889), _904887)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_904883, tc_Nat_Onat), _904889), _904885)))], (43592 ^ _780478) ^ [_1650747, _1650749, _1650751] : [hAPP(hAPP(c_List_Oappend(_1650747), _1650749), _1650751) = _1650749, -(_1650751 = c_List_Olist_ONil(_1650747))], (1704 ^ _780478) ^ [_804642, _804644] : [-(class_Divides_Osemiring__div(_804642)), _804644 = _804642, class_Divides_Osemiring__div(_804644)], (49648 ^ _780478) ^ [_1784586, _1784588] : [c_Wellfounded_Oacyclic(_1784586, _1784588), -(c_Relation_Oantisym(_1784586, c_Transitive__Closure_Ortrancl(_1784586, _1784588)))], (51823 ^ _780478) ^ [_1828394, _1828396] : [class_Orderings_Oorder(_1828394), -(class_Orderings_Oorder(tc_fun(_1828396, _1828394)))], (47085 ^ _780478) ^ [_1727674, _1727676] : [-(_1727674 = c_List_Olist_ONil(_1727676)), -(c_List_Olast(_1727676, hAPP(c_List_Orev(_1727676), _1727674)) = hAPP(c_List_Ohd(_1727676), _1727674))], (18620 ^ _780478) ^ [_1129881, _1129883, _1129885] : [class_Rings_Olinordered__semidom(_1129881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129881), c_Groups_Oone__class_Oone(_1129881)), _1129883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1129881), c_Groups_Oone__class_Oone(_1129881)), hAPP(hAPP(c_Power_Opower__class_Opower(_1129881), _1129883), hAPP(c_Nat_OSuc, _1129885)))))], (33400 ^ _780478) ^ [_1410977] : [-(c_Int_Opred(_1410977) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1410977), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38549 ^ _780478) ^ [_1521935, _1521937, _1521939, _1521941] : [hBOOL(hAPP(hAPP(c_member(_1521935), _1521937), hAPP(c_Relation_ORange(_1521939, _1521935), _1521941))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1521939, _1521935)), hAPP(hAPP(c_Product__Type_OPair(_1521939, _1521935), 38552 ^ [_1521935, _1521937, _1521939, _1521941]), _1521937)), _1521941)))], (42209 ^ _780478) ^ [_1618309, _1618311, _1618313, _1618315] : [-(_1618309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1618311), hAPP(hAPP(c_List_Olist_OCons(_1618311), _1618313), _1618315)), _1618309) = hAPP(hAPP(c_List_Onth(_1618311), _1618315), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1618309), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (18726 ^ _780478) ^ [_1132119, _1132121, _1132123, _1132125, _1132127] : [_1132119 = c_Orderings_Obot__class_Obot(tc_fun(_1132121, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1132121, tc_fun(_1132123, tc_HOL_Obool)), _1132119), hAPP(hAPP(c_COMBB(tc_fun(_1132123, tc_HOL_Obool), tc_fun(_1132123, tc_HOL_Obool), _1132121), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1132123, tc_HOL_Obool)), _1132125)), _1132127)) = c_Orderings_Otop__class_Otop(tc_fun(_1132123, tc_HOL_Obool)))], (34037 ^ _780478) ^ [_1423147, _1423149] : [class_Int_Onumber__ring(_1423147), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423147), hAPP(c_Int_Onumber__class_Onumber__of(_1423147), c_Int_OBit1(c_Int_OPls))), _1423149) = _1423149)], (31901 ^ _780478) ^ [_1382958, _1382960, _1382962] : [c_Com_Ocom_OCond(_1382958, _1382960, _1382962) = c_Com_Ocom_OSKIP], (1434 ^ _780478) ^ [_801267, _801269] : [-(class_Orderings_Otop(_801267)), _801269 = _801267, class_Orderings_Otop(_801269)], (39464 ^ _780478) ^ [_1546683, _1546685, _1546687] : [c_Relation_Orefl__on(_1546683, _1546685, _1546687), 39467 ^ _780478 : [(39474 ^ _780478) ^ [_1547167] : [hBOOL(hAPP(hAPP(c_member(_1546683), _1547167), _1546685)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546683, _1546683)), hAPP(hAPP(c_Product__Type_OPair(_1546683, _1546683), _1547167), _1547167)), _1546687)))], (39468 ^ _780478) ^ [_1546894] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1546683, _1546683)), _1546894), _1546687)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1546683, _1546683, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1546683, tc_fun(_1546683, tc_HOL_Obool), tc_fun(_1546683, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1546683, tc_HOL_Obool), tc_fun(_1546683, tc_HOL_Obool)), _1546683), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1546683)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1546683), c_fconj), hAPP(hAPP(c_COMBC(_1546683, tc_fun(_1546683, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546683)), _1546685)))), hAPP(hAPP(c_COMBC(_1546683, tc_fun(_1546683, tc_HOL_Obool), tc_HOL_Obool), c_member(_1546683)), _1546685))), _1546894)))]]], (17925 ^ _780478) ^ [_1114382, _1114384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114382), _1114384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114382)), hAPP(c_Nat_OSuc, _1114384))))], (17464 ^ _780478) ^ [_1104652, _1104654, _1104656, _1104658, _1104660] : [hBOOL(hAPP(hAPP(c_member(_1104652), _1104654), _1104656)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1104658, tc_HOL_Obool)), hAPP(_1104660, _1104654)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104652, tc_fun(_1104658, tc_HOL_Obool)), _1104656), _1104660)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104652, tc_fun(_1104658, tc_HOL_Obool)), _1104656), _1104660))], (28991 ^ _780478) ^ [_1317666, _1317668] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317666), _1317668)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1317666, tc_HOL_Obool)), hAPP(c_Set_OPow(_1317666), _1317668))))], (30087 ^ _780478) ^ [_1338749, _1338751, _1338753] : [-(hBOOL(hAPP(_1338749, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338751, _1338753)))), 30090 ^ _780478 : [(30093 ^ _780478) ^ [] : [hBOOL(hAPP(_1338749, _1338751))], (30091 ^ _780478) ^ [] : [-(_1338753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 30094 ^ _780478 : [(30099 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30097 ^ [_1338749, _1338751, _1338753]), _1338753)))], (30101 ^ _780478) ^ [] : [-(_1338751 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338753), 30096 ^ [_1338749, _1338751, _1338753])), 30097 ^ [_1338749, _1338751, _1338753]))], (30103 ^ _780478) ^ [] : [hBOOL(hAPP(_1338749, 30097 ^ [_1338749, _1338751, _1338753]))], (30095 ^ _780478) ^ [] : [_1338753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (25928 ^ _780478) ^ [_1261150, _1261152, _1261154] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1261150, tc_Nat_Onat), _1261152), _1261154) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1261150, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1261150), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1261152)), _1261154)))], (14112 ^ _780478) ^ [_1032723, _1032725] : [class_Groups_Omonoid__mult(_1032723), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032723), _1032725), c_Groups_Oone__class_Oone(_1032723)) = _1032725)], (34707 ^ _780478) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (42456 ^ _780478) ^ [_1625238, _1625240, _1625242, _1625244] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1625238), tc_List_Olist(_1625238))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1625238), tc_List_Olist(_1625238)), _1625240), _1625242)), c_List_Olistrel(_1625238, _1625244)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625238)), _1625240) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625238)), _1625242), 42462 ^ _780478 : [(42465 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1625238, _1625238, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1625238, tc_fun(tc_prod(_1625238, _1625238), tc_HOL_Obool), tc_fun(_1625238, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1625238, tc_fun(tc_fun(tc_prod(_1625238, _1625238), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1625238, _1625238), tc_HOL_Obool), tc_fun(_1625238, tc_HOL_Obool)), _1625238), c_COMBC(_1625238, tc_fun(tc_prod(_1625238, _1625238), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1625238, tc_prod(_1625238, _1625238)), tc_fun(_1625238, tc_fun(tc_fun(tc_prod(_1625238, _1625238), tc_HOL_Obool), tc_HOL_Obool)), _1625238), hAPP(c_COMBB(tc_prod(_1625238, _1625238), tc_fun(tc_fun(tc_prod(_1625238, _1625238), tc_HOL_Obool), tc_HOL_Obool), _1625238), c_member(tc_prod(_1625238, _1625238)))), c_Product__Type_OPair(_1625238, _1625238)))), _1625244)), 42461 ^ [_1625238, _1625240, _1625242, _1625244]))], (42463 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625238, _1625238)), 42461 ^ [_1625238, _1625240, _1625242, _1625244]), hAPP(c_List_Oset(tc_prod(_1625238, _1625238)), hAPP(hAPP(c_List_Ozip(_1625238, _1625238), _1625240), _1625242)))))]]], (45811 ^ _780478) ^ [_1700258, _1700260, _1700262] : [-(hBOOL(hAPP(hAPP(c_member(_1700258), _1700260), hAPP(c_List_Oset(_1700258), _1700262)))), -(hAPP(c_List_OremoveAll(_1700258, _1700260), _1700262) = _1700262)], (50401 ^ _780478) ^ [_1800276, _1800278, _1800280, _1800282] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1800276, _1800278, _1800280), c_Product__Type_Ocurry(_1800276, _1800278, _1800280, _1800282)) = _1800282)], (40542 ^ _780478) ^ [_1573464, _1573466, _1573468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573464, _1573464), tc_HOL_Obool)), _1573466), _1573468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573464, _1573464), tc_HOL_Obool)), _1573468), c_Transitive__Closure_Ortrancl(_1573464, _1573466))), -(c_Transitive__Closure_Ortrancl(_1573464, _1573468) = c_Transitive__Closure_Ortrancl(_1573464, _1573466))], (48731 ^ _780478) ^ [_1763278, _1763280] : [class_Lazy__Sequence_Osmall__lazy(_1763278), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1763278), _1763280) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1763278), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1763278)), c_List_Olist_ONil(_1763278)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1763278))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1763280)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1763278, tc_List_Olist(_1763278)), tc_List_Olist(_1763278), c_Lazy__Sequence_Oproduct(_1763278, tc_List_Olist(_1763278), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1763278, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1763280), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1763278), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1763280), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1763278, tc_List_Olist(_1763278), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1763278))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1763278), tc_List_Olist(_1763278)), tc_fun(tc_List_Olist(_1763278), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1763278))), _1763278), hAPP(c_COMBB(tc_List_Olist(_1763278), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1763278)), tc_List_Olist(_1763278)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1763278)))), c_List_Olist_OCons(_1763278))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1763278)))))], (6606 ^ _780478) ^ [_888781, _888783, _888785, _888787] : [-(hBOOL(hAPP(hAPP(c_member(_888781), _888783), _888785))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888781, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_888781), _888783), _888787)), _888785) = hAPP(hAPP(c_Set_Oinsert(_888781), _888783), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888781, tc_HOL_Obool)), _888787), _888785)))], (45133 ^ _780478) ^ [_1685279, _1685281] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1685279), _1685281) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1685279)), hAPP(c_Code__Numeral_Onat__of, _1685281))))], (13128 ^ _780478) ^ [_1013249, _1013251, _1013253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013249, tc_HOL_Obool)), _1013251), _1013253)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013249, tc_HOL_Obool)), _1013251), _1013253) = _1013253)], (22893 ^ _780478) ^ [_1206584, _1206586, _1206588] : [class_Rings_Osemiring__1(_1206584), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206584), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1206586), _1206588)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1206584), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206584), _1206586)), _1206588))], (22034 ^ _780478) ^ [_1189974, _1189976, _1189978] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1189974), _1189976)), 22037 ^ _780478 : [(22038 ^ _780478) ^ [] : [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(_1189974, tc_Nat_Onat), _1189978), _1189976))), 22041 ^ _780478 : [(22042 ^ _780478) ^ [_1190142] : [hBOOL(hAPP(hAPP(c_member(_1189974), _1190142), _1189976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1189978, _1190142))))]]], (22048 ^ _780478) ^ [] : [22050 ^ _780478 : [(22053 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1189978, 22049 ^ [_1189974, _1189976, _1189978])))], (22051 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1189974), 22049 ^ [_1189974, _1189976, _1189978]), _1189976)))]], -(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(_1189974, tc_Nat_Onat), _1189978), _1189976))))]]], (17709 ^ _780478) ^ [_1110191, _1110193, _1110195, _1110197] : [hBOOL(hAPP(hAPP(c_member(_1110191), _1110193), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1110191, tc_HOL_Obool), _1110195))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1110191, tc_HOL_Obool)), _1110197), _1110195)), -(hBOOL(hAPP(hAPP(c_member(_1110191), _1110193), _1110197)))], (13765 ^ _780478) ^ [_1026488, _1026490, _1026492] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1026488), _1026490)), 13768 ^ _780478 : [(13775 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1026488), _1026492), _1026490))), -(hAPP(c_Finite__Set_Ocard(_1026488), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026488, tc_HOL_Obool)), _1026490), hAPP(hAPP(c_Set_Oinsert(_1026488), _1026492), c_Orderings_Obot__class_Obot(tc_fun(_1026488, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1026488), _1026490))], (13769 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1026488), _1026492), _1026490)), -(hAPP(c_Finite__Set_Ocard(_1026488), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026488, tc_HOL_Obool)), _1026490), hAPP(hAPP(c_Set_Oinsert(_1026488), _1026492), c_Orderings_Obot__class_Obot(tc_fun(_1026488, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1026488), _1026490)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (49062 ^ _780478) ^ [_1770929, _1770931, _1770933] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1770929, _1770931, _1770933) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770929)], (29848 ^ _780478) ^ [_1334638, _1334640] : [class_Rings_Olinordered__idom(_1334638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334638), _1334640), c_Groups_Ozero__class_Ozero(_1334638))), -(c_Groups_Osgn__class_Osgn(_1334638, _1334640) = hAPP(c_Groups_Ouminus__class_Ouminus(_1334638), c_Groups_Oone__class_Oone(_1334638)))], (220 ^ _780478) ^ [_784000, _784002] : [-(c_Nat__Transfer_Ois__nat(_784000)), _784002 = _784000, c_Nat__Transfer_Ois__nat(_784002)], (9160 ^ _780478) ^ [_937721, _937723, _937725] : [class_Orderings_Oorder(_937721), -(_937723 = _937725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937721), _937723), _937725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937721), _937723), _937725)))], (24295 ^ _780478) ^ [_1232364, _1232366, _1232368] : [class_Orderings_Oorder(_1232364), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1232364), _1232366), _1232368)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1232364, _1232368, _1232366) = c_Orderings_Obot__class_Obot(tc_fun(_1232364, tc_HOL_Obool)))], (9078 ^ _780478) ^ [_936584, _936586, _936588] : [class_Orderings_Oorder(_936584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936584), _936586), _936588)), -(_936586 = _936588), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936584), _936586), _936588)))], (48343 ^ _780478) ^ [_1754809, _1754811, _1754813] : [c_List_Olist__ex1(_1754809, _1754811, _1754813), 48347 ^ _780478 : [(48352 ^ _780478) ^ [_1755055] : [-(_1755055 = 48346 ^ [_1754809, _1754811, _1754813]), hBOOL(hAPP(hAPP(c_member(_1754809), _1755055), hAPP(c_List_Oset(_1754809), _1754813))), hBOOL(hAPP(_1754811, _1755055))], (48350 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1754811, 48346 ^ [_1754809, _1754811, _1754813])))], (48348 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754809), 48346 ^ [_1754809, _1754811, _1754813]), hAPP(c_List_Oset(_1754809), _1754813))))]]], (1194 ^ _780478) ^ [_798267, _798269] : [-(class_Rings_Olinordered__idom(_798267)), _798269 = _798267, class_Rings_Olinordered__idom(_798269)], (13040 ^ _780478) ^ [_1011460, _1011462, _1011464, _1011466] : [13041 ^ _780478 : [(13044 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1011460), _1011462), _1011466))], (13042 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1011460), _1011462), _1011464))]], -(hBOOL(hAPP(hAPP(c_member(_1011460), _1011462), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011460, tc_HOL_Obool)), _1011464), _1011466))))], (12764 ^ _780478) ^ [_1006488, _1006490, _1006492, _1006494] : [class_Lattices_Osemilattice__sup(_1006488), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006488), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006488), _1006490), _1006492)), _1006494) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006488), _1006490), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006488), _1006492), _1006494)))], (25247 ^ _780478) ^ [_1249662, _1249664] : [class_Rings_Odivision__ring(_1249662), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249662), _1249664), c_Groups_Oone__class_Oone(_1249662)) = _1249664)], (15711 ^ _780478) ^ [_1064413, _1064415, _1064417] : [class_Lattices_Osemilattice__inf(_1064413), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064413), _1064415), _1064417) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064413), _1064417), _1064415))], (44684 ^ _780478) ^ [_1674525, _1674527, _1674529, _1674531, _1674533] : [-(hAPP(c_List_Orotate(_1674525, _1674527), hAPP(hAPP(c_List_Omap(_1674529, _1674525), _1674531), _1674533)) = hAPP(hAPP(c_List_Omap(_1674529, _1674525), _1674531), hAPP(c_List_Orotate(_1674529, _1674527), _1674533)))], (14827 ^ _780478) ^ [_1046404, _1046406, _1046408, _1046410, _1046412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046404), _1046406)), 14830 ^ _780478 : [(14837 ^ _780478) ^ [] : [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), _1046406), _1046404)), _1046408)), _1046410) = _1046412, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046406), _1046408)), _1046410) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046404), _1046408)), _1046412))], (14831 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046406), _1046408)), _1046410) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046404), _1046408)), _1046412), -(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), _1046406), _1046404)), _1046408)), _1046410) = _1046412)]]], (18504 ^ _780478) ^ [_1127166, _1127168, _1127170, _1127172, _1127174] : [_1127166 = c_Orderings_Obot__class_Obot(tc_fun(_1127168, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127170, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127168, tc_fun(_1127170, tc_HOL_Obool)), _1127166), _1127172)), _1127174) = _1127174)], (52261 ^ _780478) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (18848 ^ _780478) ^ [_1134231, _1134233, _1134235] : [class_Lattices_Olattice(_1134231), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134231), _1134233)), -(c_Big__Operators_Olattice__class_OInf__fin(_1134231, hAPP(hAPP(c_Set_Oinsert(_1134231), _1134235), _1134233)) = hAPP(hAPP(c_Finite__Set_Ofold(_1134231, _1134231, c_Lattices_Osemilattice__inf__class_Oinf(_1134231)), _1134235), _1134233))], (15675 ^ _780478) ^ [_1063759, _1063761, _1063763, _1063765, _1063767] : [hBOOL(hAPP(_1063765, hAPP(_1063763, _1063767))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1063759, _1063761, _1063763), _1063765), _1063767)))], (21199 ^ _780478) ^ [_1174477, _1174479, _1174481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174477)), 21202 ^ _780478 : [(21209 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174479), _1174481)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174477), _1174479)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174477), _1174481))))], (21203 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174477), _1174479)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174477), _1174481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174479), _1174481)))]]], (16218 ^ _780478) ^ [_1074451, _1074453] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074451, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1074451, tc_HOL_Obool))), _1074453) = _1074453)], (15717 ^ _780478) ^ [_1064522, _1064524, _1064526] : [class_Lattices_Olattice(_1064522), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064522), _1064524), _1064526) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064522), _1064526), _1064524))], (14289 ^ _780478) ^ [_1035762, _1035764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035762), _1035764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035762), _1035764))), -(_1035762 = _1035764)], (31114 ^ _780478) ^ [_1359357, _1359359] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1359357)), 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)), _1359357))), 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, _1359359))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11493 ^ _780478) ^ [_981930, _981932, _981934] : [class_Orderings_Olinorder(_981930), hBOOL(hAPP(c_Finite__Set_Ofinite(_981930), _981932)), -(_981932 = c_Orderings_Obot__class_Obot(tc_fun(_981930, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_981930, hAPP(hAPP(c_Set_Oinsert(_981930), _981934), _981932)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_981930), _981934), c_Big__Operators_Olinorder__class_OMax(_981930, _981932)))], (45719 ^ _780478) ^ [_1698614, _1698616] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698614)), c_List_Oremdups(_1698614, _1698616))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698614)), _1698616))))], (23359 ^ _780478) ^ [] : [-(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))))], (22550 ^ _780478) ^ [_1200496, _1200498] : [class_Rings_Olinordered__idom(_1200496), hBOOL(hAPP(hAPP(c_member(_1200496), _1200498), c_Int_Oring__1__class_OInts(_1200496))), 22557 ^ _780478 : [(22564 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200496), _1200498), c_Groups_Ozero__class_Ozero(_1200496))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200496), c_Groups_Oone__class_Oone(_1200496)), _1200498)), _1200498)), c_Groups_Ozero__class_Ozero(_1200496))))], (22558 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200496), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200496), c_Groups_Oone__class_Oone(_1200496)), _1200498)), _1200498)), c_Groups_Ozero__class_Ozero(_1200496))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200496), _1200498), c_Groups_Ozero__class_Ozero(_1200496))))]]], (19974 ^ _780478) ^ [_1153027, _1153029, _1153031] : [class_Rings_Oordered__cancel__semiring(_1153027), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153027), c_Groups_Ozero__class_Ozero(_1153027)), _1153029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153027), c_Groups_Ozero__class_Ozero(_1153027)), _1153031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153027), c_Groups_Ozero__class_Ozero(_1153027)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153027), _1153029), _1153031))))], (38595 ^ _780478) ^ [_1523440, _1523442, _1523444, _1523446] : [38596 ^ _780478 : [(38597 ^ _780478) ^ [_1523494] : [hBOOL(hAPP(hAPP(_1523444, _1523494), _1523446))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1523440, _1523442, _1523444), _1523446)))], (38907 ^ _780478) ^ [_1532513, _1532515, _1532517, _1532519] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1532513, _1532515)), hAPP(hAPP(c_Product__Type_OSigma(_1532513, _1532515), _1532517), hAPP(c_COMBK(tc_fun(_1532515, tc_HOL_Obool), _1532513), _1532519)))), -(_1532519 = c_Orderings_Obot__class_Obot(tc_fun(_1532515, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1532513), _1532517)))], (42977 ^ _780478) ^ [_1637868, _1637870, _1637872] : [hBOOL(hAPP(c_List_Odistinct(_1637868), _1637870)), -(hBOOL(hAPP(c_List_Odistinct(_1637868), c_List_Oremove1(_1637868, _1637872, _1637870))))], (26942 ^ _780478) ^ [_1279666, _1279668, _1279670, _1279672] : [class_Fields_Ofield__inverse__zero(_1279666), -(_1279668 = c_Groups_Ozero__class_Ozero(_1279666)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279666), _1279670), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279666), _1279672), _1279668)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279666), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279666), _1279672), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279666), _1279670), _1279668))), _1279668))], (39104 ^ _780478) ^ [_1538817, _1538819, _1538821, _1538823] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538817), _1538819)), 39110 ^ _780478 : [(39113 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538821), hAPP(_1538823, 39109 ^ [_1538817, _1538819, _1538821, _1538823])))], (39111 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538817), 39109 ^ [_1538817, _1538819, _1538821, _1538823]), _1538819)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1538817, _1538821)), hAPP(hAPP(c_Product__Type_OSigma(_1538817, _1538821), _1538819), _1538823))))], (51943 ^ _780478) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (15127 ^ _780478) ^ [_1052911, _1052913, _1052915] : [class_Lattices_Olattice(_1052911), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052911), _1052913)), hBOOL(hAPP(hAPP(c_member(_1052911), _1052915), _1052913)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1052911), _1052915), c_Big__Operators_Olattice__class_OSup__fin(_1052911, _1052913)) = c_Big__Operators_Olattice__class_OSup__fin(_1052911, _1052913))], (30191 ^ _780478) ^ [_1340488, _1340490, _1340492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1340490), 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), _1340490), _1340492))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1340488))), _1340492)))], (34749 ^ _780478) ^ [_1435670] : [class_Rings_Osemiring__1(_1435670), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435670), c_Groups_Ozero__class_Ozero(_1435670)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1435670))], (14897 ^ _780478) ^ [_1048049, _1048051, _1048053, _1048055] : [hBOOL(hAPP(hAPP(_1048053, _1048051), _1048055)), -(hBOOL(hAPP(hAPP(c_member(_1048049), _1048051), c_SetInterval_Oord_OatMost(_1048049, _1048053, _1048055))))], (44175 ^ _780478) ^ [_1664540, _1664542, _1664544] : [-(hAPP(hAPP(c_List_Odrop(_1664540), hAPP(c_Nat_OSuc, _1664542)), _1664544) = hAPP(hAPP(c_List_Odrop(_1664540), _1664542), hAPP(c_List_Otl(_1664540), _1664544)))], (49558 ^ _780478) ^ [_1782830, _1782832] : [c_Relation_Otrans(_1782830, _1782832), c_Relation_Oantisym(_1782830, _1782832), -(c_Relation_Otrans(_1782830, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1782830, _1782830), tc_HOL_Obool)), _1782832), c_Relation_OId(_1782830))))], (3012 ^ _780478) ^ [_825091, _825093, _825095, _825097] : [-(c_List_Olenlex(_825097, _825093) = c_List_Olenlex(_825095, _825091)), _825097 = _825095, _825093 = _825091], (36008 ^ _780478) ^ [_1464432, _1464434, _1464436, _1464438, _1464440] : [c_Equiv__Relations_Oequiv(_1464432, _1464434, _1464436), 36011 ^ _780478 : [(36022 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1464432, _1464432)), hAPP(hAPP(c_Product__Type_OPair(_1464432, _1464432), _1464438), _1464440)), _1464436))), hAPP(c_Relation_OImage(_1464432, _1464432, _1464436), hAPP(hAPP(c_Set_Oinsert(_1464432), _1464438), c_Orderings_Obot__class_Obot(tc_fun(_1464432, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1464432, _1464432, _1464436), hAPP(hAPP(c_Set_Oinsert(_1464432), _1464440), c_Orderings_Obot__class_Obot(tc_fun(_1464432, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1464432), _1464438), _1464434)), hBOOL(hAPP(hAPP(c_member(_1464432), _1464440), _1464434))], (36012 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1464432, _1464432)), hAPP(hAPP(c_Product__Type_OPair(_1464432, _1464432), _1464438), _1464440)), _1464436)), 36015 ^ _780478 : [(36020 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1464432), _1464440), _1464434)))], (36018 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1464432), _1464438), _1464434)))], (36016 ^ _780478) ^ [] : [-(hAPP(c_Relation_OImage(_1464432, _1464432, _1464436), hAPP(hAPP(c_Set_Oinsert(_1464432), _1464438), c_Orderings_Obot__class_Obot(tc_fun(_1464432, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1464432, _1464432, _1464436), hAPP(hAPP(c_Set_Oinsert(_1464432), _1464440), c_Orderings_Obot__class_Obot(tc_fun(_1464432, tc_HOL_Obool)))))]]]]], (27177 ^ _780478) ^ [_1283890, _1283892] : [c_Nat__Transfer_Onat__set(_1283890), c_Nat__Transfer_Onat__set(_1283892), 27184 ^ _780478 : [(27191 ^ _780478) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1283890) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1283892), -(_1283890 = _1283892)], (27185 ^ _780478) ^ [] : [_1283890 = _1283892, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1283890) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1283892))]]], (5855 ^ _780478) ^ [_873282, _873284] : [hBOOL(hAPP(hAPP(c_member(_873282), _873284), c_Orderings_Obot__class_Obot(tc_fun(_873282, tc_HOL_Obool))))], (26236 ^ _780478) ^ [_1266873, _1266875, _1266877, _1266879] : [class_Fields_Olinordered__field__inverse__zero(_1266873), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266873), _1266875), _1266877)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266873), c_Groups_Ozero__class_Ozero(_1266873)), _1266879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266873), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266873), _1266875), _1266879)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266873), _1266877), _1266879))))], (4002 ^ _780478) ^ [_840866, _840868, _840870, _840872, _840874, _840876, _840878, _840880] : [-(c_New__Random__Sequence_Opos__empty(_840880, _840876, _840872, _840868) = c_New__Random__Sequence_Opos__empty(_840878, _840874, _840870, _840866)), _840880 = _840878, _840876 = _840874, _840872 = _840870, _840868 = _840866], (11919 ^ _780478) ^ [_989935, _989937] : [class_Orderings_Olinorder(_989935), -(c_Big__Operators_Olattice_OSup__fin(_989935, c_Orderings_Oord__class_Omax(_989935), hAPP(hAPP(c_Set_Oinsert(_989935), _989937), c_Orderings_Obot__class_Obot(tc_fun(_989935, tc_HOL_Obool)))) = _989937)], (6894 ^ _780478) ^ [_894848, _894850, _894852, _894854, _894856] : [c_Finite__Set_Ofolding__one(_894848, _894850, _894852), hBOOL(hAPP(c_Finite__Set_Ofinite(_894848), _894854)), -(hBOOL(hAPP(hAPP(c_member(_894848), _894856), _894854))), -(hAPP(_894852, hAPP(hAPP(c_Set_Oinsert(_894848), _894856), _894854)) = hAPP(hAPP(c_Finite__Set_Ofold(_894848, _894848, _894850), _894856), _894854))], (39193 ^ _780478) ^ [_1541152, _1541154, _1541156, _1541158, _1541160, _1541162, _1541164, _1541166] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1541152, _1541154)), _1541156), hAPP(c_Set_Oimage(tc_prod(_1541158, _1541160), tc_prod(_1541152, _1541154), c_Product__Type_Omap__pair(_1541158, _1541152, _1541160, _1541154, _1541162, _1541164)), _1541166))), 39198 ^ _780478 : [(39201 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1541158, _1541160)), hAPP(hAPP(c_Product__Type_OPair(_1541158, _1541160), 39196 ^ [_1541152, _1541154, _1541156, _1541158, _1541160, _1541162, _1541164, _1541166]), 39197 ^ [_1541152, _1541154, _1541156, _1541158, _1541160, _1541162, _1541164, _1541166])), _1541166)))], (39199 ^ _780478) ^ [] : [-(_1541156 = hAPP(hAPP(c_Product__Type_OPair(_1541152, _1541154), hAPP(_1541162, 39196 ^ [_1541152, _1541154, _1541156, _1541158, _1541160, _1541162, _1541164, _1541166])), hAPP(_1541164, 39197 ^ [_1541152, _1541154, _1541156, _1541158, _1541160, _1541162, _1541164, _1541166])))]]], (13178 ^ _780478) ^ [_1014389, _1014391, _1014393, _1014395] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014389, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014389, tc_HOL_Obool)), _1014391), _1014393)), _1014395) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014389, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014389, tc_HOL_Obool)), _1014391), _1014395)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014389, tc_HOL_Obool)), _1014393), _1014395)))], (40341 ^ _780478) ^ [_1568560, _1568562] : [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), _1568560), _1568562)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1568560), _1568562)))], (14527 ^ _780478) ^ [_1040090, _1040092, _1040094] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040090), _1040092)), _1040094) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040092), _1040094)))], (16232 ^ _780478) ^ [_1075008, _1075010, _1075012, _1075014, _1075016] : [-(hAPP(c_Set_Ovimage(_1075008, _1075010, _1075012), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075010, tc_HOL_Obool)), _1075014), _1075016)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075008, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1075008, _1075010, _1075012), _1075014)), hAPP(c_Set_Ovimage(_1075008, _1075010, _1075012), _1075016)))], (38784 ^ _780478) ^ [_1528866, _1528868, _1528870, _1528872, _1528874] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528866, _1528868), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1528866, tc_HOL_Obool)), _1528870), _1528872)), hAPP(c_COMBK(tc_fun(_1528868, tc_HOL_Obool), _1528866), _1528874)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528866, _1528868), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1528866, _1528868), _1528870), hAPP(c_COMBK(tc_fun(_1528868, tc_HOL_Obool), _1528866), _1528874))), hAPP(hAPP(c_Product__Type_OSigma(_1528866, _1528868), _1528872), hAPP(c_COMBK(tc_fun(_1528868, tc_HOL_Obool), _1528866), _1528874))))], (37223 ^ _780478) ^ [_1488611, _1488613, _1488615] : [-(_1488611 = hAPP(hAPP(c_Product__Type_OPair(_1488613, _1488615), hAPP(c_Product__Type_Ofst(_1488613, _1488615), _1488611)), hAPP(c_Product__Type_Osnd(_1488613, _1488615), _1488611)))], (16528 ^ _780478) ^ [_1082454, _1082456, _1082458, _1082460] : [hBOOL(hAPP(hAPP(c_member(_1082454), _1082456), _1082458)), -(hAPP(c_Set_Ovimage(_1082460, _1082454, hAPP(c_COMBK(_1082454, _1082460), _1082456)), _1082458) = c_Orderings_Otop__class_Otop(tc_fun(_1082460, tc_HOL_Obool)))], (19036 ^ _780478) ^ [_1137882, _1137884, _1137886, _1137888] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1137882, tc_HOL_Obool), hAPP(c_Set_Oimage(_1137884, tc_fun(_1137882, tc_HOL_Obool), _1137886), _1137888)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1137884, tc_fun(_1137882, tc_HOL_Obool)), _1137888), _1137886))], (1144 ^ _780478) ^ [_797642, _797644] : [-(class_Rings_Oring__no__zero__divisors(_797642)), _797644 = _797642, class_Rings_Oring__no__zero__divisors(_797644)], (20346 ^ _780478) ^ [_1159896, _1159898, _1159900, _1159902] : [class_Rings_Olinordered__ring__strict(_1159896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159896), c_Groups_Ozero__class_Ozero(_1159896)), _1159898)), 20353 ^ _780478 : [(20360 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159896), _1159900), _1159902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159896), _1159898), _1159900)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159896), _1159898), _1159902))))], (20354 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159896), _1159898), _1159900)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159896), _1159898), _1159902))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159896), _1159900), _1159902)))]]], (1022 ^ _780478) ^ [_795909, _795911, _795913, _795915, _795917, _795919] : [-(c_List_Olist__ex(_795917, _795913, _795909)), c_List_Olist__ex(_795919, _795915, _795911), _795919 = _795917, _795915 = _795913, _795911 = _795909], (47015 ^ _780478) ^ [_1726289, _1726291, _1726293, _1726295, _1726297] : [c_List_Olist__all2(_1726289, _1726291, _1726293, hAPP(c_List_Orev(_1726289), _1726295), _1726297), -(c_List_Olist__all2(_1726289, _1726291, _1726293, _1726295, hAPP(c_List_Orev(_1726291), _1726297)))], (9280 ^ _780478) ^ [_939471, _939473, _939475] : [class_Orderings_Olinorder(_939471), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939471), _939473), _939475))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939471), _939475), _939473)))], (24149 ^ _780478) ^ [_1230116, _1230118] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230116)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230118)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230116), _1230118))], (10359 ^ _780478) ^ [_961206, _961208] : [class_Orderings_Olinorder(_961206), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_961206), _961208), _961208) = _961208)], (47101 ^ _780478) ^ [_1728031, _1728033, _1728035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728031), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728033)), _1728035))), -(hAPP(hAPP(c_List_Onth(_1728033), hAPP(c_List_Orev(_1728033), _1728035)), _1728031) = hAPP(hAPP(c_List_Onth(_1728033), _1728035), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728033)), _1728035)), hAPP(c_Nat_OSuc, _1728031))))], (28428 ^ _780478) ^ [_1306516, _1306518] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1306516, _1306518) = 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), _1306516), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306518))))], (32054 ^ _780478) ^ [_1385923, _1385925, _1385927, _1385929, _1385931, _1385933] : [c_Com_Ocom_OLocal(_1385923, _1385925, _1385927) = c_Com_Ocom_OLocal(_1385929, _1385931, _1385933), 32057 ^ _780478 : [(32062 ^ _780478) ^ [] : [-(_1385927 = _1385933)], (32060 ^ _780478) ^ [] : [-(_1385925 = _1385931)], (32058 ^ _780478) ^ [] : [-(_1385923 = _1385929)]]], (6594 ^ _780478) ^ [_888462, _888464, _888466, _888468] : [hBOOL(hAPP(hAPP(c_member(_888462), _888464), _888466)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888462, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_888462), _888464), _888468)), _888466) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888462, tc_HOL_Obool)), _888468), _888466))], (51957 ^ _780478) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (40967 ^ _780478) ^ [_1583430, _1583432, _1583434, _1583436, _1583438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1583432, tc_HOL_Obool)), _1583436), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1583432, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1583430, _1583432, hAPP(c_Relation_Oconverse(_1583432, _1583430), _1583434)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1583430, tc_HOL_Obool)), _1583438))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1583430, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1583432, _1583430, _1583434), _1583436)), _1583438)))], (37935 ^ _780478) ^ [_1506482, _1506484, _1506486, _1506488, _1506490] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1506482, _1506484, _1506486), _1506488), _1506490) = hAPP(c_Set_OCollect(tc_prod(_1506482, _1506486)), hAPP(c_Product__Type_Oprod_Oprod__case(_1506482, _1506486, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1506486, tc_fun(_1506484, tc_HOL_Obool)), tc_fun(_1506486, tc_HOL_Obool), _1506482), hAPP(c_COMBB(tc_fun(_1506484, tc_HOL_Obool), tc_HOL_Obool, _1506486), c_HOL_OEx(_1506484))), hAPP(hAPP(c_COMBC(_1506482, tc_fun(_1506486, tc_fun(_1506484, tc_HOL_Obool)), tc_fun(_1506486, tc_fun(_1506484, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1506484, tc_HOL_Obool), tc_fun(_1506484, tc_HOL_Obool)), tc_fun(tc_fun(_1506486, tc_fun(_1506484, tc_HOL_Obool)), tc_fun(_1506486, tc_fun(_1506484, tc_HOL_Obool))), _1506482), c_COMBB(tc_fun(_1506484, tc_HOL_Obool), tc_fun(_1506484, tc_HOL_Obool), _1506486)), hAPP(hAPP(c_COMBB(tc_fun(_1506484, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1506484, tc_HOL_Obool), tc_fun(_1506484, tc_HOL_Obool)), _1506482), c_COMBS(_1506484, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506484, tc_HOL_Obool), tc_fun(_1506484, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1506482), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506484), c_fconj)), hAPP(hAPP(c_COMBC(_1506482, tc_fun(tc_prod(_1506482, _1506484), tc_HOL_Obool), tc_fun(_1506484, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506484, tc_fun(tc_fun(tc_prod(_1506482, _1506484), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1506482, _1506484), tc_HOL_Obool), tc_fun(_1506484, tc_HOL_Obool)), _1506482), c_COMBC(_1506484, tc_fun(tc_prod(_1506482, _1506484), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506484, tc_prod(_1506482, _1506484)), tc_fun(_1506484, tc_fun(tc_fun(tc_prod(_1506482, _1506484), tc_HOL_Obool), tc_HOL_Obool)), _1506482), hAPP(c_COMBB(tc_prod(_1506482, _1506484), tc_fun(tc_fun(tc_prod(_1506482, _1506484), tc_HOL_Obool), tc_HOL_Obool), _1506484), c_member(tc_prod(_1506482, _1506484)))), c_Product__Type_OPair(_1506482, _1506484)))), _1506488))))), hAPP(hAPP(c_COMBC(_1506486, tc_fun(tc_prod(_1506484, _1506486), tc_HOL_Obool), tc_fun(_1506484, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506484, tc_fun(tc_fun(tc_prod(_1506484, _1506486), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1506484, _1506486), tc_HOL_Obool), tc_fun(_1506484, tc_HOL_Obool)), _1506486), c_COMBC(_1506484, tc_fun(tc_prod(_1506484, _1506486), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1506484, tc_prod(_1506484, _1506486)), tc_fun(_1506484, tc_fun(tc_fun(tc_prod(_1506484, _1506486), tc_HOL_Obool), tc_HOL_Obool)), _1506486), hAPP(c_COMBB(tc_prod(_1506484, _1506486), tc_fun(tc_fun(tc_prod(_1506484, _1506486), tc_HOL_Obool), tc_HOL_Obool), _1506484), c_member(tc_prod(_1506484, _1506486)))), hAPP(c_COMBC(_1506484, _1506486, tc_prod(_1506484, _1506486)), c_Product__Type_OPair(_1506484, _1506486))))), _1506490))))))], (40961 ^ _780478) ^ [_1583239, _1583241, _1583243, _1583245, _1583247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1583239, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1583241, _1583239, _1583243), _1583245)), _1583247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1583241, tc_HOL_Obool)), _1583245), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1583241, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1583239, _1583241, hAPP(c_Relation_Oconverse(_1583241, _1583239), _1583243)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1583239, tc_HOL_Obool)), _1583247))))))], (39727 ^ _780478) ^ [_1554002, _1554004, _1554006, _1554008, _1554010, _1554012, _1554014] : [-(hAPP(c_Product__Type_Oapfst(_1554002, _1554004, _1554006, _1554008), hAPP(c_Product__Type_Oapfst(_1554010, _1554002, _1554006, _1554012), _1554014)) = hAPP(c_Product__Type_Oapfst(_1554010, _1554004, _1554006, hAPP(c_Fun_Ocomp(_1554002, _1554004, _1554010, _1554008), _1554012)), _1554014))], (34817 ^ _780478) ^ [_1436802] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1436802)), 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, _1436802, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (29019 ^ _780478) ^ [_1318350, _1318352, _1318354] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1318350, tc_HOL_Obool)), _1318352), hAPP(c_Set_OPow(_1318350), _1318354))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318350, tc_HOL_Obool)), _1318352), _1318354)))], (10039 ^ _780478) ^ [_955098, _955100, _955102] : [class_Orderings_Olinorder(_955098), hBOOL(hAPP(c_Finite__Set_Ofinite(_955098), _955100)), 10049 ^ _780478 : [(10052 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955098), _955102), 10048 ^ [_955098, _955100, _955102]))], (10050 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_955098), 10048 ^ [_955098, _955100, _955102]), _955100)))]], hBOOL(hAPP(hAPP(c_member(_955098), _955102), _955100)), -(c_Big__Operators_Olinorder__class_OMin(_955098, _955100) = _955102)], (7497 ^ _780478) ^ [_906457, _906459, _906461, _906463, _906465, _906467] : [c_Fun_Oinj__on(_906457, _906459, _906461, _906463), hBOOL(hAPP(hAPP(c_member(_906457), _906465), _906463)), hBOOL(hAPP(hAPP(c_member(_906457), _906467), _906463)), 7508 ^ _780478 : [(7515 ^ _780478) ^ [] : [_906465 = _906467, -(hAPP(_906461, _906465) = hAPP(_906461, _906467))], (7509 ^ _780478) ^ [] : [hAPP(_906461, _906465) = hAPP(_906461, _906467), -(_906465 = _906467)]]], (41722 ^ _780478) ^ [_1603710, _1603712, _1603714] : [hAPP(hAPP(c_List_Olist_OCons(_1603710), _1603712), _1603714) = _1603714], (2426 ^ _780478) ^ [_816016, _816018, _816020, _816022] : [-(c_Divides_OnegDivAlg(_816022, _816018) = c_Divides_OnegDivAlg(_816020, _816016)), _816022 = _816020, _816018 = _816016], (29189 ^ _780478) ^ [_1322157, _1322159, _1322161] : [-(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, _1322157, _1322159)), _1322161), _1322159) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1322157), _1322161), _1322159))], (16266 ^ _780478) ^ [_1075940, _1075942, _1075944, _1075946] : [hBOOL(hAPP(hAPP(c_member(_1075940), _1075946), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075940, tc_HOL_Obool)), _1075942), _1075944))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075940, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1075940, tc_fun(_1075940, tc_HOL_Obool), tc_HOL_Obool), c_member(_1075940)), _1075942)), hAPP(hAPP(c_COMBC(_1075940, tc_fun(_1075940, tc_HOL_Obool), tc_HOL_Obool), c_member(_1075940)), _1075944)), _1075946)))], (30681 ^ _780478) ^ [_1350221, _1350223] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1350221), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350221, tc_HOL_Obool), _1350223))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1350221, tc_HOL_Obool)), _1350223)))], (46793 ^ _780478) ^ [_1721486, _1721488] : [class_Orderings_Olinorder(_1721486), hBOOL(hAPP(c_Finite__Set_Ofinite(_1721486), _1721488)), 46800 ^ _780478 : [(46805 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1721486), c_List_Olinorder__class_Osorted__list__of__set(_1721486, _1721488))))], (46803 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1721486, c_List_Olinorder__class_Osorted__list__of__set(_1721486, _1721488)))], (46801 ^ _780478) ^ [] : [-(hAPP(c_List_Oset(_1721486), c_List_Olinorder__class_Osorted__list__of__set(_1721486, _1721488)) = _1721488)]]], (33927 ^ _780478) ^ [_1421381, _1421383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1421381)), c_Int_OBit1(_1421383))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421381), _1421383)))], (43277 ^ _780478) ^ [_1643522, _1643524, _1643526] : [-(c_List_Olistset(_1643522, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1643522, tc_HOL_Obool)), _1643524), _1643526)) = c_List_Oset__Cons(_1643522, _1643524, c_List_Olistset(_1643522, _1643526)))], (23429 ^ _780478) ^ [_1216092, _1216094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216092), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1216094), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216092), _1216094)))], (21952 ^ _780478) ^ [_1188092, _1188094, _1188096] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1188092), _1188094)), 21955 ^ _780478 : [(21975 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1188092, tc_Nat_Onat), _1188096), _1188094) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 21976 ^ _780478 : [(21977 ^ _780478) ^ [_1188573] : [hBOOL(hAPP(hAPP(c_member(_1188092), _1188573), _1188094)), hAPP(_1188096, _1188573) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21985 ^ _780478 : [(21990 ^ _780478) ^ [] : [hAPP(_1188096, 21984 ^ [_1188092, _1188094, _1188096, _1188573]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21988 ^ _780478) ^ [] : [_1188573 = 21984 ^ [_1188092, _1188094, _1188096, _1188573]], (21986 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1188092), 21984 ^ [_1188092, _1188094, _1188096, _1188573]), _1188094)))]]]]], (21956 ^ _780478) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1188092, tc_Nat_Onat), _1188096), _1188094) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21960 ^ _780478 : [(21965 ^ _780478) ^ [_1188412] : [hBOOL(hAPP(hAPP(c_member(_1188092), _1188412), _1188094)), -(21959 ^ [_1188092, _1188094, _1188096] = _1188412), -(hAPP(_1188096, _1188412) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21963 ^ _780478) ^ [] : [-(hAPP(_1188096, 21959 ^ [_1188092, _1188094, _1188096]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (21961 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1188092), 21959 ^ [_1188092, _1188094, _1188096]), _1188094)))]]]]], (27753 ^ _780478) ^ [_1293400, _1293402, _1293404] : [27755 ^ _780478 : [(27758 ^ _780478) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1293404, 27754 ^ [_1293400, _1293402, _1293404]))], (27756 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1293400), 27754 ^ [_1293400, _1293402, _1293404]), _1293402)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293400, tc_Int_Oint), _1293404), _1293402) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293400, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1293400), c_Int_Onat), _1293404)), _1293402)))], (2636 ^ _780478) ^ [_819319, _819321] : [_819321 = _819319, -(c_Equiv__Relations_Oquotient(_819321) = c_Equiv__Relations_Oquotient(_819319))], (49127 ^ _780478) ^ [_1772360, _1772362, _1772364] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1772360, _1772362, _1772364, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1772362)], (41364 ^ _780478) ^ [_1593725, _1593727, _1593729, _1593731, _1593733] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593725, _1593725)), hAPP(hAPP(c_Product__Type_OPair(_1593725, _1593725), _1593727), _1593729)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1593725, _1593725), tc_HOL_Obool), _1593731), _1593733))), 41369 ^ _780478 : [(41372 ^ _780478) ^ [] : [-(_1593727 = _1593729)], (41370 ^ _780478) ^ [] : [-(_1593731 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41375 ^ _780478 : [(41380 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593725, _1593725)), hAPP(hAPP(c_Product__Type_OPair(_1593725, _1593725), 41373 ^ [_1593725, _1593727, _1593729, _1593731, _1593733]), _1593729)), _1593733)))], (41378 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593725, _1593725)), hAPP(hAPP(c_Product__Type_OPair(_1593725, _1593725), _1593727), 41373 ^ [_1593725, _1593727, _1593729, _1593731, _1593733])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1593725, _1593725), tc_HOL_Obool), 41374 ^ [_1593725, _1593727, _1593729, _1593731, _1593733]), _1593733))))], (41376 ^ _780478) ^ [] : [-(_1593731 = hAPP(c_Nat_OSuc, 41374 ^ [_1593725, _1593727, _1593729, _1593731, _1593733]))]]], (48417 ^ _780478) ^ [_1756541, _1756543, _1756545, _1756547, _1756549] : [-(hAPP(c_New__DSequence_Opos__bind(_1756541, _1756543, _1756545, _1756547), _1756549) = hAPP(c_Lazy__Sequence_Obind(_1756541, _1756543, hAPP(_1756545, _1756549)), hAPP(hAPP(c_COMBC(_1756541, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1756543)), _1756547), _1756549)))], (15878 ^ _780478) ^ [_1067749, _1067751, _1067753, _1067755] : [class_Lattices_Osemilattice__inf(_1067749), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067749), _1067751), _1067753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067749), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067749), _1067751), _1067755)), _1067753)))], (49782 ^ _780478) ^ [_1787171, _1787173, _1787175] : [-(c_Equiv__Relations_Oequiv(_1787171, _1787173, _1787175)), c_Relation_Orefl__on(_1787171, _1787173, _1787175), c_Relation_Osym(_1787171, _1787175), c_Relation_Otrans(_1787171, _1787175)], (43115 ^ _780478) ^ [_1640216, _1640218, _1640220, _1640222] : [_1640218 = c_List_Olist_ONil(_1640216), -(hAPP(hAPP(c_List_Olist__update(_1640216, _1640218), _1640220), _1640222) = c_List_Olist_ONil(_1640216))], (10665 ^ _780478) ^ [_966546, _966548, _966550, _966552] : [class_Orderings_Olinorder(_966546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966546), _966548), _966550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966546), _966548), _966552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966546), _966548), hAPP(hAPP(c_Orderings_Oord__class_Omin(_966546), _966550), _966552))))], (30753 ^ _780478) ^ [_1351855, _1351857] : [class_Groups_Oabs__if(_1351855), 30756 ^ _780478 : [(30763 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351855), _1351857), c_Groups_Ozero__class_Ozero(_1351855)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1351855), _1351857) = _1351857)], (30757 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351855), _1351857), c_Groups_Ozero__class_Ozero(_1351855))), -(hAPP(c_Groups_Oabs__class_Oabs(_1351855), _1351857) = hAPP(c_Groups_Ouminus__class_Ouminus(_1351855), _1351857))]]], (1404 ^ _780478) ^ [_800892, _800894] : [-(class_Lattices_Odistrib__lattice(_800892)), _800894 = _800892, class_Lattices_Odistrib__lattice(_800894)], (45011 ^ _780478) ^ [_1682680, _1682682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682680), _1682682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1682680)), hAPP(c_Code__Numeral_Oof__nat, _1682682))))], (39508 ^ _780478) ^ [_1548138] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39504 ^ [_1548138]), c_Int_OInteg)))], (12728 ^ _780478) ^ [_1005684, _1005686, _1005688] : [class_Lattices_Osemilattice__sup(_1005684), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005684), _1005686), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005684), _1005686), _1005688)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005684), _1005686), _1005688))], (50985 ^ _780478) ^ [_1813769] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1813769)))], (44801 ^ _780478) ^ [_1678020, _1678022, _1678024, _1678026, _1678028] : [hAPP(hAPP(c_List_Omap(_1678020, _1678022), _1678024), _1678026) = hAPP(hAPP(c_List_Omap(_1678020, _1678022), _1678024), _1678028), c_Fun_Oinj__on(_1678020, _1678022, _1678024, c_Orderings_Otop__class_Otop(tc_fun(_1678020, tc_HOL_Obool))), -(_1678026 = _1678028)], (44688 ^ _780478) ^ [_1674643, _1674645, _1674647, _1674649, _1674651, _1674653] : [-(hAPP(hAPP(c_List_Ozip(_1674643, _1674645), _1674647), hAPP(hAPP(c_List_Omap(_1674649, _1674645), _1674651), _1674653)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674643, _1674649), tc_prod(_1674643, _1674645)), hAPP(c_Product__Type_Oprod_Oprod__case(_1674643, _1674649, tc_prod(_1674643, _1674645)), hAPP(hAPP(c_COMBC(_1674643, tc_fun(_1674649, _1674645), tc_fun(_1674649, tc_prod(_1674643, _1674645))), hAPP(hAPP(c_COMBB(tc_fun(_1674645, tc_prod(_1674643, _1674645)), tc_fun(tc_fun(_1674649, _1674645), tc_fun(_1674649, tc_prod(_1674643, _1674645))), _1674643), c_COMBB(_1674645, tc_prod(_1674643, _1674645), _1674649)), c_Product__Type_OPair(_1674643, _1674645))), _1674651))), hAPP(hAPP(c_List_Ozip(_1674643, _1674649), _1674647), _1674653)))], (10917 ^ _780478) ^ [_970859, _970861, _970863, _970865] : [class_Orderings_Olinorder(_970859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970859), _970861), _970863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970859), hAPP(hAPP(c_Orderings_Oord__class_Omin(_970859), _970865), _970861)), _970863)))], (49574 ^ _780478) ^ [_1783091, _1783093] : [c_Relation_Oantisym(_1783091, _1783093), -(c_Relation_Oantisym(_1783091, hAPP(c_Relation_Oconverse(_1783091, _1783091), _1783093)))], (12584 ^ _780478) ^ [_1002812, _1002814, _1002816, _1002818] : [12585 ^ _780478 : [(12586 ^ _780478) ^ [_1002922] : [hBOOL(hAPP(hAPP(c_member(_1002812), _1002922), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002812, tc_HOL_Obool)), _1002814), _1002816))), hBOOL(hAPP(_1002818, _1002922))]], 12594 ^ _780478 : [(12597 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1002818, 12593 ^ [_1002812, _1002814, _1002816, _1002818])))], (12595 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1002812), 12593 ^ [_1002812, _1002814, _1002816, _1002818]), _1002814)))]], 12599 ^ _780478 : [(12602 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1002818, 12598 ^ [_1002812, _1002814, _1002816, _1002818])))], (12600 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1002812), 12598 ^ [_1002812, _1002814, _1002816, _1002818]), _1002816)))]]], (38816 ^ _780478) ^ [_1529865, _1529867, _1529869, _1529871, _1529873] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1529865, _1529867), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1529865, tc_HOL_Obool)), _1529869), _1529871)), _1529873) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1529865, _1529867), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1529865, _1529867), _1529869), _1529873)), hAPP(hAPP(c_Product__Type_OSigma(_1529865, _1529867), _1529871), _1529873)))], (8238 ^ _780478) ^ [_921463, _921465, _921467, _921469] : [class_Groups_Oordered__ab__semigroup__add(_921463), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921463), _921465), _921467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921463), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921463), _921469), _921465)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921463), _921469), _921467))))], (23973 ^ _780478) ^ [_1226195, _1226197] : [-(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)), _1226195)), 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), _1226197), _1226195))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1226195), _1226197))], (18974 ^ _780478) ^ [_1136645] : [-(hAPP(c_Nat_OSuc, _1136645) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1136645), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44019 ^ _780478) ^ [_1661476, _1661478, _1661480, _1661482] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1661476) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1661478), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1661476)), hAPP(hAPP(c_List_Olist_OCons(_1661478), _1661480), _1661482)) = hAPP(hAPP(c_List_Olist_OCons(_1661478), _1661480), _1661482))], (35401 ^ _780478) ^ [_1447482] : [class_Int_Onumber__ring(_1447482), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1447482), c_Groups_Oone__class_Oone(_1447482)) = hAPP(c_Int_Onumber__class_Onumber__of(_1447482), c_Int_OMin))], (50269 ^ _780478) ^ [_1797322, _1797324, _1797326, _1797328, _1797330, _1797332] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1797322, _1797324, _1797326, _1797328, c_Lazy__Sequence_Olazy__sequence_OInsert(_1797324, _1797330, _1797332)) = hAPP(hAPP(hAPP(_1797328, _1797330), _1797332), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1797322, _1797324, _1797326, _1797328, _1797332)))], (44720 ^ _780478) ^ [_1675845, _1675847, _1675849, _1675851] : [_1675851 = c_List_Olist_ONil(_1675847), -(c_List_Olist_ONil(_1675845) = hAPP(hAPP(c_List_Omap(_1675847, _1675845), _1675849), _1675851))], (19302 ^ _780478) ^ [_1142270, _1142272, _1142274] : [class_Groups_Oab__group__add(_1142270), 19305 ^ _780478 : [(19312 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142270), _1142272), _1142274) = c_Groups_Ozero__class_Ozero(_1142270), -(_1142272 = _1142274)], (19306 ^ _780478) ^ [] : [_1142272 = _1142274, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142270), _1142272), _1142274) = c_Groups_Ozero__class_Ozero(_1142270))]]], (12396 ^ _780478) ^ [_999366, _999368, _999370] : [class_Orderings_Olinorder(_999366), hBOOL(hAPP(c_Finite__Set_Ofinite(_999366), _999368)), -(_999368 = c_Orderings_Obot__class_Obot(tc_fun(_999366, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_999366), _999370)), -(_999370 = c_Orderings_Obot__class_Obot(tc_fun(_999366, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_999366, c_Orderings_Oord__class_Omax(_999366), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_999366, tc_HOL_Obool)), _999368), _999370)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_999366), c_Big__Operators_Olattice_OSup__fin(_999366, c_Orderings_Oord__class_Omax(_999366), _999368)), c_Big__Operators_Olattice_OSup__fin(_999366, c_Orderings_Oord__class_Omax(_999366), _999370)))], (6816 ^ _780478) ^ [_893218] : [-(c_Finite__Set_Ofun__left__comm__idem(_893218, tc_fun(_893218, tc_HOL_Obool), c_Set_Oinsert(_893218)))], (29319 ^ _780478) ^ [_1324828, _1324830] : [class_Divides_Osemiring__div(_1324828), -(c_Divides_Odiv__class_Omod(_1324828, c_Groups_Ozero__class_Ozero(_1324828), _1324830) = c_Groups_Ozero__class_Ozero(_1324828))], (14243 ^ _780478) ^ [_1035049, _1035051, _1035053] : [class_Groups_Ocomm__monoid__mult(_1035049), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1035051, _1035049), _1035053), c_Orderings_Obot__class_Obot(tc_fun(_1035051, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1035049))], (34803 ^ _780478) ^ [_1436550, _1436552] : [class_Rings_Olinordered__idom(_1436550), -(hAPP(c_Groups_Oabs__class_Oabs(_1436550), hAPP(hAPP(c_Power_Opower__class_Opower(_1436550), _1436552), 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(_1436550), _1436552), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (22706 ^ _780478) ^ [_1203140, _1203142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203140), _1203142)), -(_1203142 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1203140), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 22709 ^ [_1203140, _1203142]))))], (30458 ^ _780478) ^ [_1345824, _1345826] : [class_Groups_Oordered__ab__group__add__abs(_1345824), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345824), c_Groups_Ozero__class_Ozero(_1345824)), _1345826)), -(hAPP(c_Groups_Oabs__class_Oabs(_1345824), _1345826) = _1345826)], (11557 ^ _780478) ^ [_982974, _982976, _982978] : [class_Orderings_Olinorder(_982974), hBOOL(hAPP(c_Finite__Set_Ofinite(_982974), _982976)), -(c_Big__Operators_Olinorder__class_OMax(_982974, hAPP(hAPP(c_Set_Oinsert(_982974), _982978), _982976)) = hAPP(hAPP(c_Finite__Set_Ofold(_982974, _982974, c_Orderings_Oord__class_Omax(_982974)), _982978), _982976))], (1604 ^ _780478) ^ [_803392, _803394] : [-(class_Rings_Olinordered__semiring(_803392)), _803394 = _803392, class_Rings_Olinordered__semiring(_803394)], (13302 ^ _780478) ^ [_1017019, _1017021, _1017023, _1017025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017019, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017019, tc_HOL_Obool)), _1017021), _1017023)), _1017025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017019, tc_HOL_Obool)), _1017021), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017019, tc_HOL_Obool)), _1017023), _1017025))))], (44546 ^ _780478) ^ [_1672220, _1672222, _1672224] : [-(_1672220 = c_List_Olist_ONil(_1672222)), -(c_List_Olast(_1672222, hAPP(hAPP(c_List_Olist_OCons(_1672222), _1672224), _1672220)) = c_List_Olast(_1672222, _1672220))], (5893 ^ _780478) ^ [_874078, _874080, _874082] : [hBOOL(hAPP(hAPP(c_member(_874078), _874080), hAPP(hAPP(c_Set_Oinsert(_874078), _874082), c_Orderings_Obot__class_Obot(tc_fun(_874078, tc_HOL_Obool))))), -(_874080 = _874082)], (44173 ^ _780478) ^ [_1664490, _1664492, _1664494] : [-(hAPP(c_List_Orotate(_1664490, _1664492), _1664494) = hAPP(c_List_Orotate(_1664490, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1664492, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664490)), _1664494))), _1664494))], (9874 ^ _780478) ^ [_951691, _951693, _951695, _951697] : [class_Rings_Ocomm__semiring__1(_951691), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951691), _951693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951691), _951695), _951697)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951691), _951695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951691), _951693), _951697)))], (21400 ^ _780478) ^ [_1177828, _1177830, _1177832, _1177834] : [class_Rings_Olinordered__ring__strict(_1177828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177828), c_Groups_Ozero__class_Ozero(_1177828)), _1177830)), 21407 ^ _780478 : [(21414 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177828), _1177832), _1177834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177828), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177828), _1177830), _1177832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177828), _1177830), _1177834))))], (21408 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177828), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177828), _1177830), _1177832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1177828), _1177830), _1177834))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177828), _1177832), _1177834)))]]], (51255 ^ _780478) ^ [_1819070, _1819072, _1819074, _1819076] : [class_Rings_Ocomm__semiring__1(_1819070), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819070), _1819072), _1819074)), _1819076)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819070), _1819072), _1819076)))], (25411 ^ _780478) ^ [_1252451, _1252453, _1252455, _1252457] : [class_Fields_Ofield(_1252451), -(_1252453 = c_Groups_Ozero__class_Ozero(_1252451)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1252451), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252451), _1252455), _1252453)), _1252457) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252451), hAPP(hAPP(c_Power_Opower__class_Opower(_1252451), _1252455), _1252457)), hAPP(hAPP(c_Power_Opower__class_Opower(_1252451), _1252453), _1252457)))], (48473 ^ _780478) ^ [_1757899, _1757901, _1757903, _1757905, _1757907] : [hBOOL(hAPP(hAPP(_1757899, _1757901), _1757903)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757905, _1757907, _1757899), _1757903), _1757901)))], (6079 ^ _780478) ^ [_877222, _877224, _877226, _877228] : [6080 ^ _780478 : [(6083 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_877222), _877224), _877228))], (6081 ^ _780478) ^ [] : [_877224 = _877226]], -(hBOOL(hAPP(hAPP(c_member(_877222), _877224), hAPP(hAPP(c_Set_Oinsert(_877222), _877226), _877228))))], (42438 ^ _780478) ^ [_1624185, _1624187, _1624189] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1624185), _1624187)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1624185)), hAPP(c_Set_OCollect(tc_List_Olist(_1624185)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1624185), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1624185)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1624185), tc_fun(_1624185, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1624185, tc_HOL_Obool), tc_fun(tc_fun(_1624185, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1624185)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1624185, tc_HOL_Obool))), c_List_Oset(_1624185))), _1624187))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1624185), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1624185)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1624185)))), _1624189))))))], (17484 ^ _780478) ^ [_1105176, _1105178, _1105180, _1105182, _1105184] : [_1105176 = c_Orderings_Obot__class_Obot(tc_fun(_1105178, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105178, tc_fun(_1105180, tc_HOL_Obool)), _1105176), hAPP(hAPP(c_COMBB(tc_fun(_1105180, tc_HOL_Obool), tc_fun(_1105180, tc_HOL_Obool), _1105178), hAPP(c_Set_Oinsert(_1105180), _1105182)), _1105184)) = c_Orderings_Obot__class_Obot(tc_fun(_1105180, tc_HOL_Obool)))], (19940 ^ _780478) ^ [_1152437, _1152439, _1152441] : [class_Rings_Olinordered__ring__strict(_1152437), 19943 ^ _780478 : [(19958 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152437), _1152439), _1152441)), c_Groups_Ozero__class_Ozero(_1152437)))), 19959 ^ _780478 : [(19966 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152437), _1152439), c_Groups_Ozero__class_Ozero(_1152437))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152437), c_Groups_Ozero__class_Ozero(_1152437)), _1152441))], (19960 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152437), c_Groups_Ozero__class_Ozero(_1152437)), _1152439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152437), _1152441), c_Groups_Ozero__class_Ozero(_1152437)))]]], (19944 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1152437), _1152439), _1152441)), c_Groups_Ozero__class_Ozero(_1152437))), 19949 ^ _780478 : [(19952 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152437), _1152441), c_Groups_Ozero__class_Ozero(_1152437))))], (19950 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152437), c_Groups_Ozero__class_Ozero(_1152437)), _1152439)))]], 19953 ^ _780478 : [(19956 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152437), c_Groups_Ozero__class_Ozero(_1152437)), _1152441)))], (19954 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1152437), _1152439), c_Groups_Ozero__class_Ozero(_1152437))))]]]]], (31381 ^ _780478) ^ [_1366722, _1366724, _1366726] : [class_Orderings_Olinorder(_1366722), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366722), _1366724)), -(_1366724 = c_Orderings_Obot__class_Obot(tc_fun(_1366722, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1366722), _1366726), c_Big__Operators_Olattice_OInf__fin(_1366722, c_Orderings_Oord__class_Omin(_1366722), _1366724)) = c_Big__Operators_Olattice_OInf__fin(_1366722, c_Orderings_Oord__class_Omin(_1366722), hAPP(c_Set_OCollect(_1366722), hAPP(hAPP(c_COMBB(tc_fun(_1366722, tc_HOL_Obool), tc_HOL_Obool, _1366722), c_HOL_OEx(_1366722)), hAPP(hAPP(c_COMBC(_1366722, tc_fun(_1366722, tc_HOL_Obool), tc_fun(_1366722, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366722, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1366722, tc_HOL_Obool), tc_fun(_1366722, tc_HOL_Obool)), _1366722), c_COMBS(_1366722, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366722, tc_HOL_Obool), tc_fun(_1366722, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1366722), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1366722), c_fconj)), hAPP(hAPP(c_COMBC(_1366722, tc_fun(_1366722, _1366722), tc_fun(_1366722, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1366722, tc_HOL_Obool), tc_fun(tc_fun(_1366722, _1366722), tc_fun(_1366722, tc_HOL_Obool)), _1366722), c_COMBB(_1366722, tc_HOL_Obool, _1366722)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1366722), _1366726))))), hAPP(hAPP(c_COMBC(_1366722, tc_fun(_1366722, tc_HOL_Obool), tc_HOL_Obool), c_member(_1366722)), _1366724))))))], (28308 ^ _780478) ^ [_1304465] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304465) = 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), _1304465))))], (37141 ^ _780478) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33078 ^ _780478) ^ [_1405608] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405608)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405608))], (26388 ^ _780478) ^ [_1269611, _1269613, _1269615, _1269617] : [class_Fields_Olinordered__field(_1269611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269611), _1269613), _1269615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269611), c_Groups_Ozero__class_Ozero(_1269611)), _1269617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269611), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269611), _1269613), _1269617)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269611), _1269615), _1269617))))], (25922 ^ _780478) ^ [_1261033, _1261035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261033)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1261033), _1261035)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1261033)), _1261035))], (5999 ^ _780478) ^ [_875864, _875866, _875868] : [-(hAPP(hAPP(c_Set_Oinsert(_875864), _875866), hAPP(hAPP(c_Set_Oinsert(_875864), _875866), _875868)) = hAPP(hAPP(c_Set_Oinsert(_875864), _875866), _875868))], (38630 ^ _780478) ^ [_1524182, _1524184] : [-(hAPP(c_Relation_ODomain(_1524182, _1524182), c_Relation_OId__on(_1524182, _1524184)) = _1524184)], (43702 ^ _780478) ^ [_1653330, _1653332, _1653334] : [-(hBOOL(hAPP(c_List_Odistinct(_1653330), hAPP(hAPP(c_List_Oappend(_1653330), _1653332), _1653334)))), hBOOL(hAPP(c_List_Odistinct(_1653330), _1653332)), hBOOL(hAPP(c_List_Odistinct(_1653330), _1653334)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1653330, tc_HOL_Obool)), hAPP(c_List_Oset(_1653330), _1653332)), hAPP(c_List_Oset(_1653330), _1653334)) = c_Orderings_Obot__class_Obot(tc_fun(_1653330, tc_HOL_Obool))], (52051 ^ _780478) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (15538 ^ _780478) ^ [_1060810, _1060812, _1060814, _1060816, _1060818] : [class_Groups_Ocomm__monoid__mult(_1060810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060812), _1060814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1060812, tc_HOL_Obool)), _1060816), _1060814)), 15552 ^ _780478 : [(15555 ^ _780478) ^ [] : [hAPP(_1060818, 15551 ^ [_1060810, _1060812, _1060814, _1060816, _1060818]) = c_Groups_Oone__class_Oone(_1060810)], (15553 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1060812), 15551 ^ [_1060810, _1060812, _1060814, _1060816, _1060818]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1060812, tc_HOL_Obool)), _1060814), _1060816))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1060812, _1060810), _1060818), _1060816) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1060812, _1060810), _1060818), _1060814))], (49796 ^ _780478) ^ [_1787364, _1787366, _1787368] : [c_Relation_Orefl__on(_1787364, _1787366, _1787368), c_Relation_Osym(_1787364, _1787368), c_Relation_Otrans(_1787364, _1787368), -(c_Equiv__Relations_Oequiv(_1787364, _1787366, _1787368))], (35367 ^ _780478) ^ [_1446985] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1446985) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1446985))], (42748 ^ _780478) ^ [_1632666, _1632668, _1632670, _1632672] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632666), tc_List_Olist(_1632666))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632666), tc_List_Olist(_1632666)), _1632668), _1632670)), c_List_Olistrel1(_1632666, _1632672))), 42753 ^ _780478 : [(42758 ^ _780478) ^ [] : [-(_1632670 = hAPP(hAPP(c_List_Olist__update(_1632666, _1632668), 42752 ^ [_1632666, _1632668, _1632670, _1632672]), 42751 ^ [_1632666, _1632668, _1632670, _1632672]))], (42756 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42752 ^ [_1632666, _1632668, _1632670, _1632672]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632666)), _1632668))))], (42754 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1632666, _1632666)), hAPP(hAPP(c_Product__Type_OPair(_1632666, _1632666), hAPP(hAPP(c_List_Onth(_1632666), _1632668), 42752 ^ [_1632666, _1632668, _1632670, _1632672])), 42751 ^ [_1632666, _1632668, _1632670, _1632672])), _1632672)))]]], (4966 ^ _780478) ^ [_856268, _856270, _856272, _856274] : [-(c_List_Olistrel(_856274, _856270) = c_List_Olistrel(_856272, _856268)), _856274 = _856272, _856270 = _856268], (13162 ^ _780478) ^ [_1013950, _1013952, _1013954, _1013956, _1013958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013950, tc_HOL_Obool)), _1013952), _1013954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013950, tc_HOL_Obool)), _1013956), _1013958)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013950, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013950, tc_HOL_Obool)), _1013952), _1013956)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013950, tc_HOL_Obool)), _1013954), _1013958))))], (22761 ^ _780478) ^ [_1204196, _1204198] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204196)), _1204198) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1204196), _1204198)))], (27856 ^ _780478) ^ [_1295811, _1295813, _1295815] : [class_Orderings_Oorder(_1295811), 27859 ^ _780478 : [(27866 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295811), _1295813), _1295815))), -(c_Orderings_Obot__class_Obot(tc_fun(_1295811, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1295811, _1295813, _1295815))], (27860 ^ _780478) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1295811, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1295811, _1295813, _1295815), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295811), _1295813), _1295815))]]], (28022 ^ _780478) ^ [_1298842, _1298844, _1298846, _1298848, _1298850] : [class_Orderings_Olinorder(_1298842), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298842, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1298842, _1298844, _1298846)), c_SetInterval_Oord__class_OatLeastAtMost(_1298842, _1298848, _1298850)) = c_SetInterval_Oord__class_OatLeastAtMost(_1298842, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1298842), _1298844), _1298848), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1298842), _1298846), _1298850)))], (25421 ^ _780478) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34515 ^ _780478) ^ [_1431326, _1431328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431326), _1431328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1431326)), c_Int_OBit1(_1431328))))], (7108 ^ _780478) ^ [_899125, _899127, _899129, _899131] : [class_Orderings_Oorder(_899125), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899125), _899127), _899129)), _899127 = _899131, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899125), _899131), _899129)))], (48225 ^ _780478) ^ [_1752565, _1752567, _1752569] : [c_FunDef_Ois__measure(_1752565, _1752567), -(c_FunDef_Ois__measure(tc_prod(_1752565, _1752569), hAPP(hAPP(c_COMBB(_1752565, tc_Nat_Onat, tc_prod(_1752565, _1752569)), _1752567), c_Product__Type_Ofst(_1752565, _1752569))))], (24191 ^ _780478) ^ [_1230813, _1230815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230813), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24194 ^ _780478 : [(24201 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230815), _1230813)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24195 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230815), _1230813)), 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)), _1230815)))]]], (51185 ^ _780478) ^ [_1817741, _1817743, _1817745, _1817747, _1817749] : [class_Divides_Osemiring__div(_1817741), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817741), _1817743), _1817745)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817741), _1817747), _1817749)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817741), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817741), _1817745), _1817743)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817741), _1817749), _1817747)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817741), _1817745), _1817749)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817741), _1817743), _1817747)))], (46995 ^ _780478) ^ [_1725792, _1725794, _1725796, _1725798] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725792)), _1725794) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725796)), _1725798), -(hAPP(hAPP(c_List_Ozip(_1725792, _1725796), hAPP(c_List_Orev(_1725792), _1725794)), hAPP(c_List_Orev(_1725796), _1725798)) = hAPP(c_List_Orev(tc_prod(_1725792, _1725796)), hAPP(hAPP(c_List_Ozip(_1725792, _1725796), _1725794), _1725798)))], (42095 ^ _780478) ^ [_1615264, _1615266, _1615268, _1615270] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615264)), hAPP(hAPP(c_List_Olist_OCons(_1615264), _1615266), _1615268)), c_List_Olists(_1615264, _1615270))), 42098 ^ _780478 : [(42101 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615264)), _1615268), c_List_Olists(_1615264, _1615270))))], (42099 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1615264), _1615266), _1615270)))]]], (11081 ^ _780478) ^ [_973999, _974001, _974003] : [-(hBOOL(hAPP(hAPP(c_member(_973999), _974001), _974003))), -(hBOOL(hAPP(hAPP(c_member(_973999), _974001), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973999, tc_HOL_Obool)), _974003))))], (6146 ^ _780478) ^ [_878628, _878630, _878632, _878634, _878636] : [-(hAPP(hAPP(c_Set_Oinsert(_878628), _878630), hAPP(hAPP(c_Set_Oinsert(_878628), _878632), c_Orderings_Obot__class_Obot(tc_fun(_878628, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_878628), _878634), hAPP(hAPP(c_Set_Oinsert(_878628), _878636), c_Orderings_Obot__class_Obot(tc_fun(_878628, tc_HOL_Obool))))), 6147 ^ _780478 : [(6154 ^ _780478) ^ [] : [_878630 = _878636, _878632 = _878634], (6148 ^ _780478) ^ [] : [_878630 = _878634, _878632 = _878636]]], (39325 ^ _780478) ^ [_1543948, _1543950] : [c_Wellfounded_Owf(_1543948, _1543950), -(c_Wellfounded_OwfP(_1543948, c_FunDef_Oin__rel(_1543948, _1543948, _1543950)))], (5728 ^ _780478) ^ [_868159, _868161, _868163, _868165] : [-(tc_fun(_868165, _868161) = tc_fun(_868163, _868159)), _868165 = _868163, _868161 = _868159], (24001 ^ _780478) ^ [_1226750, _1226752, _1226754, _1226756, _1226758] : [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), _1226750), _1226752)), _1226754)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226750), _1226756)), _1226758))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226758), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226750), _1226758)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226750), _1226754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226756), _1226752)))], (4086 ^ _780478) ^ [_842240, _842242, _842244, _842246, _842248, _842250, _842252, _842254] : [-(c_New__DSequence_Opos__bind(_842254, _842250, _842246, _842242) = c_New__DSequence_Opos__bind(_842252, _842248, _842244, _842240)), _842254 = _842252, _842250 = _842248, _842246 = _842244, _842242 = _842240], (50775 ^ _780478) ^ [_1807497, _1807499, _1807501] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1807497, _1807497)), hAPP(hAPP(c_Product__Type_OPair(_1807497, _1807497), hAPP(_1807499, hAPP(c_Nat_OSuc, 50776 ^ [_1807497, _1807499, _1807501]))), hAPP(_1807499, 50776 ^ [_1807497, _1807499, _1807501]))), c_Transitive__Closure_Ortrancl(_1807497, _1807501))), c_Wellfounded_Owf(_1807497, c_Transitive__Closure_Otrancl(_1807497, _1807501)), 50784 ^ _780478 : [(50785 ^ _780478) ^ [_1807763] : [-(hAPP(_1807499, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50783 ^ [_1807497, _1807499, _1807501]), _1807763)) = hAPP(_1807499, 50783 ^ [_1807497, _1807499, _1807501]))]]], (47393 ^ _780478) ^ [_1734137, _1734139, _1734141, _1734143, _1734145] : [hBOOL(hAPP(hAPP(c_member(_1734137), _1734139), hAPP(c_List_Oset(_1734137), _1734141))), -(hBOOL(hAPP(_1734143, _1734139))), -(c_List_OdropWhile(_1734137, _1734143, hAPP(hAPP(c_List_Oappend(_1734137), _1734141), _1734145)) = hAPP(hAPP(c_List_Oappend(_1734137), c_List_OdropWhile(_1734137, _1734143, _1734141)), _1734145))], (44372 ^ _780478) ^ [_1668922, _1668924, _1668926, _1668928] : [class_Orderings_Olinorder(_1668922), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1668924, _1668922, _1668926), _1668928), c_List_Olist_ONil(_1668924)) = hAPP(hAPP(c_List_Olist_OCons(_1668924), _1668928), c_List_Olist_ONil(_1668924)))], (38610 ^ _780478) ^ [_1523764, _1523766, _1523768] : [c_Wellfounded_Owf(_1523764, _1523766), c_Wellfounded_Owf(_1523764, _1523768), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1523764, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1523764, _1523764), _1523766)), hAPP(c_Relation_ORange(_1523764, _1523764), _1523768)) = c_Orderings_Obot__class_Obot(tc_fun(_1523764, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1523764, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1523764, _1523764), tc_HOL_Obool)), _1523766), _1523768)))], (48539 ^ _780478) ^ [_1759872, _1759874, _1759876, _1759878] : [-(hAPP(hAPP(c_List_Oappend(_1759872), c_List_Oreplicate(_1759872, _1759874, _1759876)), hAPP(hAPP(c_List_Olist_OCons(_1759872), _1759876), _1759878)) = hAPP(hAPP(c_List_Olist_OCons(_1759872), _1759876), hAPP(hAPP(c_List_Oappend(_1759872), c_List_Oreplicate(_1759872, _1759874, _1759876)), _1759878)))], (44163 ^ _780478) ^ [_1664329, _1664331] : [-(c_List_Orotate(_1664329, _1664331) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1664329), tc_List_Olist(_1664329)), _1664331), c_List_Orotate1(_1664329)))], (20938 ^ _780478) ^ [_1170301] : [20939 ^ _780478 : [(20940 ^ _780478) ^ [_1170343] : [_1170301 = hAPP(c_Nat_OSuc, _1170343)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170301)))], (48820 ^ _780478) ^ [_1765131, _1765133, _1765135] : [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), _1765131), _1765133))), -(hBOOL(hAPP(hAPP(_1765135, _1765131), _1765133))), 48827 ^ _780478 : [(48830 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48825 ^ [_1765131, _1765133, _1765135]), 48826 ^ [_1765131, _1765133, _1765135]))), -(hBOOL(hAPP(hAPP(_1765135, 48825 ^ [_1765131, _1765133, _1765135]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48826 ^ [_1765131, _1765133, _1765135]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48836 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1765135, 48825 ^ [_1765131, _1765133, _1765135]), 48826 ^ [_1765131, _1765133, _1765135]))], (48828 ^ _780478) ^ [] : [-(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), 48825 ^ [_1765131, _1765133, _1765135]), 48826 ^ [_1765131, _1765133, _1765135]))))]]], (42658 ^ _780478) ^ [_1630561, _1630563, _1630565, _1630567, _1630569, _1630571, _1630573] : [-(hAPP(hAPP(c_List_Ozip(_1630561, _1630563), hAPP(hAPP(c_List_Olist__update(_1630561, _1630565), _1630567), _1630569)), hAPP(hAPP(c_List_Olist__update(_1630563, _1630571), _1630567), _1630573)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1630561, _1630563), hAPP(hAPP(c_List_Ozip(_1630561, _1630563), _1630565), _1630571)), _1630567), hAPP(hAPP(c_Product__Type_OPair(_1630561, _1630563), _1630569), _1630573)))], (25613 ^ _780478) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29439 ^ _780478) ^ [_1327154, _1327156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327156)), -(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, _1327154, _1327156))))], (43039 ^ _780478) ^ [_1638859, _1638861] : [-(hAPP(hAPP(c_List_Otake(_1638859), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1638861) = c_List_Olist_ONil(_1638859))], (22359 ^ _780478) ^ [_1196268, _1196270, _1196272] : [class_Groups_Ocomm__monoid__add(_1196268), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1196268), _1196270), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1196272))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1196268), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1196268), _1196270), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1196272))), hAPP(_1196270, _1196272)))], (34691 ^ _780478) ^ [_1434550, _1434552] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1434550), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1434552))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1434550), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434552))), 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))))], (37491 ^ _780478) ^ [_1495321, _1495323] : [c_Equiv__Relations_Oequiv(_1495321, c_Orderings_Otop__class_Otop(tc_fun(_1495321, tc_HOL_Obool)), _1495323), -(c_Equiv__Relations_Oequivp(_1495321, hAPP(hAPP(c_COMBC(_1495321, tc_fun(tc_prod(_1495321, _1495321), tc_HOL_Obool), tc_fun(_1495321, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495321, tc_fun(tc_fun(tc_prod(_1495321, _1495321), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495321, _1495321), tc_HOL_Obool), tc_fun(_1495321, tc_HOL_Obool)), _1495321), c_COMBC(_1495321, tc_fun(tc_prod(_1495321, _1495321), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495321, tc_prod(_1495321, _1495321)), tc_fun(_1495321, tc_fun(tc_fun(tc_prod(_1495321, _1495321), tc_HOL_Obool), tc_HOL_Obool)), _1495321), hAPP(c_COMBB(tc_prod(_1495321, _1495321), tc_fun(tc_fun(tc_prod(_1495321, _1495321), tc_HOL_Obool), tc_HOL_Obool), _1495321), c_member(tc_prod(_1495321, _1495321)))), c_Product__Type_OPair(_1495321, _1495321)))), _1495323)))], (50924 ^ _780478) ^ [_1812636, _1812638, _1812640] : [c_List_Oall__interval__nat(_1812636, _1812638, _1812640), -(c_List_Olist__all(tc_Nat_Onat, _1812636, c_List_Oupt(_1812638, _1812640)))], (43049 ^ _780478) ^ [_1639042, _1639044] : [-(c_List_Olistrelp(_1639042, _1639044, c_List_Olist_ONil(_1639042), c_List_Olist_ONil(_1639042)))], (20512 ^ _780478) ^ [_1162981, _1162983, _1162985, _1162987] : [class_Rings_Olinordered__comm__semiring__strict(_1162981), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162981), _1162983), _1162985)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162981), c_Groups_Ozero__class_Ozero(_1162981)), _1162987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162981), _1162987), _1162983)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162981), _1162987), _1162985))))], (39091 ^ _780478) ^ [_1538480, _1538482, _1538484, _1538486] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538480), _1538482)), 39097 ^ _780478 : [(39100 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1538484), hAPP(_1538486, 39096 ^ [_1538480, _1538482, _1538484, _1538486])))], (39098 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1538480), 39096 ^ [_1538480, _1538482, _1538484, _1538486]), _1538482)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1538480, _1538484)), hAPP(hAPP(c_Product__Type_OSigma(_1538480, _1538484), _1538482), _1538486)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1538480, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1538484, tc_HOL_Obool), tc_Nat_Onat, _1538480), c_Finite__Set_Ocard(_1538484)), _1538486)), _1538482))], (23587 ^ _780478) ^ [_1218899, _1218901] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218899), _1218901)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1218899)), hAPP(c_Nat_OSuc, _1218901)))], (43638 ^ _780478) ^ [_1651563, _1651565, _1651567, _1651569] : [-(hAPP(hAPP(c_List_Otake(_1651563), _1651565), hAPP(hAPP(c_List_Oappend(_1651563), _1651567), _1651569)) = hAPP(hAPP(c_List_Oappend(_1651563), hAPP(hAPP(c_List_Otake(_1651563), _1651565), _1651567)), hAPP(hAPP(c_List_Otake(_1651563), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1651565), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651563)), _1651567))), _1651569)))], (44670 ^ _780478) ^ [_1674236, _1674238, _1674240] : [c_Fun_Oinj__on(_1674236, _1674238, _1674240, c_Orderings_Otop__class_Otop(tc_fun(_1674236, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1674236), tc_List_Olist(_1674238), hAPP(c_List_Omap(_1674236, _1674238), _1674240), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1674236), tc_HOL_Obool))))], (19590 ^ _780478) ^ [_1146441] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1146441) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17949 ^ _780478) ^ [_1114772, _1114774] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114772), _1114774))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114774), hAPP(c_Nat_OSuc, _1114772))))], (51993 ^ _780478) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (35039 ^ _780478) ^ [_1440639, _1440641, _1440643] : [class_Rings_Olinordered__idom(_1440639), 35042 ^ _780478 : [(35043 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440639), c_Groups_Ozero__class_Ozero(_1440639)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440639), hAPP(hAPP(c_Power_Opower__class_Opower(_1440639), _1440641), 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(_1440639), _1440643), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1440641 = c_Groups_Ozero__class_Ozero(_1440639), _1440643 = c_Groups_Ozero__class_Ozero(_1440639)], (35053 ^ _780478) ^ [] : [35054 ^ _780478 : [(35057 ^ _780478) ^ [] : [-(_1440643 = c_Groups_Ozero__class_Ozero(_1440639))], (35055 ^ _780478) ^ [] : [-(_1440641 = c_Groups_Ozero__class_Ozero(_1440639))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1440639), c_Groups_Ozero__class_Ozero(_1440639)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440639), hAPP(hAPP(c_Power_Opower__class_Opower(_1440639), _1440641), 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(_1440639), _1440643), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (13716 ^ _780478) ^ [_1025582, _1025584, _1025586] : [class_Lattices_Oab__semigroup__idem__mult(_1025582), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025582), _1025584)), -(_1025584 = c_Orderings_Obot__class_Obot(tc_fun(_1025582, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025582), _1025586)), -(_1025586 = c_Orderings_Obot__class_Obot(tc_fun(_1025582, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1025582, c_Groups_Otimes__class_Otimes(_1025582)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025582, tc_HOL_Obool)), _1025584), _1025586)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025582), hAPP(c_Finite__Set_Ofold1(_1025582, c_Groups_Otimes__class_Otimes(_1025582)), _1025584)), hAPP(c_Finite__Set_Ofold1(_1025582, c_Groups_Otimes__class_Otimes(_1025582)), _1025586)))], (43949 ^ _780478) ^ [_1659696, _1659698, _1659700, _1659702] : [_1659696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1659698), _1659696), hAPP(hAPP(c_List_Olist_OCons(_1659698), _1659700), _1659702)) = hAPP(hAPP(c_List_Olist_OCons(_1659698), _1659700), _1659702))], (20178 ^ _780478) ^ [_1156869, _1156871, _1156873] : [class_Rings_Oordered__cancel__semiring(_1156869), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156869), _1156871), _1156873)), c_Groups_Ozero__class_Ozero(_1156869)))), 20183 ^ _780478 : [(20190 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156869), _1156871), c_Groups_Ozero__class_Ozero(_1156869))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156869), c_Groups_Ozero__class_Ozero(_1156869)), _1156873))], (20184 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156869), c_Groups_Ozero__class_Ozero(_1156869)), _1156871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156869), _1156873), c_Groups_Ozero__class_Ozero(_1156869)))]]], (25773 ^ _780478) ^ [_1258470, _1258472] : [-(hAPP(c_Int_Onat, _1258470) = _1258472), 25776 ^ _780478 : [(25779 ^ _780478) ^ [] : [_1258470 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258472)], (25777 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258470)))]], 25780 ^ _780478 : [(25783 ^ _780478) ^ [] : [_1258472 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25781 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258470))]]], (24395 ^ _780478) ^ [_1233887, _1233889, _1233891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233889)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233889), _1233891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233887), _1233891)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233887), _1233889))))], (44815 ^ _780478) ^ [_1678312, _1678314, _1678316, _1678318] : [-(hAPP(hAPP(c_List_Omap(_1678312, _1678314), _1678316), c_List_Obutlast(_1678312, _1678318)) = c_List_Obutlast(_1678314, hAPP(hAPP(c_List_Omap(_1678312, _1678314), _1678316), _1678318)))], (41218 ^ _780478) ^ [_1589896, _1589898, _1589900] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589896, _1589896)), _1589898), c_Transitive__Closure_Ortrancl(_1589896, _1589900))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589896, _1589896)), _1589898), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589896, _1589896), tc_HOL_Obool), 41221 ^ [_1589896, _1589898, _1589900]), _1589900))))], (31692 ^ _780478) ^ [_1378786, _1378788, _1378790, _1378792] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1378786), _1378788)), 31698 ^ _780478 : [(31701 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1378790), hAPP(_1378792, 31697 ^ [_1378786, _1378788, _1378790, _1378792])))], (31699 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1378786), 31697 ^ [_1378786, _1378788, _1378790, _1378792]), _1378788)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1378790), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378786, tc_fun(_1378790, tc_HOL_Obool)), _1378788), _1378792))))], (3452 ^ _780478) ^ [_831969, _831971, _831973, _831975, _831977, _831979, _831981, _831983] : [-(c_List_Olist_Olist__case(_831983, _831979, _831975, _831971) = c_List_Olist_Olist__case(_831981, _831977, _831973, _831969)), _831983 = _831981, _831979 = _831977, _831975 = _831973, _831971 = _831969], (45593 ^ _780478) ^ [_1695663, _1695665, _1695667, _1695669, _1695671, _1695673, _1695675, _1695677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695663), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695665)), _1695667))), c_List_Olist__all2(_1695665, _1695669, _1695671, _1695667, _1695673), hBOOL(hAPP(hAPP(_1695671, _1695675), _1695677)), -(c_List_Olist__all2(_1695665, _1695669, _1695671, hAPP(hAPP(c_List_Olist__update(_1695665, _1695667), _1695663), _1695675), hAPP(hAPP(c_List_Olist__update(_1695669, _1695673), _1695663), _1695677)))], (37694 ^ _780478) ^ [_1499809, _1499811, _1499813, _1499815] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1499809), _1499811)), 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)), _1499813), _1499809)), 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)), _1499815), _1499811)), 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)), _1499813), _1499815)), _1499811)), c_FunDef_Omax__weak)))], (18077 ^ _780478) ^ [_1116935] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116935, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1116935, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1116935, tc_HOL_Obool)))], (31504 ^ _780478) ^ [_1371422, _1371424, _1371426] : [class_Lattices_Odistrib__lattice(_1371422), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371422), _1371424)), -(_1371424 = c_Orderings_Obot__class_Obot(tc_fun(_1371422, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1371422), _1371426)), -(_1371426 = c_Orderings_Obot__class_Obot(tc_fun(_1371422, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1371422), c_Big__Operators_Olattice__class_OInf__fin(_1371422, _1371424)), c_Big__Operators_Olattice__class_OInf__fin(_1371422, _1371426)) = c_Big__Operators_Olattice__class_OInf__fin(_1371422, hAPP(c_Set_OCollect(_1371422), hAPP(hAPP(c_COMBB(tc_fun(_1371422, tc_HOL_Obool), tc_HOL_Obool, _1371422), c_HOL_OEx(_1371422)), hAPP(hAPP(c_COMBB(tc_fun(_1371422, tc_fun(_1371422, tc_HOL_Obool)), tc_fun(_1371422, tc_HOL_Obool), _1371422), hAPP(c_COMBB(tc_fun(_1371422, tc_HOL_Obool), tc_HOL_Obool, _1371422), c_HOL_OEx(_1371422))), hAPP(hAPP(c_COMBC(_1371422, tc_fun(_1371422, tc_fun(_1371422, tc_HOL_Obool)), tc_fun(_1371422, tc_fun(_1371422, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1371422, tc_fun(tc_fun(_1371422, tc_HOL_Obool), tc_fun(_1371422, tc_HOL_Obool))), tc_fun(tc_fun(_1371422, tc_fun(_1371422, tc_HOL_Obool)), tc_fun(_1371422, tc_fun(_1371422, tc_HOL_Obool))), _1371422), c_COMBS(_1371422, tc_fun(_1371422, tc_HOL_Obool), tc_fun(_1371422, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1371422, tc_fun(_1371422, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1371422, tc_fun(tc_fun(_1371422, tc_HOL_Obool), tc_fun(_1371422, tc_HOL_Obool))), _1371422), hAPP(c_COMBB(tc_fun(_1371422, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1371422, tc_HOL_Obool), tc_fun(_1371422, tc_HOL_Obool)), _1371422), c_COMBS(_1371422, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1371422, tc_fun(_1371422, tc_HOL_Obool)), tc_fun(_1371422, tc_fun(_1371422, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1371422), hAPP(c_COMBB(tc_fun(_1371422, tc_HOL_Obool), tc_fun(_1371422, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1371422), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1371422), c_fconj))), hAPP(hAPP(c_COMBC(_1371422, tc_fun(_1371422, tc_fun(_1371422, _1371422)), tc_fun(_1371422, tc_fun(_1371422, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1371422, _1371422), tc_fun(_1371422, tc_HOL_Obool)), tc_fun(tc_fun(_1371422, tc_fun(_1371422, _1371422)), tc_fun(_1371422, tc_fun(_1371422, tc_HOL_Obool))), _1371422), c_COMBB(tc_fun(_1371422, _1371422), tc_fun(_1371422, tc_HOL_Obool), _1371422)), hAPP(hAPP(c_COMBB(tc_fun(_1371422, tc_HOL_Obool), tc_fun(tc_fun(_1371422, _1371422), tc_fun(_1371422, tc_HOL_Obool)), _1371422), c_COMBB(_1371422, tc_HOL_Obool, _1371422)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1371422)))))), hAPP(hAPP(c_COMBC(_1371422, tc_fun(_1371422, tc_HOL_Obool), tc_fun(_1371422, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1371422, tc_HOL_Obool), tc_fun(_1371422, tc_HOL_Obool)), _1371422), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1371422)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1371422), c_fconj), hAPP(hAPP(c_COMBC(_1371422, tc_fun(_1371422, tc_HOL_Obool), tc_HOL_Obool), c_member(_1371422)), _1371424)))), hAPP(hAPP(c_COMBC(_1371422, tc_fun(_1371422, tc_HOL_Obool), tc_HOL_Obool), c_member(_1371422)), _1371426))))))))], (36036 ^ _780478) ^ [_1465032, _1465034, _1465036, _1465038, _1465040] : [c_Equiv__Relations_Oequiv(_1465032, _1465034, _1465036), hBOOL(hAPP(hAPP(c_member(tc_prod(_1465032, _1465032)), hAPP(hAPP(c_Product__Type_OPair(_1465032, _1465032), _1465038), _1465040)), _1465036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465032, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1465032, _1465032, _1465036), hAPP(hAPP(c_Set_Oinsert(_1465032), _1465038), c_Orderings_Obot__class_Obot(tc_fun(_1465032, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1465032, _1465032, _1465036), hAPP(hAPP(c_Set_Oinsert(_1465032), _1465040), c_Orderings_Obot__class_Obot(tc_fun(_1465032, tc_HOL_Obool)))))))], (47371 ^ _780478) ^ [_1733761, _1733763, _1733765, _1733767] : [hBOOL(hAPP(_1733761, _1733763)), -(c_List_OdropWhile(_1733765, _1733761, hAPP(hAPP(c_List_Olist_OCons(_1733765), _1733763), _1733767)) = c_List_OdropWhile(_1733765, _1733761, _1733767))], (29936 ^ _780478) ^ [_1336059] : [class_Groups_Osgn__if(_1336059), -(c_Groups_Osgn__class_Osgn(_1336059, c_Groups_Ozero__class_Ozero(_1336059)) = c_Groups_Ozero__class_Ozero(_1336059))], (16226 ^ _780478) ^ [_1074701, _1074703, _1074705, _1074707] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074701, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074701, tc_HOL_Obool)), _1074703), _1074705)), _1074707) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074701, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074701, tc_HOL_Obool)), _1074703), _1074707)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074701, tc_HOL_Obool)), _1074705), _1074707)))], (44193 ^ _780478) ^ [_1664952, _1664954] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664952)), hAPP(c_List_Otl(_1664952), _1664954)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664952)), _1664954)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13624 ^ _780478) ^ [_1023746, _1023748, _1023750, _1023752, _1023754, _1023756, _1023758] : [c_Big__Operators_Ocomm__monoid__big(_1023746, _1023748, _1023750, _1023752, _1023754), 13627 ^ _780478 : [(13634 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1023748), _1023756))), -(hAPP(hAPP(_1023754, _1023758), _1023756) = _1023752)], (13628 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1023748), _1023756)), -(hAPP(hAPP(_1023754, _1023758), _1023756) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1023746, _1023748, _1023750), _1023758), _1023752), _1023756))]]], (11539 ^ _780478) ^ [_982660, _982662, _982664] : [class_Orderings_Olinorder(_982660), hBOOL(hAPP(c_Finite__Set_Ofinite(_982660), _982662)), -(_982664 = c_Orderings_Obot__class_Obot(tc_fun(_982660, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_982660, tc_HOL_Obool)), _982664), _982662)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_982660), c_Big__Operators_Olinorder__class_OMin(_982660, _982664)), c_Big__Operators_Olinorder__class_OMin(_982660, _982662)) = c_Big__Operators_Olinorder__class_OMin(_982660, _982662))], (38208 ^ _780478) ^ [_1514486, _1514488] : [-(c_Wellfounded_Owf(_1514486, hAPP(c_Wellfounded_Omeasure(_1514486), _1514488)))], (4044 ^ _780478) ^ [_841553, _841555, _841557, _841559, _841561, _841563, _841565, _841567] : [-(c_New__Random__Sequence_Oneg__map(_841567, _841563, _841559, _841555) = c_New__Random__Sequence_Oneg__map(_841565, _841561, _841557, _841553)), _841567 = _841565, _841563 = _841561, _841559 = _841557, _841555 = _841553], (19424 ^ _780478) ^ [_1144072] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1144072)], (21231 ^ _780478) ^ [_1175013, _1175015] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1175013), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175013), _1175015)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30506 ^ _780478) ^ [_1346606, _1346608, _1346610, _1346612, _1346614] : [class_Rings_Olinordered__idom(_1346606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346606), hAPP(c_Groups_Oabs__class_Oabs(_1346606), _1346608)), _1346610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346606), hAPP(c_Groups_Oabs__class_Oabs(_1346606), _1346612)), _1346614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346606), hAPP(c_Groups_Oabs__class_Oabs(_1346606), _1346608)), hAPP(c_Groups_Oabs__class_Oabs(_1346606), _1346612))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346606), _1346610), _1346614))))], (27559 ^ _780478) ^ [_1290030, _1290032] : [class_Rings_Oring__1(_1290030), -(hAPP(c_Int_Oring__1__class_Oof__int(_1290030), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1290032)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1290030), hAPP(c_Int_Oring__1__class_Oof__int(_1290030), _1290032)))], (35143 ^ _780478) ^ [_1442855, _1442857, _1442859] : [class_Rings_Olinordered__idom(_1442855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1442855), _1442857), c_Groups_Ozero__class_Ozero(_1442855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1442855), hAPP(hAPP(c_Power_Opower__class_Opower(_1442855), _1442857), 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)))), _1442859)))), c_Groups_Ozero__class_Ozero(_1442855))))], (7585 ^ _780478) ^ [_908101, _908103, _908105, _908107] : [hBOOL(hAPP(hAPP(c_member(_908101), _908103), _908105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908101, tc_HOL_Obool)), _908105), _908107)), -(hBOOL(hAPP(hAPP(c_member(_908101), _908103), _908107)))], (44131 ^ _780478) ^ [_1663696, _1663698, _1663700] : [hBOOL(hAPP(c_List_Odistinct(_1663696), _1663700)), -(hBOOL(hAPP(c_List_Odistinct(_1663696), hAPP(c_List_Orotate(_1663696, _1663698), _1663700))))], (48519 ^ _780478) ^ [_1759160, _1759162, _1759164, _1759166, _1759168] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1759162, _1759160)), hAPP(hAPP(c_Product__Type_OPair(_1759162, _1759160), _1759166), _1759168)), hAPP(c_Relation_Oconverse(_1759160, _1759162), _1759164))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1759160, _1759162, hAPP(hAPP(c_COMBC(_1759160, tc_fun(tc_prod(_1759160, _1759162), tc_HOL_Obool), tc_fun(_1759162, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1759162, tc_fun(tc_fun(tc_prod(_1759160, _1759162), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1759160, _1759162), tc_HOL_Obool), tc_fun(_1759162, tc_HOL_Obool)), _1759160), c_COMBC(_1759162, tc_fun(tc_prod(_1759160, _1759162), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1759162, tc_prod(_1759160, _1759162)), tc_fun(_1759162, tc_fun(tc_fun(tc_prod(_1759160, _1759162), tc_HOL_Obool), tc_HOL_Obool)), _1759160), hAPP(c_COMBB(tc_prod(_1759160, _1759162), tc_fun(tc_fun(tc_prod(_1759160, _1759162), tc_HOL_Obool), tc_HOL_Obool), _1759162), c_member(tc_prod(_1759160, _1759162)))), c_Product__Type_OPair(_1759160, _1759162)))), _1759164)), _1759166), _1759168)))], (44394 ^ _780478) ^ [_1669427, _1669429, _1669431, _1669433, _1669435] : [class_Orderings_Olinorder(_1669427), -(hAPP(c_List_Oset(_1669429), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669429, _1669427, _1669431), _1669433), _1669435)) = hAPP(hAPP(c_Set_Oinsert(_1669429), _1669433), hAPP(c_List_Oset(_1669429), _1669435)))], (530 ^ _780478) ^ [_788437, _788439, _788441, _788443, _788445, _788447, _788449, _788451, _788453, _788455] : [-(c_Typedef_Otype__definition(_788453, _788449, _788445, _788441, _788437)), c_Typedef_Otype__definition(_788455, _788451, _788447, _788443, _788439), _788455 = _788453, _788451 = _788449, _788447 = _788445, _788443 = _788441, _788439 = _788437], (45869 ^ _780478) ^ [_1701392, _1701394, _1701396, _1701398] : [class_Orderings_Olinorder(_1701392), -(hAPP(c_List_Oset(_1701394), c_List_Olinorder__class_Osort__key(_1701394, _1701392, _1701396, _1701398)) = hAPP(c_List_Oset(_1701394), _1701398))], (16284 ^ _780478) ^ [_1076491, _1076493] : [class_Lattices_Oboolean__algebra(_1076491), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076491), _1076493), hAPP(c_Groups_Ouminus__class_Ouminus(_1076491), _1076493)) = c_Orderings_Obot__class_Obot(_1076491))], (5058 ^ _780478) ^ [_857708, _857710] : [_857710 = _857708, -(c_Set_OCollect(_857710) = c_Set_OCollect(_857708))], (26862 ^ _780478) ^ [_1278167, _1278169, _1278171, _1278173] : [class_Fields_Olinordered__field(_1278167), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278167), _1278169), _1278171)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278167), c_Groups_Ozero__class_Ozero(_1278167)), _1278173)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278167), c_Groups_Ozero__class_Ozero(_1278167)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278167), _1278171), _1278169))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278167), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278167), _1278173), _1278171)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278167), _1278173), _1278169))))], (37742 ^ _780478) ^ [_1500887] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1500887)), -(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))), _1500887)), c_FunDef_Omax__weak)))], (10269 ^ _780478) ^ [_959415, _959417, _959419, _959421] : [class_Orderings_Olinorder(_959415), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_959415), _959417), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959415), _959419), _959421)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_959415), _959419), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959415), _959417), _959421)))], (47093 ^ _780478) ^ [_1727771, _1727773] : [-(hAPP(c_List_Orev(_1727771), _1727773) = hAPP(c_List_Ofoldl(tc_List_Olist(_1727771), _1727771, hAPP(c_COMBC(_1727771, tc_List_Olist(_1727771), tc_List_Olist(_1727771)), c_List_Olist_OCons(_1727771)), c_List_Olist_ONil(_1727771)), _1727773))], (22817 ^ _780478) ^ [_1205236] : [class_Rings_Osemiring__1(_1205236), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205236), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1205236))], (51889 ^ _780478) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11113 ^ _780478) ^ [_974534, _974536, _974538] : [class_Groups_Oab__group__add(_974534), -(hAPP(c_Groups_Ouminus__class_Ouminus(_974534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974534), _974536), _974538)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_974534), _974538), _974536))], (35559 ^ _780478) ^ [] : [-(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)))], (18323 ^ _780478) ^ [_1123307, _1123309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123307), _1123309)), 18326 ^ _780478 : [(18333 ^ _780478) ^ [] : [_1123309 = _1123307, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123309), hAPP(c_Nat_OSuc, _1123307))))], (18327 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123309), hAPP(c_Nat_OSuc, _1123307))), -(_1123309 = _1123307)]]], (8290 ^ _780478) ^ [_922467, _922469, _922471] : [class_Groups_Ogroup__add(_922467), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_922467), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922467), _922469), _922471)), _922471) = _922469)], (1574 ^ _780478) ^ [_803017, _803019] : [-(class_Rings_Oordered__cancel__semiring(_803017)), _803019 = _803017, class_Rings_Oordered__cancel__semiring(_803019)], (51667 ^ _780478) ^ [_1826048, _1826050, _1826052, _1826054] : [class_Divides_Osemiring__div(_1826048), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826048), _1826050), _1826052)), -(c_Divides_Odiv__class_Omod(_1826048, c_Divides_Odiv__class_Omod(_1826048, _1826054, _1826052), _1826050) = c_Divides_Odiv__class_Omod(_1826048, _1826054, _1826050))], (17360 ^ _780478) ^ [_1101211, _1101213, _1101215, _1101217] : [_1101211 = c_Orderings_Obot__class_Obot(tc_fun(_1101213, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101213, tc_fun(_1101215, tc_HOL_Obool)), _1101211), hAPP(c_COMBK(tc_fun(_1101215, tc_HOL_Obool), _1101213), _1101217)) = c_Orderings_Obot__class_Obot(tc_fun(_1101215, tc_HOL_Obool)))], (39658 ^ _780478) ^ [_1552660, _1552662] : [39659 ^ _780478 : [(39660 ^ _780478) ^ [_1552706] : [hBOOL(hAPP(_1552660, _1552706))]], -(hBOOL(hAPP(_1552660, c_Hilbert__Choice_OEps(_1552662, _1552660))))], (3786 ^ _780478) ^ [_837226, _837228] : [_837228 = _837226, -(c_Enum_Oenum__class_Oenum__ex(_837228) = c_Enum_Oenum__class_Oenum__ex(_837226))], (32674 ^ _780478) ^ [_1397596, _1397598, _1397600, _1397602] : [class_Fields_Olinordered__field__inverse__zero(_1397596), class_Int_Onumber(_1397596), 32681 ^ _780478 : [(32682 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), _1397598), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1397596), _1397600), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602)))), 32685 ^ _780478 : [(32692 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), c_Groups_Ozero__class_Ozero(_1397596)), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602)))), 32695 ^ _780478 : [(32702 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602)), c_Groups_Ozero__class_Ozero(_1397596)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), _1397598), c_Groups_Ozero__class_Ozero(_1397596))))], (32696 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602)), c_Groups_Ozero__class_Ozero(_1397596))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), _1397600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397596), _1397598), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602)))))]]], (32686 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), c_Groups_Ozero__class_Ozero(_1397596)), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397596), _1397598), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602))), _1397600)))]]], (32708 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), _1397598), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1397596), _1397600), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602))))), 32711 ^ _780478 : [(32714 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397596), _1397598), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602))), _1397600))], (32712 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), c_Groups_Ozero__class_Ozero(_1397596)), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602))))]], 32715 ^ _780478 : [(32718 ^ _780478) ^ [] : [32719 ^ _780478 : [(32722 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), _1397600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1397596), _1397598), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602))))], (32720 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602)), c_Groups_Ozero__class_Ozero(_1397596))))]], 32723 ^ _780478 : [(32726 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), _1397598), c_Groups_Ozero__class_Ozero(_1397596)))], (32724 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602)), c_Groups_Ozero__class_Ozero(_1397596)))]]], (32716 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1397596), c_Groups_Ozero__class_Ozero(_1397596)), hAPP(c_Int_Onumber__class_Onumber__of(_1397596), _1397602)))]]]]], (51901 ^ _780478) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (23719 ^ _780478) ^ [_1221531, _1221533, _1221535] : [class_Rings_Osemiring__1(_1221531), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1221531, _1221533, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1221535) = _1221535)], (34143 ^ _780478) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (51525 ^ _780478) ^ [_1823650, _1823652, _1823654] : [class_Divides_Oring__div(_1823650), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823650), _1823652), _1823654)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1823650), hAPP(c_Groups_Ouminus__class_Ouminus(_1823650), _1823654)), _1823652) = hAPP(c_Groups_Ouminus__class_Ouminus(_1823650), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1823650), _1823654), _1823652)))], (1594 ^ _780478) ^ [_803267, _803269] : [-(class_Groups_Ocancel__semigroup__add(_803267)), _803269 = _803267, class_Groups_Ocancel__semigroup__add(_803269)], (12922 ^ _780478) ^ [_1009418, _1009420, _1009422, _1009424] : [class_Lattices_Osemilattice__sup(_1009418), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009418), _1009420), _1009422)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009418), _1009424), _1009422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009418), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009418), _1009420), _1009424)), _1009422)))], (6564 ^ _780478) ^ [_887834, _887836] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887834, tc_HOL_Obool)), _887836), c_Orderings_Obot__class_Obot(tc_fun(_887834, tc_HOL_Obool))) = _887836)], (45953 ^ _780478) ^ [_1703174, _1703176, _1703178] : [c_List_Oconcat(_1703174, _1703176) = c_List_Oconcat(_1703174, _1703178), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1703174))), _1703176) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1703174))), _1703178), 45963 ^ _780478 : [(45966 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1703174), tc_List_Olist(_1703174), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1703174), tc_fun(tc_List_Olist(_1703174), tc_Nat_Onat), tc_fun(tc_List_Olist(_1703174), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1703174), tc_Nat_Onat), tc_fun(tc_List_Olist(_1703174), tc_HOL_Obool)), tc_List_Olist(_1703174)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1703174))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1703174)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1703174))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1703174)))), 45962 ^ [_1703174, _1703176, _1703178]))], (45964 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1703174), tc_List_Olist(_1703174))), 45962 ^ [_1703174, _1703176, _1703178]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1703174), tc_List_Olist(_1703174))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1703174), tc_List_Olist(_1703174)), _1703176), _1703178)))))]], -(_1703176 = _1703178)], (52073 ^ _780478) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (2220 ^ _780478) ^ [_812933, _812935] : [_812935 = _812933, -(c_SetInterval_Oord__class_OgreaterThan(_812935) = c_SetInterval_Oord__class_OgreaterThan(_812933))], (11347 ^ _780478) ^ [_979099, _979101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_979099, tc_HOL_Obool)), _979101), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_979099, tc_HOL_Obool)), _979101))), -(_979101 = c_Orderings_Obot__class_Obot(tc_fun(_979099, tc_HOL_Obool)))], (25051 ^ _780478) ^ [_1245797, _1245799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1245797)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245797), _1245799)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1245799), _1245797) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1245799), _1245797)), _1245797)))], (23539 ^ _780478) ^ [_1218012, _1218014, _1218016, _1218018, _1218020] : [class_Orderings_Olinorder(_1218012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218012), _1218014), _1218016)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218012), _1218018), _1218020)), 23550 ^ _780478 : [(23559 ^ _780478) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218012, _1218014), _1218016) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218012, _1218018), _1218020)), _1218014 = _1218018, _1218016 = _1218020], (23551 ^ _780478) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218012, _1218014), _1218016) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218012, _1218018), _1218020), 23554 ^ _780478 : [(23557 ^ _780478) ^ [] : [-(_1218016 = _1218020)], (23555 ^ _780478) ^ [] : [-(_1218014 = _1218018)]]]]], (51977 ^ _780478) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (10463 ^ _780478) ^ [_963005, _963007, _963009, _963011] : [class_Orderings_Olinorder(_963005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963005), _963007), _963009)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963005), _963007), hAPP(hAPP(c_Orderings_Oord__class_Omax(_963005), _963011), _963009))))], (41111 ^ _780478) ^ [_1587164, _1587166, _1587168] : [41114 ^ _780478 : [(41120 ^ _780478) ^ [] : [41113 ^ [_1587164, _1587166, _1587168] = 41116 ^ [_1587164, _1587166, _1587168]], (41118 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587164, _1587166)), hAPP(hAPP(c_Product__Type_OPair(_1587164, _1587166), 41112 ^ [_1587164, _1587166, _1587168]), 41116 ^ [_1587164, _1587166, _1587168])), _1587168)))], (41115 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587164, _1587166)), hAPP(hAPP(c_Product__Type_OPair(_1587164, _1587166), 41112 ^ [_1587164, _1587166, _1587168]), 41113 ^ [_1587164, _1587166, _1587168])), _1587168)))]], -(c_Relation_Osingle__valued(_1587164, _1587166, _1587168))], (26600 ^ _780478) ^ [_1273266, _1273268, _1273270, _1273272, _1273274] : [class_Fields_Olinordered__field(_1273266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273266), c_Groups_Ozero__class_Ozero(_1273266)), _1273268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273266), _1273268), _1273270)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273266), c_Groups_Ozero__class_Ozero(_1273266)), _1273272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273266), _1273272), _1273274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273266), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273266), _1273268), _1273274)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273266), _1273270), _1273272))))], (50405 ^ _780478) ^ [_1800358, _1800360, _1800362, _1800364] : [c_Fun_Obij__betw(_1800358, _1800360, _1800362, c_Orderings_Otop__class_Otop(tc_fun(_1800358, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800360, tc_HOL_Obool))), 50408 ^ _780478 : [(50415 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1800360), _1800364)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1800358), hAPP(c_Set_Ovimage(_1800358, _1800360, _1800362), _1800364))))], (50409 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1800358), hAPP(c_Set_Ovimage(_1800358, _1800360, _1800362), _1800364))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1800360), _1800364)))]]], (34301 ^ _780478) ^ [_1427451, _1427453] : [class_Int_Onumber__ring(_1427451), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1427451), hAPP(c_Int_Onumber__class_Onumber__of(_1427451), _1427453)), c_Groups_Oone__class_Oone(_1427451)) = hAPP(c_Int_Onumber__class_Onumber__of(_1427451), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1427453), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (25980 ^ _780478) ^ [_1262072, _1262074] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1262072, _1262074)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1262074), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1262072), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (15507 ^ _780478) ^ [_1060144, _1060146, _1060148, _1060150] : [class_Complete__Lattice_Ocomplete__lattice(_1060144), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060146), _1060148)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1060146, _1060144), _1060148), _1060150) = hAPP(hAPP(c_Finite__Set_Ofold(_1060146, _1060144, hAPP(hAPP(c_COMBB(_1060144, tc_fun(_1060144, _1060144), _1060146), c_Lattices_Osemilattice__sup__class_Osup(_1060144)), _1060150)), c_Orderings_Obot__class_Obot(_1060144)), _1060148))], (16394 ^ _780478) ^ [_1079028, _1079030, _1079032, _1079034] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079028, tc_HOL_Obool)), _1079030), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1079028, tc_HOL_Obool)), _1079032), _1079034)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079028, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079028, tc_HOL_Obool)), _1079030), _1079032)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079028, tc_HOL_Obool)), _1079030), _1079034)))], (27681 ^ _780478) ^ [_1292113, _1292115] : [class_Rings_Olinordered__idom(_1292113), 27684 ^ _780478 : [(27691 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292113), c_Groups_Ozero__class_Ozero(_1292113)), hAPP(c_Int_Oring__1__class_Oof__int(_1292113), _1292115))))], (27685 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292113), c_Groups_Ozero__class_Ozero(_1292113)), hAPP(c_Int_Oring__1__class_Oof__int(_1292113), _1292115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292115)))]]], (18654 ^ _780478) ^ [_1130750, _1130752, _1130754, _1130756, _1130758] : [_1130750 = c_Orderings_Obot__class_Obot(tc_fun(_1130752, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130754, tc_HOL_Obool)), _1130756), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1130752, tc_fun(_1130754, tc_HOL_Obool)), _1130750), _1130758)) = _1130756)], (5606 ^ _780478) ^ [_866318, _866320, _866322, _866324] : [-(tc_prod(_866324, _866320) = tc_prod(_866322, _866318)), _866324 = _866322, _866320 = _866318], (2516 ^ _780478) ^ [_817475, _817477, _817479, _817481] : [-(c_FunDef_Orp__inv__image(_817481, _817477) = c_FunDef_Orp__inv__image(_817479, _817475)), _817481 = _817479, _817477 = _817475], (18428 ^ _780478) ^ [_1125322, _1125324, _1125326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125324), _1125326)), -(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, _1125322)), _1125324)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1125322)), _1125326))))], (35477 ^ _780478) ^ [_1448651, _1448653] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1448651), _1448653) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 35478 ^ _780478 : [(35485 ^ _780478) ^ [] : [_1448651 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1448653 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (35479 ^ _780478) ^ [] : [_1448651 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1448653 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (39539 ^ _780478) ^ [_1548844, _1548846, _1548848, _1548850] : [c_Equiv__Relations_Ocongruent(_1548844, _1548846, _1548848, _1548850), 39542 ^ _780478 : [(39543 ^ _780478) ^ [_1548989] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548844, _1548844)), _1548989), _1548848)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1548844, _1548844, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1548844, tc_fun(_1548844, _1548846), tc_fun(_1548844, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548846, tc_HOL_Obool), tc_fun(tc_fun(_1548844, _1548846), tc_fun(_1548844, tc_HOL_Obool)), _1548844), c_COMBB(_1548846, tc_HOL_Obool, _1548844)), hAPP(hAPP(c_COMBB(_1548846, tc_fun(_1548846, tc_HOL_Obool), _1548844), c_fequal), _1548850))), _1548850)), _1548989)))]]], (27800 ^ _780478) ^ [_1294732, _1294734] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1294732, _1294734))))], (45266 ^ _780478) ^ [_1687824, _1687826, _1687828] : [hBOOL(hAPP(c_List_Olistsp(_1687824, _1687826), _1687828)), 45269 ^ _780478 : [(45270 ^ _780478) ^ [_1687913] : [hBOOL(hAPP(hAPP(c_member(_1687824), _1687913), hAPP(c_List_Oset(_1687824), _1687828))), -(hBOOL(hAPP(_1687826, _1687913)))]]], (10527 ^ _780478) ^ [_964106, _964108, _964110] : [class_Orderings_Olinorder(_964106), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964106), _964108), hAPP(hAPP(c_Orderings_Oord__class_Omax(_964106), _964108), _964110))))], (14619 ^ _780478) ^ [_1041841, _1041843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041841), _1041843)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041843), _1041841)), _1041841) = _1041843)], (37415 ^ _780478) ^ [_1492780] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1492780)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1492780)], (30863 ^ _780478) ^ [_1353839, _1353841, _1353843, _1353845, _1353847] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1353839, tc_fun(_1353841, tc_HOL_Obool)), _1353843), hAPP(hAPP(c_COMBS(_1353839, tc_fun(_1353841, tc_HOL_Obool), tc_fun(_1353841, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1353841, tc_HOL_Obool), tc_fun(tc_fun(_1353841, tc_HOL_Obool), tc_fun(_1353841, tc_HOL_Obool)), _1353839), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353841, tc_HOL_Obool))), _1353845)), _1353847)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353841, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353841, tc_HOL_Obool), hAPP(c_Set_Oimage(_1353839, tc_fun(_1353841, tc_HOL_Obool), _1353845), _1353843))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353841, tc_HOL_Obool), hAPP(c_Set_Oimage(_1353839, tc_fun(_1353841, tc_HOL_Obool), _1353847), _1353843))))], (9844 ^ _780478) ^ [_950908, _950910, _950912, _950914, _950916] : [class_Rings_Ocomm__semiring__1(_950908), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950908), _950910), _950912)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950908), _950914), _950916)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950908), _950914), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950908), _950910), _950912)), _950916)))], (43648 ^ _780478) ^ [_1651914, _1651916, _1651918, _1651920] : [hBOOL(hAPP(hAPP(c_member(_1651914), _1651916), hAPP(c_List_Oset(_1651914), _1651918))), -(c_List_Oremove1(_1651914, _1651916, hAPP(hAPP(c_List_Oappend(_1651914), _1651918), _1651920)) = hAPP(hAPP(c_List_Oappend(_1651914), c_List_Oremove1(_1651914, _1651916, _1651918)), _1651920))], (4292 ^ _780478) ^ [_845393, _845395, _845397, _845399] : [-(c_List_Omap(_845399, _845395) = c_List_Omap(_845397, _845393)), _845399 = _845397, _845395 = _845393], (624 ^ _780478) ^ [_789914, _789916, _789918, _789920] : [-(c_FunDef_Ois__measure(_789918, _789914)), c_FunDef_Ois__measure(_789920, _789916), _789920 = _789918, _789916 = _789914], (43009 ^ _780478) ^ [_1638427, _1638429, _1638431, _1638433] : [-(_1638427 = _1638429), -(c_List_Oremove1(_1638431, _1638427, hAPP(hAPP(c_List_Olist_OCons(_1638431), _1638429), _1638433)) = hAPP(hAPP(c_List_Olist_OCons(_1638431), _1638429), c_List_Oremove1(_1638431, _1638427, _1638433)))], (34015 ^ _780478) ^ [_1422753] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1422753)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422753))))], (34435 ^ _780478) ^ [_1429898, _1429900] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1429898)), c_Int_OBit0(_1429900)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1429898), _1429900)))], (34169 ^ _780478) ^ [_1425138, _1425140] : [class_Int_Onumber__ring(_1425138), class_Rings_Olinordered__idom(_1425138), 34176 ^ _780478 : [(34183 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1425140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425138), c_Groups_Oone__class_Oone(_1425138)), hAPP(c_Int_Onumber__class_Onumber__of(_1425138), _1425140))))], (34177 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425138), c_Groups_Oone__class_Oone(_1425138)), hAPP(c_Int_Onumber__class_Onumber__of(_1425138), _1425140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1425140)))]]], (49582 ^ _780478) ^ [_1783213] : [-(c_Relation_Oantisym(_1783213, c_Relation_OId(_1783213)))], (37969 ^ _780478) ^ [_1508012, _1508014, _1508016, _1508018, _1508020, _1508022, _1508024] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1508012, _1508014, _1508016), hAPP(hAPP(c_Relation_Orel__comp(_1508012, _1508018, _1508014), _1508020), _1508022)), _1508024) = hAPP(hAPP(c_Relation_Orel__comp(_1508012, _1508018, _1508016), _1508020), hAPP(hAPP(c_Relation_Orel__comp(_1508018, _1508014, _1508016), _1508022), _1508024)))], (23631 ^ _780478) ^ [_1219562, _1219564, _1219566, _1219568, _1219570] : [class_Orderings_Olinorder(_1219562), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219562, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219562, _1219564), _1219566)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219562, _1219568), _1219570))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219562), _1219566), _1219564))), 23642 ^ _780478 : [(23645 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219562), _1219566), _1219570)))], (23643 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219562), _1219568), _1219564)))]]], (45498 ^ _780478) ^ [_1693640, _1693642, _1693644, _1693646, _1693648, _1693650] : [c_List_Olist__all2(_1693640, _1693642, _1693644, _1693646, _1693648), -(c_List_Olist__all2(_1693640, _1693642, _1693644, hAPP(hAPP(c_List_Otake(_1693640), _1693650), _1693646), hAPP(hAPP(c_List_Otake(_1693642), _1693650), _1693648)))], (33650 ^ _780478) ^ [_1415046] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415046) = 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(_1415046)))))], (42595 ^ _780478) ^ [_1629285, _1629287] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1629285, _1629287) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1629285), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1629287)))], (6087 ^ _780478) ^ [_877387, _877389, _877391] : [-(hBOOL(hAPP(hAPP(c_member(_877387), _877389), hAPP(hAPP(c_Set_Oinsert(_877387), _877389), _877391))))], (42268 ^ _780478) ^ [_1619996, _1619998, _1620000] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1619996, tc_HOL_Obool)), hAPP(c_List_Oset(_1619996), _1619998)), hAPP(c_List_Oset(_1619996), hAPP(hAPP(c_List_Olist_OCons(_1619996), _1620000), _1619998)))))], (36782 ^ _780478) ^ [_1480127, _1480129] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480127, _1480129), c_Divides_Odivmod__nat(_1480127, _1480129))))], (14821 ^ _780478) ^ [_1046203, _1046205, _1046207, _1046209, _1046211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046203), _1046205)), -(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), _1046205), _1046207)), _1046209)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046203), _1046207)), _1046211)) = 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), _1046205), _1046203)), _1046207)), _1046209)), _1046211))], (19176 ^ _780478) ^ [_1140373, _1140375] : [class_Groups_Omonoid__add(_1140373), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140373), _1140375), c_Groups_Ozero__class_Ozero(_1140373)) = _1140375)], (21233 ^ _780478) ^ [_1175059, _1175061] : [_1175059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1175061), _1175059) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (19676 ^ _780478) ^ [_1147740] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1147740), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1147740)], (14993 ^ _780478) ^ [_1050019, _1050021, _1050023, _1050025, _1050027, _1050029] : [hBOOL(hAPP(hAPP(c_member(_1050019), _1050021), c_SetInterval_Oord_OgreaterThanAtMost(_1050019, _1050023, _1050025, _1050027, _1050029))), 14996 ^ _780478 : [(14999 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1050023, _1050021), _1050029)))], (14997 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1050025, _1050027), _1050021)))]]], (23489 ^ _780478) ^ [_1217156] : [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)), _1217156)), _1217156)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217156), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6428 ^ _780478) ^ [_884970, _884972, _884974, _884976, _884978] : [c_Finite__Set_Ofolding__one(_884970, _884972, _884974), hBOOL(hAPP(c_Finite__Set_Ofinite(_884970), _884976)), hBOOL(hAPP(hAPP(c_member(_884970), _884978), _884976)), 6439 ^ _780478 : [(6446 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_884970, tc_HOL_Obool)), _884976), hAPP(hAPP(c_Set_Oinsert(_884970), _884978), c_Orderings_Obot__class_Obot(tc_fun(_884970, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_884970, tc_HOL_Obool))), -(hAPP(_884974, _884976) = hAPP(hAPP(_884972, _884978), hAPP(_884974, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_884970, tc_HOL_Obool)), _884976), hAPP(hAPP(c_Set_Oinsert(_884970), _884978), c_Orderings_Obot__class_Obot(tc_fun(_884970, tc_HOL_Obool)))))))], (6440 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_884970, tc_HOL_Obool)), _884976), hAPP(hAPP(c_Set_Oinsert(_884970), _884978), c_Orderings_Obot__class_Obot(tc_fun(_884970, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_884970, tc_HOL_Obool)), -(hAPP(_884974, _884976) = _884978)]]], (34527 ^ _780478) ^ [_1431528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1431528)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1431528))))], (40853 ^ _780478) ^ [_1580442, _1580444, _1580446, _1580448] : [-(hAPP(c_Relation_Oconverse(_1580442, _1580444), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1580442, _1580444), tc_HOL_Obool)), _1580446), _1580448)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1580444, _1580442), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1580442, _1580444), _1580446)), hAPP(c_Relation_Oconverse(_1580442, _1580444), _1580448)))], (10153 ^ _780478) ^ [_956863, _956865, _956867] : [class_Groups_Ogroup__add(_956863), 10156 ^ _780478 : [(10163 ^ _780478) ^ [] : [_956867 = hAPP(c_Groups_Ouminus__class_Ouminus(_956863), _956865), -(_956865 = hAPP(c_Groups_Ouminus__class_Ouminus(_956863), _956867))], (10157 ^ _780478) ^ [] : [_956865 = hAPP(c_Groups_Ouminus__class_Ouminus(_956863), _956867), -(_956867 = hAPP(c_Groups_Ouminus__class_Ouminus(_956863), _956865))]]], (44205 ^ _780478) ^ [_1665213, _1665215] : [class_Lattices_Oab__semigroup__idem__mult(_1665213), -(_1665215 = c_List_Olist_ONil(_1665213)), -(hAPP(c_Finite__Set_Ofold1(_1665213, c_Groups_Otimes__class_Otimes(_1665213)), hAPP(c_List_Oset(_1665213), _1665215)) = hAPP(c_List_Ofoldl(_1665213, _1665213, c_Groups_Otimes__class_Otimes(_1665213), hAPP(c_List_Ohd(_1665213), _1665215)), hAPP(c_List_Otl(_1665213), _1665215)))], (42418 ^ _780478) ^ [_1623442, _1623444, _1623446] : [-(hBOOL(hAPP(hAPP(c_member(_1623442), _1623444), hAPP(c_List_Oset(_1623442), _1623446)))), 42419 ^ _780478 : [(42420 ^ _780478) ^ [_1623516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623516), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623442)), _1623446))), hAPP(hAPP(c_List_Onth(_1623442), _1623446), _1623516) = _1623444]]], (36272 ^ _780478) ^ [_1470292, _1470294, _1470296, _1470298, _1470300, _1470302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470292, tc_fun(_1470294, tc_HOL_Obool))), _1470296), _1470298)), hBOOL(hAPP(hAPP(_1470296, _1470300), _1470302)), -(hBOOL(hAPP(hAPP(_1470298, _1470300), _1470302)))], (34385 ^ _780478) ^ [_1429040] : [_1429040 = c_Int_OPls, -(c_Int_OBit0(_1429040) = c_Int_OPls)], (23761 ^ _780478) ^ [_1222293, _1222295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222295)), -(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), _1222293), _1222295))))], (30687 ^ _780478) ^ [_1350332, _1350334] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1350332, tc_HOL_Obool), tc_HOL_Obool)), _1350334), hAPP(c_Set_OPow(_1350332), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350332, tc_HOL_Obool), _1350334)))))], (45939 ^ _780478) ^ [_1702836, _1702838, _1702840, _1702842, _1702844] : [class_Orderings_Olinorder(_1702836), -(c_List_Olinorder__class_Osort__key(_1702838, _1702836, _1702840, hAPP(hAPP(c_List_Olist_OCons(_1702838), _1702842), _1702844)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1702838, _1702836, _1702840), _1702842), c_List_Olinorder__class_Osort__key(_1702838, _1702836, _1702840, _1702844)))], (6600 ^ _780478) ^ [_888632, _888634, _888636, _888638] : [hBOOL(hAPP(hAPP(c_member(_888632), _888634), _888636)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888632, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_888632), _888634), _888638)), _888636) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888632, tc_HOL_Obool)), _888638), _888636))], (39729 ^ _780478) ^ [_1554069, _1554071, _1554073, _1554075, _1554077, _1554079] : [c_Fun_Oinj__on(_1554069, _1554071, hAPP(c_Fun_Ocomp(_1554073, _1554071, _1554069, _1554075), _1554077), _1554079), -(c_Fun_Oinj__on(_1554069, _1554073, _1554077, _1554079))], (48176 ^ _780478) ^ [_1751737, _1751739, _1751741, _1751743] : [c_List_Olist__all(_1751737, _1751739, hAPP(hAPP(c_List_Oappend(_1751737), _1751741), _1751743)), 48179 ^ _780478 : [(48182 ^ _780478) ^ [] : [-(c_List_Olist__all(_1751737, _1751739, _1751743))], (48180 ^ _780478) ^ [] : [-(c_List_Olist__all(_1751737, _1751739, _1751741))]]], (23423 ^ _780478) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (42834 ^ _780478) ^ [_1634649, _1634651] : [hBOOL(hAPP(c_List_Odistinct(_1634649), _1634651)), -(hAPP(c_Finite__Set_Ocard(_1634649), hAPP(c_List_Oset(_1634649), _1634651)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634649)), _1634651))], (43105 ^ _780478) ^ [_1640012, _1640014, _1640016] : [-(hAPP(hAPP(c_List_Olist__update(_1640012, c_List_Olist_ONil(_1640012)), _1640014), _1640016) = c_List_Olist_ONil(_1640012))], (39664 ^ _780478) ^ [_1552764, _1552766, _1552768] : [hBOOL(hAPP(_1552764, _1552766)), -(hBOOL(hAPP(_1552764, c_Hilbert__Choice_OEps(_1552768, _1552764))))], (46127 ^ _780478) ^ [_1707830, _1707832, _1707834, _1707836] : [hBOOL(hAPP(hAPP(c_member(_1707830), _1707832), hAPP(c_List_Oset(_1707830), _1707834))), -(hBOOL(hAPP(_1707836, _1707832))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707830)), hAPP(c_List_Ofilter(_1707830, _1707836), _1707834))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707830)), _1707834))))], (36510 ^ _780478) ^ [_1475027] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1475027) = 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)))], (13990 ^ _780478) ^ [_1030628, _1030630, _1030632] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030628), _1030630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030632), _1030630), -(_1030628 = _1030632)], (20002 ^ _780478) ^ [_1153537, _1153539, _1153541] : [class_Rings_Oordered__cancel__semiring(_1153537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153537), c_Groups_Ozero__class_Ozero(_1153537)), _1153539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153537), _1153541), c_Groups_Ozero__class_Ozero(_1153537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153537), _1153541), _1153539)), c_Groups_Ozero__class_Ozero(_1153537))))], (14717 ^ _780478) ^ [_1043877, _1043879, _1043881, _1043883] : [class_Groups_Ocomm__monoid__mult(_1043877), 14720 ^ _780478 : [(14727 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1043879), _1043881))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1043879, _1043877), _1043883), _1043881) = c_Groups_Oone__class_Oone(_1043877))], (14721 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1043879), _1043881)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1043879, _1043877), _1043883), _1043881) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1043877, _1043879, c_Groups_Otimes__class_Otimes(_1043877)), _1043883), c_Groups_Oone__class_Oone(_1043877)), _1043881))]]], (27958 ^ _780478) ^ [_1297424, _1297426] : [class_Orderings_Oorder(_1297424), -(c_SetInterval_Oord__class_OatLeastAtMost(_1297424, _1297426, _1297426) = hAPP(hAPP(c_Set_Oinsert(_1297424), _1297426), c_Orderings_Obot__class_Obot(tc_fun(_1297424, tc_HOL_Obool))))], (38820 ^ _780478) ^ [_1530058, _1530060, _1530062, _1530064, _1530066] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530058, _1530060), _1530062), hAPP(hAPP(c_COMBS(_1530058, tc_fun(_1530060, tc_HOL_Obool), tc_fun(_1530060, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1530060, tc_HOL_Obool), tc_fun(tc_fun(_1530060, tc_HOL_Obool), tc_fun(_1530060, tc_HOL_Obool)), _1530058), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1530060, tc_HOL_Obool))), _1530064)), _1530066)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1530058, _1530060), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530058, _1530060), _1530062), _1530064)), hAPP(hAPP(c_Product__Type_OSigma(_1530058, _1530060), _1530062), _1530066)))], (1384 ^ _780478) ^ [_800642, _800644] : [-(class_Lattices_Osemilattice__sup(_800642)), _800644 = _800642, class_Lattices_Osemilattice__sup(_800644)], (43377 ^ _780478) ^ [_1646065, _1646067, _1646069, _1646071, _1646073] : [-(hAPP(hAPP(c_List_Olist_OCons(_1646065), _1646067), _1646069) = hAPP(hAPP(c_List_Oappend(_1646065), _1646071), _1646073)), 43378 ^ _780478 : [(43385 ^ _780478) ^ [_1646248] : [hAPP(hAPP(c_List_Olist_OCons(_1646065), _1646067), _1646248) = _1646071, _1646069 = hAPP(hAPP(c_List_Oappend(_1646065), _1646248), _1646073)], (43379 ^ _780478) ^ [] : [_1646071 = c_List_Olist_ONil(_1646065), hAPP(hAPP(c_List_Olist_OCons(_1646065), _1646067), _1646069) = _1646073]]], (12912 ^ _780478) ^ [_1009257, _1009259, _1009261] : [class_Lattices_Osemilattice__sup(_1009257), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009257), _1009259), _1009261)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009257), _1009261), _1009259) = _1009261)], (14016 ^ _780478) ^ [_1031105, _1031107, _1031109] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031107), _1031109)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031105), _1031109)))], (1824 ^ _780478) ^ [_806142, _806144] : [-(class_Rings_Osemiring(_806142)), _806144 = _806142, class_Rings_Osemiring(_806144)], (48427 ^ _780478) ^ [_1756868, _1756870, _1756872, _1756874] : [-(c_New__Random__Sequence_Opos__map(_1756868, _1756870, _1756872, _1756874) = c_New__Random__Sequence_Opos__bind(_1756868, _1756870, _1756874, hAPP(c_Fun_Ocomp(_1756870, 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(_1756870))))), _1756868, c_New__Random__Sequence_Opos__single(_1756870)), _1756872)))], (38654 ^ _780478) ^ [_1524733, _1524735, _1524737] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1524733, _1524735)), _1524737)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1524733), hAPP(c_Relation_ODomain(_1524733, _1524735), _1524737))))], (10193 ^ _780478) ^ [_957650, _957652, _957654, _957656] : [class_Orderings_Olinorder(_957650), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957650), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957650), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957650), _957652), _957654)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957650), _957652), _957656))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957650), _957652), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957650), _957654), _957656)))))], (49750 ^ _780478) ^ [_1786659, _1786661] : [c_Relation_Osym(_1786659, hAPP(c_Relation_Oconverse(_1786659, _1786659), _1786661)), -(c_Relation_Osym(_1786659, _1786661))], (18259 ^ _780478) ^ [_1121991, _1121993, _1121995] : [class_Rings_Ocomm__semiring__1(_1121991), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121991), hAPP(hAPP(c_Power_Opower__class_Opower(_1121991), _1121993), _1121995)), _1121993) = hAPP(hAPP(c_Power_Opower__class_Opower(_1121991), _1121993), hAPP(c_Nat_OSuc, _1121995)))], (34165 ^ _780478) ^ [] : [-(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)))))], (20724 ^ _780478) ^ [_1166700, _1166702] : [class_Groups_Oordered__ab__group__add(_1166700), 20727 ^ _780478 : [(20734 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166700), c_Groups_Ozero__class_Ozero(_1166700)), _1166702)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166700), hAPP(c_Groups_Ouminus__class_Ouminus(_1166700), _1166702)), c_Groups_Ozero__class_Ozero(_1166700))))], (20728 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166700), hAPP(c_Groups_Ouminus__class_Ouminus(_1166700), _1166702)), c_Groups_Ozero__class_Ozero(_1166700))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166700), c_Groups_Ozero__class_Ozero(_1166700)), _1166702)))]]], (21768 ^ _780478) ^ [_1184625, _1184627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1184625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1184627)), -(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), _1184627), _1184625))))], (31787 ^ _780478) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (26402 ^ _780478) ^ [_1269880, _1269882, _1269884, _1269886] : [class_Fields_Olinordered__field(_1269880), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269880), _1269882), _1269884)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269880), _1269886), c_Groups_Ozero__class_Ozero(_1269880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269880), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269880), _1269884), _1269886)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269880), _1269882), _1269886))))], (24501 ^ _780478) ^ [_1235679, _1235681, _1235683] : [class_Groups_Oordered__ab__group__add(_1235679), -(hAPP(c_Set_Oimage(_1235679, _1235679, c_Groups_Ouminus__class_Ouminus(_1235679)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1235679, _1235681, _1235683)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1235679, hAPP(c_Groups_Ouminus__class_Ouminus(_1235679), _1235683), hAPP(c_Groups_Ouminus__class_Ouminus(_1235679), _1235681)))], (6532 ^ _780478) ^ [_887128, _887130, _887132, _887134] : [hBOOL(hAPP(hAPP(c_member(_887128), _887130), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887128, tc_HOL_Obool)), _887132), _887134))), hBOOL(hAPP(hAPP(c_member(_887128), _887130), _887134))], (29836 ^ _780478) ^ [_1334499, _1334501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334499)), -(c_SMT_Oz3mod(_1334501, _1334499) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1334501, _1334499))], (52241 ^ _780478) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (47651 ^ _780478) ^ [_1740017, _1740019, _1740021, _1740023, _1740025] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1740017, _1740019)), hAPP(_1740017, _1740021))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1740023, _1740023)), hAPP(hAPP(c_Product__Type_OPair(_1740023, _1740023), _1740019), _1740021)), c_List_Omeasures(_1740023, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1740023, tc_Nat_Onat)), _1740017), _1740025)))))], (37127 ^ _780478) ^ [_1486654] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1486654)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1486654)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19194 ^ _780478) ^ [_1140658, _1140660] : [class_Rings_Ocomm__semiring__1(_1140658), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140658), _1140660), c_Groups_Ozero__class_Ozero(_1140658)) = _1140660)], (720 ^ _780478) ^ [_791316, _791318, _791320, _791322, _791324, _791326, _791328, _791330] : [-(c_Wellfounded_Omax__extp(_791328, _791324, _791320, _791316)), c_Wellfounded_Omax__extp(_791330, _791326, _791322, _791318), _791330 = _791328, _791326 = _791324, _791322 = _791320, _791318 = _791316], (43225 ^ _780478) ^ [_1642400, _1642402] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642400)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642402)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642400), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1642402)) = c_List_Olist_ONil(tc_Int_Oint))], (43095 ^ _780478) ^ [_1639843, _1639845] : [_1639845 = c_List_Olist_ONil(_1639843), -(c_Orderings_Obot__class_Obot(tc_fun(_1639843, tc_HOL_Obool)) = hAPP(c_List_Oset(_1639843), _1639845))], (51961 ^ _780478) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (33989 ^ _780478) ^ [_1422327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1422327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1422327)))], (23503 ^ _780478) ^ [_1217398, _1217400, _1217402, _1217404, _1217406] : [class_Orderings_Olinorder(_1217398), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217398, _1217400), _1217402) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1217398, _1217404), _1217406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217398), _1217400), _1217402)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217398), _1217404), _1217406)), -(_1217402 = _1217406)], (30590 ^ _780478) ^ [_1348299, _1348301, _1348303] : [class_Rings_Olinordered__idom(_1348299), 30593 ^ _780478 : [(30602 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348299), hAPP(c_Groups_Oabs__class_Oabs(_1348299), _1348301)), _1348303))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348299), _1348301), _1348303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348299), hAPP(c_Groups_Ouminus__class_Ouminus(_1348299), _1348301)), _1348303))], (30594 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348299), hAPP(c_Groups_Oabs__class_Oabs(_1348299), _1348301)), _1348303)), 30597 ^ _780478 : [(30600 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348299), hAPP(c_Groups_Ouminus__class_Ouminus(_1348299), _1348301)), _1348303)))], (30598 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1348299), _1348301), _1348303)))]]]]], (48461 ^ _780478) ^ [_1757716, _1757718, _1757720] : [-(_1757718 = _1757720), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757716, _1757716, hAPP(hAPP(c_COMBB(tc_fun(_1757716, tc_HOL_Obool), tc_fun(_1757716, tc_HOL_Obool), _1757716), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1757716), c_fNot)), c_fequal)), _1757718), _1757720)))], (44147 ^ _780478) ^ [_1664034] : [-(hAPP(c_List_Otl(_1664034), c_List_Olist_ONil(_1664034)) = c_List_Olist_ONil(_1664034))], (29492 ^ _780478) ^ [_1328007, _1328009, _1328011] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1328007), _1328009)), _1328011) = 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), _1328007), _1328011)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1328009), _1328011))), 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, _1328007, _1328011)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328009, _1328011))), _1328011)))], (51401 ^ _780478) ^ [_1821566, _1821568] : [51402 ^ _780478 : [(51405 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821568), _1821566))], (51403 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821566), _1821568)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821566, _1821568))], (35357 ^ _780478) ^ [_1446854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1446854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1446854))))], (51971 ^ _780478) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (25221 ^ _780478) ^ [_1249147, _1249149, _1249151, _1249153] : [class_Fields_Ofield__inverse__zero(_1249147), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1249147), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249147), _1249149), _1249151)), _1249153) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249147), hAPP(hAPP(c_Power_Opower__class_Opower(_1249147), _1249149), _1249153)), hAPP(hAPP(c_Power_Opower__class_Opower(_1249147), _1249151), _1249153)))], (1274 ^ _780478) ^ [_799267, _799269] : [-(class_Int_Onumber__ring(_799267)), _799269 = _799267, class_Int_Onumber__ring(_799269)], (40915 ^ _780478) ^ [_1582026, _1582028] : [-(c_Transitive__Closure_Otrancl(_1582026, hAPP(c_Relation_Oconverse(_1582026, _1582026), _1582028)) = hAPP(c_Relation_Oconverse(_1582026, _1582026), c_Transitive__Closure_Otrancl(_1582026, _1582028)))], (49975 ^ _780478) ^ [_1790383, _1790385] : [c_Equiv__Relations_Opart__equivp(_1790383, _1790385), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1790383, tc_HOL_Obool)), 49978 ^ [_1790383, _1790385]), hAPP(hAPP(c_COMBB(tc_fun(_1790383, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1790383, tc_HOL_Obool)), c_HOL_OEx(_1790383)), hAPP(hAPP(c_COMBB(tc_fun(_1790383, tc_HOL_Obool), tc_fun(_1790383, tc_HOL_Obool), tc_fun(_1790383, tc_HOL_Obool)), hAPP(c_COMBS(_1790383, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1790383), c_fconj), hAPP(hAPP(c_COMBS(_1790383, _1790383, tc_HOL_Obool), _1790385), c_COMBI(_1790383))))), hAPP(hAPP(c_COMBC(tc_fun(_1790383, tc_HOL_Obool), tc_fun(_1790383, tc_fun(_1790383, tc_HOL_Obool)), tc_fun(_1790383, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1790383, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1790383, tc_fun(_1790383, tc_HOL_Obool)), tc_fun(_1790383, tc_HOL_Obool)), tc_fun(_1790383, tc_HOL_Obool)), c_COMBB(tc_fun(_1790383, tc_HOL_Obool), tc_HOL_Obool, _1790383)), c_fequal)), _1790385))))))], (37722 ^ _780478) ^ [_1500371, _1500373, _1500375, _1500377] : [-(hAPP(c_Relation_OField(_1500371), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1500371, _1500371)), hAPP(hAPP(c_Product__Type_OPair(_1500371, _1500371), _1500373), _1500375)), _1500377)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1500371, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1500371), _1500373), hAPP(hAPP(c_Set_Oinsert(_1500371), _1500375), c_Orderings_Obot__class_Obot(tc_fun(_1500371, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1500371), _1500377)))], (25914 ^ _780478) ^ [_1260858, _1260860, _1260862] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1260858, tc_Nat_Onat), _1260860), _1260862) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1260858, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1260858), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1260860)), _1260862)))], (11945 ^ _780478) ^ [_990374, _990376, _990378] : [class_Orderings_Olinorder(_990374), hBOOL(hAPP(c_Finite__Set_Ofinite(_990374), _990376)), -(_990376 = c_Orderings_Obot__class_Obot(tc_fun(_990374, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_990374, c_Orderings_Oord__class_Omin(_990374), hAPP(hAPP(c_Set_Oinsert(_990374), _990378), _990376)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_990374), _990378), c_Big__Operators_Olattice_OInf__fin(_990374, c_Orderings_Oord__class_Omin(_990374), _990376)))], (51437 ^ _780478) ^ [_1822214, _1822216] : [51438 ^ _780478 : [(51441 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822216), _1822214))], (51439 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822214), _1822216)))]], -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822214, _1822216) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (33094 ^ _780478) ^ [_1405891, _1405893] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405891)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405893)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1405891), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1405893))))], (3810 ^ _780478) ^ [_837612, _837614] : [_837614 = _837612, -(c_New__DSequence_Opos__not__seq(_837614) = c_New__DSequence_Opos__not__seq(_837612))], (3758 ^ _780478) ^ [_836776, _836778, _836780, _836782] : [-(c_List_Omeasures(_836782, _836778) = c_List_Omeasures(_836780, _836776)), _836782 = _836780, _836778 = _836776], (14743 ^ _780478) ^ [_1044344, _1044346, _1044348] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044344), _1044346)), -(hAPP(c_Finite__Set_Ocard(_1044344), hAPP(hAPP(c_Set_Oinsert(_1044344), _1044348), _1044346)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1044344), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044344, tc_HOL_Obool)), _1044346), hAPP(hAPP(c_Set_Oinsert(_1044344), _1044348), c_Orderings_Obot__class_Obot(tc_fun(_1044344, tc_HOL_Obool)))))))], (40935 ^ _780478) ^ [_1582422, _1582424, _1582426] : [-(hAPP(c_Relation_ORange(_1582422, _1582424), _1582426) = hAPP(c_Relation_ODomain(_1582424, _1582422), hAPP(c_Relation_Oconverse(_1582422, _1582424), _1582426)))], (3516 ^ _780478) ^ [_832959, _832961] : [_832961 = _832959, -(c_SetInterval_Oord__class_OlessThan(_832961) = c_SetInterval_Oord__class_OlessThan(_832959))], (40377 ^ _780478) ^ [_1569368, _1569370] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569368, _1569368)), hAPP(hAPP(c_Product__Type_OPair(_1569368, _1569368), 40378 ^ [_1569368, _1569370]), 40378 ^ [_1569368, _1569370])), c_Transitive__Closure_Otrancl(_1569368, _1569370)))), -(c_Wellfounded_Oacyclic(_1569368, _1569370))], (3748 ^ _780478) ^ [_836627, _836629, _836631, _836633] : [-(c_List_Olex(_836633, _836629) = c_List_Olex(_836631, _836627)), _836633 = _836631, _836629 = _836627], (3550 ^ _780478) ^ [_833486, _833488] : [_833488 = _833486, -(c_SetInterval_Oord__class_OatMost(_833488) = c_SetInterval_Oord__class_OatMost(_833486))], (30053 ^ _780478) ^ [_1338021, _1338023, _1338025] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338021, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338023), _1338025)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338023), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1338021), _1338023), _1338025))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338021, _1338023)))], (51841 ^ _780478) ^ [_1828631, _1828633] : [class_Orderings_Obot(_1828631), -(class_Orderings_Obot(tc_fun(_1828633, _1828631)))], (10383 ^ _780478) ^ [_961600, _961602] : [class_Orderings_Olinorder(_961600), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_961600), _961602), _961602) = _961602)], (17310 ^ _780478) ^ [_1099964, _1099966, _1099968, _1099970, _1099972, _1099974, _1099976] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099964, tc_fun(_1099966, tc_fun(_1099968, tc_HOL_Obool))), _1099970), _1099972), _1099974), _1099976))), 17311 ^ _780478 : [(17312 ^ _780478) ^ [_1100049] : [hBOOL(hAPP(hAPP(c_member(_1099964), _1100049), _1099970)), hBOOL(hAPP(hAPP(hAPP(_1099972, _1100049), _1099974), _1099976))]]], (33903 ^ _780478) ^ [_1420975, _1420977] : [c_Int_OBit1(_1420975) = c_Int_OBit1(_1420977), -(_1420975 = _1420977)], (18456 ^ _780478) ^ [_1126163, _1126165, _1126167, _1126169, _1126171] : [hBOOL(hAPP(hAPP(c_member(_1126163), _1126165), _1126167)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1126169, tc_HOL_Obool)), hAPP(_1126171, _1126165)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1126163, tc_fun(_1126169, tc_HOL_Obool)), _1126167), _1126171)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1126163, tc_fun(_1126169, tc_HOL_Obool)), _1126167), _1126171))], (24739 ^ _780478) ^ [_1240094, _1240096, _1240098] : [class_Orderings_Olinorder(_1240094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240094), _1240096), _1240098)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1240094, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1240094, _1240096, _1240098)), hAPP(hAPP(c_Set_Oinsert(_1240094), _1240098), c_Orderings_Obot__class_Obot(tc_fun(_1240094, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1240094, _1240096, _1240098))], (13140 ^ _780478) ^ [_1013489, _1013491, _1013493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013489, tc_HOL_Obool)), _1013491), _1013493)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013489, tc_HOL_Obool)), _1013491), _1013493) = _1013493)], (9862 ^ _780478) ^ [_951405, _951407, _951409, _951411] : [class_Rings_Ocomm__semiring__1(_951405), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951405), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951405), _951407), _951409)), _951411) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951405), _951407), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951405), _951409), _951411)))], (43179 ^ _780478) ^ [_1641520, _1641522, _1641524, _1641526] : [-(hAPP(hAPP(c_List_Otake(_1641520), _1641522), hAPP(hAPP(c_List_Olist_OCons(_1641520), _1641524), _1641526)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1641520), c_List_Olist_ONil(_1641520), hAPP(hAPP(c_COMBB(tc_List_Olist(_1641520), tc_List_Olist(_1641520), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1641520), _1641524)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1641520), tc_List_Olist(_1641520)), c_List_Otake(_1641520)), _1641526)), _1641522))], (46909 ^ _780478) ^ [_1723909, _1723911, _1723913, _1723915] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1723909), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1723909))), _1723911))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723913), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1723909))), c_List_Otranspose(_1723909, _1723911)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723915), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1723909))), hAPP(c_List_Ofilter(tc_List_Olist(_1723909), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1723909)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723913)), c_Nat_Osize__class_Osize(tc_List_Olist(_1723909)))), _1723911)))), -(hAPP(hAPP(c_List_Onth(_1723909), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1723909)), c_List_Otranspose(_1723909, _1723911)), _1723913)), _1723915) = hAPP(hAPP(c_List_Onth(_1723909), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1723909)), _1723911), _1723915)), _1723913))], (8676 ^ _780478) ^ [_930601, _930603, _930605, _930607] : [class_Groups_Oab__semigroup__mult(_930601), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930601), _930603), _930605)), _930607) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930601), _930603), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930601), _930605), _930607)))], (11411 ^ _780478) ^ [_980398, _980400, _980402, _980404] : [class_Orderings_Olinorder(_980398), hBOOL(hAPP(c_Finite__Set_Ofinite(_980398), _980400)), -(hAPP(hAPP(c_Finite__Set_Ofold(_980398, _980398, c_Orderings_Oord__class_Omin(_980398)), _980402), hAPP(hAPP(c_Set_Oinsert(_980398), _980404), _980400)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_980398), _980404), hAPP(hAPP(c_Finite__Set_Ofold(_980398, _980398, c_Orderings_Oord__class_Omin(_980398)), _980402), _980400)))], (11155 ^ _780478) ^ [_975561] : [class_Orderings_Olinorder(_975561), -(c_Finite__Set_Ofun__left__comm__idem(_975561, _975561, c_Orderings_Oord__class_Omin(_975561)))], (278 ^ _780478) ^ [_784761, _784763, _784765, _784767] : [-(c_FunDef_Oreduction__pair(_784765, _784761)), c_FunDef_Oreduction__pair(_784767, _784763), _784767 = _784765, _784763 = _784761], (50228 ^ _780478) ^ [_1796705, _1796707] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1796705), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1796707, hAPP(c_Code__Numeral_Onat__of, 50233 ^ [_1796705, _1796707]))), -(hBOOL(hAPP(_1796707, _1796705)))], (32992 ^ _780478) ^ [_1403853, _1403855, _1403857, _1403859, _1403861, _1403863] : [c_Equiv__Relations_Oequiv(_1403853, _1403855, _1403857), c_Equiv__Relations_Ocongruent(_1403853, tc_fun(_1403859, tc_HOL_Obool), _1403857, _1403861), hBOOL(hAPP(hAPP(c_member(_1403853), _1403863), _1403855)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403853, tc_fun(_1403859, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403853, _1403853, _1403857), hAPP(hAPP(c_Set_Oinsert(_1403853), _1403863), c_Orderings_Obot__class_Obot(tc_fun(_1403853, tc_HOL_Obool))))), _1403861) = hAPP(_1403861, _1403863))], (38180 ^ _780478) ^ [_1514008, _1514010, _1514012, _1514014, _1514016, _1514018, _1514020, _1514022] : [hBOOL(hAPP(hAPP(_1514008, _1514010), _1514012)), hBOOL(hAPP(hAPP(_1514014, _1514012), _1514016)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1514018, _1514020, _1514022, _1514008, _1514014), _1514010), _1514016)))], (44276 ^ _780478) ^ [_1666686, _1666688, _1666690, _1666692, _1666694] : [c_Finite__Set_Ofun__left__comm__idem(_1666686, _1666688, _1666690), -(hAPP(hAPP(c_Finite__Set_Ofold(_1666686, _1666688, _1666690), _1666692), hAPP(c_List_Oset(_1666686), _1666694)) = hAPP(c_List_Ofoldl(_1666688, _1666686, hAPP(c_COMBC(_1666686, _1666688, _1666688), _1666690), _1666692), _1666694))], (46631 ^ _780478) ^ [_1718343, _1718345, _1718347, _1718349, _1718351] : [class_Orderings_Olinorder(_1718343), c_List_Olinorder__class_Osorted(_1718343, hAPP(hAPP(c_List_Omap(_1718345, _1718343), _1718347), _1718349)), -(c_List_Olinorder__class_Osorted(_1718343, hAPP(hAPP(c_List_Omap(_1718345, _1718343), _1718347), c_List_Oremove1(_1718345, _1718351, _1718349))))], (49133 ^ _780478) ^ [_1772502, _1772504, _1772506, _1772508] : [-(c_Random__Sequence_Omap(_1772502, _1772504, _1772506, _1772508) = c_Random__Sequence_Obind(_1772502, _1772504, _1772508, hAPP(c_Fun_Ocomp(_1772504, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1772504)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1772502, c_Random__Sequence_Osingle(_1772504)), _1772506)))], (17821 ^ _780478) ^ [_1112682, _1112684] : [hAPP(c_Nat_OSuc, _1112682) = hAPP(c_Nat_OSuc, _1112684), -(_1112682 = _1112684)], (28396 ^ _780478) ^ [_1305942, _1305944] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1305942), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1305944), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1305942, _1305944))], (49258 ^ _780478) ^ [_1775555, _1775557, _1775559] : [hBOOL(hAPP(hAPP(c_member(_1775557), _1775555), c_Orderings_Obot__class_Obot(tc_fun(_1775557, tc_HOL_Obool)))), hBOOL(hAPP(_1775559, _1775555))], (5164 ^ _780478) ^ [_859393, _859395] : [_859395 = _859393, -(c_Orderings_Otop__class_Otop(_859395) = c_Orderings_Otop__class_Otop(_859393))], (8060 ^ _780478) ^ [_917999, _918001, _918003, _918005, _918007, _918009] : [c_Finite__Set_Ofun__left__comm(_917999, _918001, _918003), hBOOL(hAPP(c_Finite__Set_Ofinite(_917999), _918005)), -(hBOOL(hAPP(hAPP(c_member(_917999), _918007), _918005))), -(hAPP(hAPP(c_Finite__Set_Ofold(_917999, _918001, _918003), _918009), hAPP(hAPP(c_Set_Oinsert(_917999), _918007), _918005)) = hAPP(hAPP(c_Finite__Set_Ofold(_917999, _918001, _918003), hAPP(hAPP(_918003, _918007), _918009)), _918005))], (18281 ^ _780478) ^ [_1122477, _1122479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122477), _1122479)), -(_1122479 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122477), 18284 ^ [_1122477, _1122479])))], (20470 ^ _780478) ^ [_1162188, _1162190, _1162192] : [class_Rings_Olinordered__ring__strict(_1162188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162188), _1162190), c_Groups_Ozero__class_Ozero(_1162188))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162188), _1162192), c_Groups_Ozero__class_Ozero(_1162188))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162188), c_Groups_Ozero__class_Ozero(_1162188)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162188), _1162190), _1162192))))], (17819 ^ _780478) ^ [_1112641] : [hAPP(c_Nat_OSuc, _1112641) = _1112641], (40369 ^ _780478) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (43915 ^ _780478) ^ [_1658860, _1658862, _1658864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658860)), _1658864)), _1658862)), -(hAPP(hAPP(c_List_Odrop(_1658860), _1658862), _1658864) = c_List_Olist_ONil(_1658860))], (44215 ^ _780478) ^ [_1665373, _1665375, _1665377, _1665379] : [44216 ^ _780478 : [(44217 ^ _780478) ^ [_1665470, _1665472] : [_1665373 = hAPP(hAPP(c_List_Olist_OCons(_1665375), _1665472), _1665470)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1665375), tc_List_Olist(_1665375))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1665375), tc_List_Olist(_1665375)), _1665377), hAPP(hAPP(c_List_Oappend(_1665375), _1665377), _1665373))), c_List_Olexord(_1665375, _1665379))))], (17105 ^ _780478) ^ [_1095059, _1095061, _1095063] : [class_Orderings_Olinorder(_1095059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095059), _1095061)), -(_1095061 = c_Orderings_Obot__class_Obot(tc_fun(_1095059, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1095059), _1095063)), -(_1095063 = c_Orderings_Obot__class_Obot(tc_fun(_1095059, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1095059, tc_HOL_Obool)), _1095061), _1095063) = c_Orderings_Obot__class_Obot(tc_fun(_1095059, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1095059, c_Orderings_Oord__class_Omin(_1095059), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1095059, tc_HOL_Obool)), _1095061), _1095063)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095059), c_Big__Operators_Olattice_OInf__fin(_1095059, c_Orderings_Oord__class_Omin(_1095059), _1095061)), c_Big__Operators_Olattice_OInf__fin(_1095059, c_Orderings_Oord__class_Omin(_1095059), _1095063)))], (34821 ^ _780478) ^ [_1436883, _1436885] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1436883)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1436885))) = 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), _1436883), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1436885))))], (18191 ^ _780478) ^ [_1120666, _1120668, _1120670, _1120672, _1120674, _1120676] : [-(hAPP(c_Set_Ovimage(_1120666, _1120668, _1120670), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120672, tc_fun(_1120668, tc_HOL_Obool)), _1120674), _1120676)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120672, tc_fun(_1120666, tc_HOL_Obool)), _1120674), hAPP(hAPP(c_COMBB(tc_fun(_1120668, tc_HOL_Obool), tc_fun(_1120666, tc_HOL_Obool), _1120672), c_Set_Ovimage(_1120666, _1120668, _1120670)), _1120676)))], (52041 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (51989 ^ _780478) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (43825 ^ _780478) ^ [_1656777, _1656779, _1656781, _1656783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656777), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656779)), _1656781))), -(hAPP(hAPP(c_List_Olist__update(_1656779, _1656781), _1656777), _1656783) = hAPP(hAPP(c_List_Oappend(_1656779), hAPP(hAPP(c_List_Otake(_1656779), _1656777), _1656781)), hAPP(hAPP(c_List_Olist_OCons(_1656779), _1656783), hAPP(hAPP(c_List_Odrop(_1656779), hAPP(c_Nat_OSuc, _1656777)), _1656781))))], (39626 ^ _780478) ^ [_1551856, _1551858, _1551860, _1551862, _1551864, _1551866, _1551868] : [hAPP(c_Fun_Ocomp(_1551856, _1551858, _1551860, _1551862), _1551864) = hAPP(c_Fun_Ocomp(_1551858, _1551858, _1551860, c_Fun_Oid(_1551858)), _1551866), -(hAPP(_1551862, hAPP(_1551864, _1551868)) = hAPP(_1551866, _1551868))], (6552 ^ _780478) ^ [_887587, _887589, _887591, _887593] : [-(hBOOL(hAPP(hAPP(c_member(_887587), _887589), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887587, tc_HOL_Obool)), _887591), _887593)))), hBOOL(hAPP(hAPP(c_member(_887587), _887589), _887591)), -(hBOOL(hAPP(hAPP(c_member(_887587), _887589), _887593)))], (7876 ^ _780478) ^ [_914123, _914125, _914127, _914129, _914131, _914133] : [-(hBOOL(hAPP(hAPP(c_member(_914123), _914125), _914127))), -(hAPP(c_Fun_Ooverride__on(_914123, _914129, _914131, _914133, _914127), _914125) = hAPP(_914131, _914125))], (7559 ^ _780478) ^ [_907601, _907603, _907605, _907607] : [-(c_Nitpick_Ofold__graph_H(_907601, _907603, _907605, _907607, c_Orderings_Obot__class_Obot(tc_fun(_907601, tc_HOL_Obool)), _907607))], (44342 ^ _780478) ^ [_1668189, _1668191] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1668189), hAPP(c_List_Oset(tc_Nat_Onat), _1668191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1668189), 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)), _1668191))))], (33190 ^ _780478) ^ [_1407626] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407626))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407626)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36638 ^ _780478) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (48425 ^ _780478) ^ [_1756832, _1756834, _1756836] : [-(hAPP(c_New__DSequence_Oneg__single(_1756832, _1756834), _1756836) = c_Lazy__Sequence_Ohb__single(_1756832, _1756834))], (35255 ^ _780478) ^ [_1445323] : [c_Int_OBit1(_1445323) = c_Int_OMin, -(_1445323 = c_Int_OMin)], (51893 ^ _780478) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (13855 ^ _780478) ^ [] : [-(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))], (38556 ^ _780478) ^ [_1522092, _1522094, _1522096, _1522098] : [38557 ^ _780478 : [(38558 ^ _780478) ^ [_1522167] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1522096, _1522092)), hAPP(hAPP(c_Product__Type_OPair(_1522096, _1522092), _1522167), _1522094)), _1522098))]], -(hBOOL(hAPP(hAPP(c_member(_1522092), _1522094), hAPP(c_Relation_ORange(_1522096, _1522092), _1522098))))], (25401 ^ _780478) ^ [_1252303, _1252305, _1252307] : [class_Rings_Odivision__ring(_1252303), -(_1252305 = c_Groups_Ozero__class_Ozero(_1252303)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1252303), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252303), _1252307), _1252305)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252303), _1252307), hAPP(c_Groups_Ouminus__class_Ouminus(_1252303), _1252305)))], (24489 ^ _780478) ^ [_1235454, _1235456, _1235458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1235454), _1235456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235458), 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), _1235456), _1235458)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235454), _1235458))))], (11329 ^ _780478) ^ [_978727, _978729, _978731] : [class_Groups_Oab__group__add(_978727), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_978727), _978729), _978731) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978727), _978729), hAPP(c_Groups_Ouminus__class_Ouminus(_978727), _978731)))], (51965 ^ _780478) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (10275 ^ _780478) ^ [_959558, _959560, _959562, _959564] : [class_Orderings_Olinorder(_959558), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_959558), _959560), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959558), _959562), _959564)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_959558), _959562), hAPP(hAPP(c_Orderings_Oord__class_Omax(_959558), _959560), _959564)))], (35882 ^ _780478) ^ [_1461605, _1461607, _1461609, _1461611, _1461613] : [hBOOL(hAPP(hAPP(c_member(_1461605), _1461607), hAPP(c_Relation_OImage(_1461609, _1461605, _1461611), hAPP(hAPP(c_Set_Oinsert(_1461609), _1461613), c_Orderings_Obot__class_Obot(tc_fun(_1461609, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1461609, _1461605)), hAPP(hAPP(c_Product__Type_OPair(_1461609, _1461605), _1461613), _1461607)), _1461611)))], (51759 ^ _780478) ^ [_1827554, _1827556] : [class_Complete__Lattice_Ocomplete__lattice(_1827554), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1827556, _1827554)))], (18193 ^ _780478) ^ [_1120750, _1120752, _1120754] : [class_Complete__Lattice_Ocomplete__lattice(_1120750), 18196 ^ _780478 : [(18197 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120750), _1120752), c_Complete__Lattice_OInf__class_OInf(_1120750, _1120754))), 18200 ^ _780478 : [(18201 ^ _780478) ^ [_1120908] : [hBOOL(hAPP(hAPP(c_member(_1120750), _1120908), _1120754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120750), _1120752), _1120908)))]]], (18207 ^ _780478) ^ [] : [18209 ^ _780478 : [(18212 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120750), _1120752), 18208 ^ [_1120750, _1120752, _1120754]))], (18210 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1120750), 18208 ^ [_1120750, _1120752, _1120754]), _1120754)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120750), _1120752), c_Complete__Lattice_OInf__class_OInf(_1120750, _1120754))))]]], (28002 ^ _780478) ^ [_1298442, _1298444, _1298446, _1298448] : [class_Orderings_Olinorder(_1298442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298442), _1298444), _1298446)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1298442), _1298446), _1298448)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1298442, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1298442, _1298444), _1298446)), c_SetInterval_Oord__class_OatLeastAtMost(_1298442, _1298446, _1298448)) = c_SetInterval_Oord__class_OatLeastAtMost(_1298442, _1298444, _1298448))], (42694 ^ _780478) ^ [_1631531, _1631533, _1631535, _1631537, _1631539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631531), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631533)), _1631535))), 42697 ^ _780478 : [(42704 ^ _780478) ^ [] : [-(_1631531 = _1631537), -(hAPP(hAPP(c_List_Onth(_1631533), hAPP(hAPP(c_List_Olist__update(_1631533, _1631535), _1631531), _1631539)), _1631537) = hAPP(hAPP(c_List_Onth(_1631533), _1631535), _1631537))], (42698 ^ _780478) ^ [] : [_1631531 = _1631537, -(hAPP(hAPP(c_List_Onth(_1631533), hAPP(hAPP(c_List_Olist__update(_1631533, _1631535), _1631531), _1631539)), _1631537) = _1631539)]]], (51275 ^ _780478) ^ [_1819428, _1819430, _1819432, _1819434] : [class_Rings_Oidom(_1819428), 51278 ^ _780478 : [(51279 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819428), _1819430), _1819432)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819428), _1819430), _1819434))), -(_1819430 = c_Groups_Ozero__class_Ozero(_1819428)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819428), _1819432), _1819434)))], (51289 ^ _780478) ^ [] : [51290 ^ _780478 : [(51293 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819428), _1819432), _1819434))], (51291 ^ _780478) ^ [] : [_1819430 = c_Groups_Ozero__class_Ozero(_1819428)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819428), _1819430), _1819432)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819428), _1819430), _1819434))))]]], (50377 ^ _780478) ^ [_1799735, _1799737, _1799739, _1799741, _1799743] : [c_Fun_Obij__betw(_1799735, _1799737, _1799739, c_Orderings_Otop__class_Otop(tc_fun(_1799735, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799737, tc_HOL_Obool))), c_Fun_Obij__betw(_1799737, _1799741, _1799743, c_Orderings_Otop__class_Otop(tc_fun(_1799737, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799741, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1799735, _1799741, hAPP(c_Fun_Ocomp(_1799737, _1799741, _1799735, _1799743), _1799739), c_Orderings_Otop__class_Otop(tc_fun(_1799735, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1799741, tc_HOL_Obool))))], (7768 ^ _780478) ^ [_911903, _911905, _911907, _911909] : [-(hBOOL(hAPP(hAPP(c_member(_911903), _911905), _911907))), 7771 ^ _780478 : [(7778 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911903, tc_HOL_Obool)), _911907), _911909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911903, tc_HOL_Obool)), _911907), hAPP(hAPP(c_Set_Oinsert(_911903), _911905), _911909))))], (7772 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911903, tc_HOL_Obool)), _911907), hAPP(hAPP(c_Set_Oinsert(_911903), _911905), _911909))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911903, tc_HOL_Obool)), _911907), _911909)))]]], (28504 ^ _780478) ^ [_1308093, _1308095, _1308097] : [class_Orderings_Oorder(_1308093), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308093, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1308093), _1308095)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1308093, _1308095, _1308097)) = c_Orderings_Obot__class_Obot(tc_fun(_1308093, tc_HOL_Obool)))], (12181 ^ _780478) ^ [_994694, _994696] : [class_Orderings_Olinorder(_994694), hBOOL(hAPP(c_Finite__Set_Ofinite(_994694), _994696)), -(_994696 = c_Orderings_Obot__class_Obot(tc_fun(_994694, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_994694), hAPP(hAPP(c_Orderings_Oord__class_Omin(_994694), 12194 ^ [_994694, _994696]), 12195 ^ [_994694, _994696])), hAPP(hAPP(c_Set_Oinsert(_994694), 12194 ^ [_994694, _994696]), hAPP(hAPP(c_Set_Oinsert(_994694), 12195 ^ [_994694, _994696]), c_Orderings_Obot__class_Obot(tc_fun(_994694, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_994694), c_Big__Operators_Olattice_OInf__fin(_994694, c_Orderings_Oord__class_Omin(_994694), _994696)), _994696)))], (6226 ^ _780478) ^ [_880279, _880281, _880283, _880285, _880287, _880289] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_880279, _880281, _880283, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_880279), _880285), _880287), _880289)) = hAPP(hAPP(hAPP(_880283, _880285), _880287), _880289))], (25902 ^ _780478) ^ [_1260627, _1260629] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1260627), _1260629) = 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)), _1260627)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1260629))))], (10723 ^ _780478) ^ [_967545, _967547, _967549, _967551] : [class_Orderings_Olinorder(_967545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967545), _967547), _967549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967545), hAPP(hAPP(c_Orderings_Oord__class_Omin(_967545), _967547), _967551)), _967549)))], (43660 ^ _780478) ^ [_1652139, _1652141, _1652143, _1652145] : [43661 ^ _780478 : [(43664 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1652139), _1652141), hAPP(c_List_Oset(_1652139), c_List_Obutlast(_1652139, _1652145))))], (43662 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1652139), _1652141), hAPP(c_List_Oset(_1652139), c_List_Obutlast(_1652139, _1652143))))]], -(hBOOL(hAPP(hAPP(c_member(_1652139), _1652141), hAPP(c_List_Oset(_1652139), c_List_Obutlast(_1652139, hAPP(hAPP(c_List_Oappend(_1652139), _1652143), _1652145))))))], (4682 ^ _780478) ^ [_851740, _851742, _851744, _851746, _851748, _851750, _851752, _851754] : [-(c_Product__Type_Oscomp(_851754, _851750, _851746, _851742) = c_Product__Type_Oscomp(_851752, _851748, _851744, _851740)), _851754 = _851752, _851750 = _851748, _851746 = _851744, _851742 = _851740], (22668 ^ _780478) ^ [_1202561] : [_1202561 = 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), _1202561)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33146 ^ _780478) ^ [_1406744, _1406746] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406744) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406746)), 33149 ^ _780478 : [(33152 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406746)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33150 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406744))))]], 33153 ^ _780478 : [(33156 ^ _780478) ^ [] : [33157 ^ _780478 : [(33160 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406744) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (33158 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406746))))]], 33161 ^ _780478 : [(33164 ^ _780478) ^ [] : [_1406744 = _1406746], (33162 ^ _780478) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406746)))]]], (33154 ^ _780478) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406744)))]]], (1654 ^ _780478) ^ [_804017, _804019] : [-(class_Rings_Oordered__semiring(_804017)), _804019 = _804017, class_Rings_Oordered__semiring(_804019)], (31246 ^ _780478) ^ [_1362327, _1362329, _1362331, _1362333] : [-(hBOOL(hAPP(hAPP(c_member(_1362327), _1362329), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1362327, tc_HOL_Obool)), _1362331), hAPP(c_Set_OCollect(_1362327), _1362333))))), hBOOL(hAPP(hAPP(c_member(_1362327), _1362329), _1362331)), hBOOL(hAPP(_1362333, _1362329))], (29750 ^ _780478) ^ [_1332850, _1332852, _1332854] : [-(hBOOL(hAPP(_1332850, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1332852, _1332854)))), 29753 ^ _780478 : [(29756 ^ _780478) ^ [] : [hBOOL(hAPP(_1332850, _1332852))], (29754 ^ _780478) ^ [] : [-(_1332854 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 29759 ^ _780478 : [(29760 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332854)))], (29766 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 29762 ^ [_1332850, _1332852, _1332854]), _1332854)))], (29770 ^ _780478) ^ [] : [hBOOL(hAPP(_1332850, 29762 ^ [_1332850, _1332852, _1332854]))], (29768 ^ _780478) ^ [] : [-(_1332852 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332854), 29761 ^ [_1332850, _1332852, _1332854])), 29762 ^ [_1332850, _1332852, _1332854]))], (29764 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29762 ^ [_1332850, _1332852, _1332854])))]], 29771 ^ _780478 : [(29772 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1332854), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29778 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 29774 ^ [_1332850, _1332852, _1332854]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29782 ^ _780478) ^ [] : [hBOOL(hAPP(_1332850, 29774 ^ [_1332850, _1332852, _1332854]))], (29780 ^ _780478) ^ [] : [-(_1332852 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1332854), 29773 ^ [_1332850, _1332852, _1332854])), 29774 ^ [_1332850, _1332852, _1332854]))], (29776 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1332854), 29774 ^ [_1332850, _1332852, _1332854])))]]], (33254 ^ _780478) ^ [_1408771, _1408773] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408771))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408771)), _1408773) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1408773))], (31409 ^ _780478) ^ [_1367718, _1367720, _1367722] : [class_Orderings_Olinorder(_1367718), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367718), _1367720)), -(_1367720 = c_Orderings_Obot__class_Obot(tc_fun(_1367718, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367718), _1367722)), -(_1367722 = c_Orderings_Obot__class_Obot(tc_fun(_1367718, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1367718), c_Big__Operators_Olattice_OInf__fin(_1367718, c_Orderings_Oord__class_Omin(_1367718), _1367720)), c_Big__Operators_Olattice_OInf__fin(_1367718, c_Orderings_Oord__class_Omin(_1367718), _1367722)) = c_Big__Operators_Olattice_OInf__fin(_1367718, c_Orderings_Oord__class_Omin(_1367718), hAPP(c_Set_OCollect(_1367718), hAPP(hAPP(c_COMBB(tc_fun(_1367718, tc_HOL_Obool), tc_HOL_Obool, _1367718), c_HOL_OEx(_1367718)), hAPP(hAPP(c_COMBB(tc_fun(_1367718, tc_fun(_1367718, tc_HOL_Obool)), tc_fun(_1367718, tc_HOL_Obool), _1367718), hAPP(c_COMBB(tc_fun(_1367718, tc_HOL_Obool), tc_HOL_Obool, _1367718), c_HOL_OEx(_1367718))), hAPP(hAPP(c_COMBC(_1367718, tc_fun(_1367718, tc_fun(_1367718, tc_HOL_Obool)), tc_fun(_1367718, tc_fun(_1367718, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1367718, tc_fun(tc_fun(_1367718, tc_HOL_Obool), tc_fun(_1367718, tc_HOL_Obool))), tc_fun(tc_fun(_1367718, tc_fun(_1367718, tc_HOL_Obool)), tc_fun(_1367718, tc_fun(_1367718, tc_HOL_Obool))), _1367718), c_COMBS(_1367718, tc_fun(_1367718, tc_HOL_Obool), tc_fun(_1367718, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1367718, tc_fun(_1367718, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1367718, tc_fun(tc_fun(_1367718, tc_HOL_Obool), tc_fun(_1367718, tc_HOL_Obool))), _1367718), hAPP(c_COMBB(tc_fun(_1367718, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1367718, tc_HOL_Obool), tc_fun(_1367718, tc_HOL_Obool)), _1367718), c_COMBS(_1367718, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1367718, tc_fun(_1367718, tc_HOL_Obool)), tc_fun(_1367718, tc_fun(_1367718, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1367718), hAPP(c_COMBB(tc_fun(_1367718, tc_HOL_Obool), tc_fun(_1367718, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1367718), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1367718), c_fconj))), hAPP(hAPP(c_COMBC(_1367718, tc_fun(_1367718, tc_fun(_1367718, _1367718)), tc_fun(_1367718, tc_fun(_1367718, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1367718, _1367718), tc_fun(_1367718, tc_HOL_Obool)), tc_fun(tc_fun(_1367718, tc_fun(_1367718, _1367718)), tc_fun(_1367718, tc_fun(_1367718, tc_HOL_Obool))), _1367718), c_COMBB(tc_fun(_1367718, _1367718), tc_fun(_1367718, tc_HOL_Obool), _1367718)), hAPP(hAPP(c_COMBB(tc_fun(_1367718, tc_HOL_Obool), tc_fun(tc_fun(_1367718, _1367718), tc_fun(_1367718, tc_HOL_Obool)), _1367718), c_COMBB(_1367718, tc_HOL_Obool, _1367718)), c_fequal))), c_Orderings_Oord__class_Omax(_1367718)))))), hAPP(hAPP(c_COMBC(_1367718, tc_fun(_1367718, tc_HOL_Obool), tc_fun(_1367718, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1367718, tc_HOL_Obool), tc_fun(_1367718, tc_HOL_Obool)), _1367718), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1367718)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1367718), c_fconj), hAPP(hAPP(c_COMBC(_1367718, tc_fun(_1367718, tc_HOL_Obool), tc_HOL_Obool), c_member(_1367718)), _1367720)))), hAPP(hAPP(c_COMBC(_1367718, tc_fun(_1367718, tc_HOL_Obool), tc_HOL_Obool), c_member(_1367718)), _1367722))))))))], (27647 ^ _780478) ^ [] : [-(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)))], (51373 ^ _780478) ^ [_1821110, _1821112, _1821114] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821110, _1821112) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1821114), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 51376 ^ _780478 : [(51379 ^ _780478) ^ [] : [-(_1821112 = _1821114)], (51377 ^ _780478) ^ [] : [-(_1821110 = _1821112)]]], (15633 ^ _780478) ^ [_1062816, _1062818, _1062820] : [15634 ^ _780478 : [(15637 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062816), _1062820))], (15635 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062816), _1062818))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1062816), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062816, tc_HOL_Obool)), _1062818), _1062820))))], (22755 ^ _780478) ^ [_1204114, _1204116] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204114)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204116)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1204114), _1204116)))], (46218 ^ _780478) ^ [_1710770, _1710772, _1710774] : [class_Groups_Omonoid__add(_1710770), -(hAPP(c_List_Ofoldl(_1710770, _1710770, c_Groups_Oplus__class_Oplus(_1710770), _1710772), _1710774) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1710770), _1710772), c_List_Ofoldr(_1710770, _1710770, c_Groups_Oplus__class_Oplus(_1710770), _1710774, c_Groups_Ozero__class_Ozero(_1710770))))], (39434 ^ _780478) ^ [_1546201, _1546203] : [-(c_Nitpick_Owf_H(_1546201, _1546203)), c_Wellfounded_Oacyclic(_1546201, _1546203), 39439 ^ _780478 : [(39442 ^ _780478) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (39440 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1546201, _1546201)), _1546203))]]], (45137 ^ _780478) ^ [_1685354] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1685354)) = _1685354)], (50014 ^ _780478) ^ [_1791451, _1791453, _1791455, _1791457] : [c_Fun_Oinj__on(_1791451, _1791453, _1791455, c_Orderings_Otop__class_Otop(tc_fun(_1791451, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1791451, _1791453, c_Orderings_Otop__class_Otop(tc_fun(_1791451, tc_HOL_Obool)), _1791455), hAPP(_1791455, _1791457)) = _1791457)], (5622 ^ _780478) ^ [_866552, _866554] : [_866554 = _866552, -(c_COMBI(_866554) = c_COMBI(_866552))], (39613 ^ _780478) ^ [_1551585, _1551587] : [39615 ^ _780478 : [(39618 ^ _780478) ^ [] : [39614 ^ [_1551585, _1551587] = c_Orderings_Obot__class_Obot(tc_fun(_1551585, tc_HOL_Obool))], (39616 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1551585, tc_HOL_Obool)), 39614 ^ [_1551585, _1551587]), hAPP(c_Relation_OImage(_1551585, _1551585, _1551587), 39614 ^ [_1551585, _1551587]))))]], -(c_Wellfounded_Owf(_1551585, _1551587))], (46667 ^ _780478) ^ [_1719020, _1719022, _1719024, _1719026, _1719028] : [class_Orderings_Olinorder(_1719020), -(c_List_Olinorder__class_Osorted(_1719020, hAPP(hAPP(c_List_Omap(_1719022, _1719020), _1719024), hAPP(c_List_Ofilter(_1719022, hAPP(hAPP(c_COMBC(_1719022, _1719020, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1719020, tc_fun(_1719020, tc_HOL_Obool), _1719022), c_fequal), _1719024)), hAPP(_1719026, _1719028))), _1719028))))], (7136 ^ _780478) ^ [_899563, _899565, _899567, _899569] : [class_Orderings_Oorder(_899563), _899565 = _899567, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899563), _899569), _899567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899563), _899569), _899565)))], (17779 ^ _780478) ^ [_1111655, _1111657, _1111659, _1111661, _1111663, _1111665, _1111667, _1111669] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1111655, tc_fun(_1111657, tc_fun(_1111659, tc_HOL_Obool))), _1111661), _1111663), _1111665), _1111667)), -(hBOOL(hAPP(hAPP(hAPP(_1111663, _1111669), _1111665), _1111667))), hBOOL(hAPP(hAPP(c_member(_1111655), _1111669), _1111661))], (43153 ^ _780478) ^ [_1640895, _1640897] : [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(_1640895)), _1640897))), _1640897 = c_List_Olist_ONil(_1640895)], (35311 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (4910 ^ _780478) ^ [_855328, _855330, _855332, _855334, _855336, _855338, _855340, _855342, _855344, _855346, _855348, _855350] : [-(c_Partial__Function_Ofun__lub(_855350, _855346, _855342, _855338, _855334, _855330) = c_Partial__Function_Ofun__lub(_855348, _855344, _855340, _855336, _855332, _855328)), _855350 = _855348, _855346 = _855344, _855342 = _855340, _855338 = _855336, _855334 = _855332, _855330 = _855328], (35984 ^ _780478) ^ [_1463884, _1463886, _1463888, _1463890, _1463892] : [c_Equiv__Relations_Oequiv(_1463884, _1463886, _1463888), hBOOL(hAPP(hAPP(c_member(_1463884), _1463890), _1463886)), hBOOL(hAPP(hAPP(c_member(_1463884), _1463892), _1463886)), 35995 ^ _780478 : [(36002 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1463884, _1463884)), hAPP(hAPP(c_Product__Type_OPair(_1463884, _1463884), _1463890), _1463892)), _1463888)), -(hAPP(c_Relation_OImage(_1463884, _1463884, _1463888), hAPP(hAPP(c_Set_Oinsert(_1463884), _1463890), c_Orderings_Obot__class_Obot(tc_fun(_1463884, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1463884, _1463884, _1463888), hAPP(hAPP(c_Set_Oinsert(_1463884), _1463892), c_Orderings_Obot__class_Obot(tc_fun(_1463884, tc_HOL_Obool)))))], (35996 ^ _780478) ^ [] : [hAPP(c_Relation_OImage(_1463884, _1463884, _1463888), hAPP(hAPP(c_Set_Oinsert(_1463884), _1463890), c_Orderings_Obot__class_Obot(tc_fun(_1463884, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1463884, _1463884, _1463888), hAPP(hAPP(c_Set_Oinsert(_1463884), _1463892), c_Orderings_Obot__class_Obot(tc_fun(_1463884, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1463884, _1463884)), hAPP(hAPP(c_Product__Type_OPair(_1463884, _1463884), _1463890), _1463892)), _1463888)))]]], (12680 ^ _780478) ^ [_1004840, _1004842] : [class_Lattices_Obounded__lattice__top(_1004840), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004840), c_Orderings_Otop__class_Otop(_1004840)), _1004842) = c_Orderings_Otop__class_Otop(_1004840))], (40560 ^ _780478) ^ [_1573887, _1573889, _1573891] : [-(c_Transitive__Closure_Ortrancl(_1573887, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573887, _1573887), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573887, _1573889)), c_Transitive__Closure_Ortrancl(_1573887, _1573891))) = c_Transitive__Closure_Ortrancl(_1573887, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1573887, _1573887), tc_HOL_Obool)), _1573889), _1573891)))], (22674 ^ _780478) ^ [_1202666] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202666) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1202666 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31284 ^ _780478) ^ [_1363142, _1363144, _1363146] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363142, tc_HOL_Obool)), _1363144), _1363146) = hAPP(c_Set_OCollect(_1363142), hAPP(hAPP(c_COMBS(_1363142, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1363142), c_fconj), hAPP(hAPP(c_COMBC(_1363142, tc_fun(_1363142, tc_HOL_Obool), tc_HOL_Obool), c_member(_1363142)), _1363144))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1363142), c_fNot), hAPP(hAPP(c_COMBC(_1363142, tc_fun(_1363142, tc_HOL_Obool), tc_HOL_Obool), c_member(_1363142)), _1363146)))))], (34485 ^ _780478) ^ [_1430791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430791)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430791), c_Int_OPls)))], (22291 ^ _780478) ^ [_1194947, _1194949, _1194951] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1194947), _1194949)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1194947), _1194951)), 22301 ^ _780478 : [(22304 ^ _780478) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22302 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1194947), 22300 ^ [_1194947, _1194949, _1194951]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1194947, tc_HOL_Obool)), _1194949), _1194951))))]], -(hAPP(c_Finite__Set_Ocard(_1194947), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1194947, tc_HOL_Obool)), _1194949), _1194951)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1194947), _1194949)), hAPP(c_Finite__Set_Ocard(_1194947), _1194951)))], (19582 ^ _780478) ^ [_1146298, _1146300, _1146302] : [19583 ^ _780478 : [(19586 ^ _780478) ^ [] : [_1146300 = _1146302], (19584 ^ _780478) ^ [] : [_1146298 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146298), _1146300) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146298), _1146302))], (1874 ^ _780478) ^ [_806767, _806769] : [-(class_Int_Onumber(_806767)), _806769 = _806767, class_Int_Onumber(_806769)], (51427 ^ _780478) ^ [_1822053, _1822055] : [c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822053, _1822055) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822053), _1822055)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822055), _1822053)))], (35283 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (2924 ^ _780478) ^ [_823777, _823779, _823781, _823783] : [-(c_Nitpick_Oinverse__frac(_823783, _823779) = c_Nitpick_Oinverse__frac(_823781, _823777)), _823783 = _823781, _823779 = _823777], (22995 ^ _780478) ^ [_1208453, _1208455] : [class_Rings_Osemiring__1(_1208453), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208453), hAPP(c_Nat_OSuc, _1208455)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208453), c_Groups_Oone__class_Oone(_1208453)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208453), _1208455)))], (33242 ^ _780478) ^ [_1408587, _1408589] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408587))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408587)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408589)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11737 ^ _780478) ^ [_986287] : [class_Orderings_Oord(_986287), -(c_Orderings_Oord__class_Omax(_986287) = c_Orderings_Oord_Omax(_986287, c_Orderings_Oord__class_Oless__eq(_986287)))], (19468 ^ _780478) ^ [_1144681, _1144683] : [19469 ^ _780478 : [(19472 ^ _780478) ^ [] : [_1144683 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19470 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144681))]], -(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), _1144681), _1144683))))], (38367 ^ _780478) ^ [_1517681, _1517683] : [38369 ^ _780478 : [(38370 ^ _780478) ^ [_1517706] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517681, _1517681)), hAPP(hAPP(c_Product__Type_OPair(_1517681, _1517681), hAPP(38368 ^ [_1517681, _1517683], hAPP(c_Nat_OSuc, _1517706))), hAPP(38368 ^ [_1517681, _1517683], _1517706))), _1517683)))]], -(c_Wellfounded_Owf(_1517681, _1517683))], (22161 ^ _780478) ^ [_1192417, _1192419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1192417), _1192419))), 22164 ^ _780478 : [(22167 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1192417), _1192419)))], (22165 ^ _780478) ^ [] : [_1192419 = c_Orderings_Obot__class_Obot(tc_fun(_1192417, tc_HOL_Obool))]]], (2884 ^ _780478) ^ [_823165, _823167, _823169, _823171, _823173, _823175] : [-(c_Nitpick_Otimes__frac(_823175, _823171, _823167) = c_Nitpick_Otimes__frac(_823173, _823169, _823165)), _823175 = _823173, _823171 = _823169, _823167 = _823165], (46396 ^ _780478) ^ [_1714292, _1714294, _1714296, _1714298, _1714300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714292), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1714294), _1714296))), -(hAPP(hAPP(c_List_Onth(_1714298), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1714298), _1714300), c_List_Oupt(_1714296, _1714294))), _1714292) = hAPP(_1714300, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1714296), _1714292)))], (25593 ^ _780478) ^ [_1255550, _1255552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255552)), 25600 ^ _780478 : [(25607 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255550), _1255552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1255550)), hAPP(c_Int_Onat, _1255552))))], (25601 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1255550)), hAPP(c_Int_Onat, _1255552))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255550), _1255552)))]]], (40466 ^ _780478) ^ [_1571495, _1571497, _1571499, _1571501] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571495, _1571495)), _1571497), c_Transitive__Closure_Otrancl(_1571495, _1571499))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1571495, _1571495), tc_HOL_Obool)), _1571499), _1571501)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571495, _1571495)), _1571497), c_Transitive__Closure_Otrancl(_1571495, _1571501))))], (25146 ^ _780478) ^ [_1247602, _1247604] : [-(c_Sum__Type_OPlus(_1247602, _1247604, c_Orderings_Otop__class_Otop(tc_fun(_1247602, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1247604, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1247602, _1247604), tc_HOL_Obool)))], (45649 ^ _780478) ^ [_1697074, _1697076] : [-(c_Enum_Oenum__the(_1697074, _1697076) = c_HOL_OThe(_1697074, _1697076))], (47961 ^ _780478) ^ [_1747177, _1747179, _1747181] : [class_Enum_Oenum(_1747177), class_Enum_Oenum(_1747179), 47968 ^ _780478 : [(47975 ^ _780478) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1747179), hAPP(hAPP(c_COMBB(tc_fun(_1747177, tc_HOL_Obool), tc_HOL_Obool, _1747179), c_Enum_Oenum__class_Oenum__all(_1747177)), hAPP(hAPP(c_COMBB(tc_fun(_1747177, tc_prod(_1747179, _1747177)), tc_fun(_1747177, tc_HOL_Obool), _1747179), hAPP(c_COMBB(tc_prod(_1747179, _1747177), tc_HOL_Obool, _1747177), _1747181)), c_Product__Type_OPair(_1747179, _1747177))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1747179, _1747177)), _1747181)))], (47969 ^ _780478) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1747179, _1747177)), _1747181)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1747179), hAPP(hAPP(c_COMBB(tc_fun(_1747177, tc_HOL_Obool), tc_HOL_Obool, _1747179), c_Enum_Oenum__class_Oenum__all(_1747177)), hAPP(hAPP(c_COMBB(tc_fun(_1747177, tc_prod(_1747179, _1747177)), tc_fun(_1747177, tc_HOL_Obool), _1747179), hAPP(c_COMBB(tc_prod(_1747179, _1747177), tc_HOL_Obool, _1747177), _1747181)), c_Product__Type_OPair(_1747179, _1747177))))))]]], (24145 ^ _780478) ^ [_1230059, _1230061] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1230059, _1230061))))], (18253 ^ _780478) ^ [_1121860, _1121862, _1121864] : [class_Rings_Ocomm__semiring__1(_1121860), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121860), _1121862), hAPP(hAPP(c_Power_Opower__class_Opower(_1121860), _1121862), _1121864)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1121860), _1121862), hAPP(c_Nat_OSuc, _1121864)))], (31308 ^ _780478) ^ [_1363750, _1363752, _1363754] : [-(hAPP(c_Set_OCollect(_1363750), hAPP(hAPP(c_COMBS(_1363750, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1363750), c_fimplies), _1363752)), _1363754)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363750, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1363750, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1363750), _1363752))), hAPP(c_Set_OCollect(_1363750), _1363754)))], (16540 ^ _780478) ^ [_1082646, _1082648, _1082650, _1082652, _1082654, _1082656, _1082658, _1082660] : [c_Finite__Set_Ofolding__image__simple(_1082646, _1082648, _1082650, _1082652, _1082654, _1082656), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082648), _1082658)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082648), _1082660)), -(hAPP(hAPP(_1082650, hAPP(_1082656, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1082648, tc_HOL_Obool)), _1082658), _1082660))), hAPP(_1082656, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1082648, tc_HOL_Obool)), _1082658), _1082660))) = hAPP(hAPP(_1082650, hAPP(_1082656, _1082658)), hAPP(_1082656, _1082660)))], (51065 ^ _780478) ^ [_1815357, _1815359, _1815361, _1815363] : [class_Rings_Ocomm__ring(_1815357), class_Rings_Odvd(_1815357), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815357), _1815359), _1815361)), 51076 ^ _780478 : [(51083 ^ _780478) ^ [_1815783, _1815785] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815357), _1815359), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1815357), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1815357), _1815785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815357), _1815783), _1815361))), _1815363))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815357), _1815359), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1815357), _1815785), _1815363))))], (51077 ^ _780478) ^ [_1815610, _1815612] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815357), _1815359), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1815357), _1815612), _1815363))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1815357), _1815359), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1815357), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1815357), _1815612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1815357), _1815610), _1815361))), _1815363))))]]], (46344 ^ _780478) ^ [_1713250, _1713252, _1713254, _1713256] : [-(c_List_Oupt(_1713250, _1713252) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1713254), _1713256)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713250), _1713252)), _1713250 = _1713254, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713250), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1713252) = _1713256], (16380 ^ _780478) ^ [_1078592, _1078594, _1078596, _1078598] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078592, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078592, tc_HOL_Obool)), _1078594), _1078596)), _1078598) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078592, tc_HOL_Obool)), _1078594), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078592, tc_HOL_Obool)), _1078596), _1078598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1078592, tc_HOL_Obool)), _1078598), _1078594)))], (1534 ^ _780478) ^ [_802517, _802519] : [-(class_Rings_Olinordered__semiring__strict(_802517)), _802519 = _802517, class_Rings_Olinordered__semiring__strict(_802519)], (39331 ^ _780478) ^ [_1544048, _1544050] : [c_Wellfounded_OwfP(_1544048, hAPP(hAPP(c_COMBC(_1544048, tc_fun(tc_prod(_1544048, _1544048), tc_HOL_Obool), tc_fun(_1544048, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544048, tc_fun(tc_fun(tc_prod(_1544048, _1544048), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1544048, _1544048), tc_HOL_Obool), tc_fun(_1544048, tc_HOL_Obool)), _1544048), c_COMBC(_1544048, tc_fun(tc_prod(_1544048, _1544048), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544048, tc_prod(_1544048, _1544048)), tc_fun(_1544048, tc_fun(tc_fun(tc_prod(_1544048, _1544048), tc_HOL_Obool), tc_HOL_Obool)), _1544048), hAPP(c_COMBB(tc_prod(_1544048, _1544048), tc_fun(tc_fun(tc_prod(_1544048, _1544048), tc_HOL_Obool), tc_HOL_Obool), _1544048), c_member(tc_prod(_1544048, _1544048)))), c_Product__Type_OPair(_1544048, _1544048)))), _1544050)), -(c_Wellfounded_Owf(_1544048, _1544050))], (11749 ^ _780478) ^ [_986461, _986463] : [class_Orderings_Olinorder(_986461), hBOOL(hAPP(c_Finite__Set_Ofinite(_986461), _986463)), -(_986463 = c_Orderings_Obot__class_Obot(tc_fun(_986461, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_986461), hAPP(hAPP(c_Orderings_Oord__class_Omax(_986461), 11762 ^ [_986461, _986463]), 11763 ^ [_986461, _986463])), hAPP(hAPP(c_Set_Oinsert(_986461), 11762 ^ [_986461, _986463]), hAPP(hAPP(c_Set_Oinsert(_986461), 11763 ^ [_986461, _986463]), c_Orderings_Obot__class_Obot(tc_fun(_986461, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_986461), c_Big__Operators_Olinorder__class_OMax(_986461, _986463)), _986463)))], (42941 ^ _780478) ^ [_1637173, _1637175, _1637177, _1637179] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1637173) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1637175), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1637173)), hAPP(hAPP(c_List_Olist_OCons(_1637175), _1637177), _1637179)) = c_List_Olist_ONil(_1637175))], (5863 ^ _780478) ^ [_873483, _873485, _873487, _873489] : [_873483 = c_Orderings_Obot__class_Obot(tc_fun(_873485, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_873485, _873487, hAPP(c_COMBK(_873487, _873485), _873489)), _873483) = c_Orderings_Obot__class_Obot(tc_fun(_873487, tc_HOL_Obool)))], (7317 ^ _780478) ^ [_902728, _902730, _902732] : [-(_902728 = _902730), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902732, tc_HOL_Obool)), _902728), _902730)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902732, tc_HOL_Obool)), _902730), _902728))], (23477 ^ _780478) ^ [_1216946] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216946)), -(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)), _1216946))))], (39506 ^ _780478) ^ [_1548110] : [-(_1548110 = hAPP(c_Int_OAbs__Integ, 39504 ^ [_1548110]))], (10109 ^ _780478) ^ [_956238, _956240, _956242] : [-(hBOOL(hAPP(hAPP(c_member(_956238), _956240), _956242))), -(hBOOL(hAPP(hAPP(c_member(_956238), _956240), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_956238, tc_HOL_Obool)), _956242))))], (51717 ^ _780478) ^ [_1826884, _1826886] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826884), _1826886)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826886), _1826884))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826886), _1826884)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826884), _1826886)))], (50963 ^ _780478) ^ [_1813386, _1813388, _1813390] : [-(c_Lazy__Sequence_Omap(_1813386, _1813388, _1813390, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1813386)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1813388))], (45191 ^ _780478) ^ [_1686244, _1686246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686244)), hAPP(c_Code__Numeral_Onat__of, _1686246))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1686244), _1686246)))], (43740 ^ _780478) ^ [_1654154, _1654156, _1654158, _1654160] : [-(c_List_Osublist(_1654154, hAPP(hAPP(c_List_Oappend(_1654154), _1654156), _1654158), _1654160) = hAPP(hAPP(c_List_Oappend(_1654154), c_List_Osublist(_1654154, _1654156, _1654160)), c_List_Osublist(_1654154, _1654158, 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(_1654154)), _1654156)))), _1654160)))))], (52077 ^ _780478) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (38800 ^ _780478) ^ [_1529519, _1529521, _1529523, _1529525] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1529519), _1529521)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1529523), _1529525)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1529519, _1529523)), hAPP(hAPP(c_Product__Type_OSigma(_1529519, _1529523), _1529521), hAPP(c_COMBK(tc_fun(_1529523, tc_HOL_Obool), _1529519), _1529525)))))], (42075 ^ _780478) ^ [_1614872] : [-(c_List_Olists(_1614872, c_Orderings_Otop__class_Otop(tc_fun(_1614872, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1614872), tc_HOL_Obool)))], (52279 ^ _780478) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (48711 ^ _780478) ^ [_1762991, _1762993, _1762995] : [-(_1762991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1762993), c_List_Oreplicate(_1762993, _1762991, _1762995)) = hAPP(hAPP(c_Set_Oinsert(_1762993), _1762995), c_Orderings_Obot__class_Obot(tc_fun(_1762993, tc_HOL_Obool))))], (4884 ^ _780478) ^ [_854945, _854947] : [_854947 = _854945, -(c_List_Oset(_854947) = c_List_Oset(_854945))], (38323 ^ _780478) ^ [_1516594, _1516596] : [c_Wellfounded_Owf(_1516594, _1516596), 38326 ^ _780478 : [(38327 ^ _780478) ^ [_1516663] : [-(hBOOL(hAPP(hAPP(c_member(_1516594), _1516663), c_Wellfounded_Oacc(_1516594, _1516596))))]]], (5757 ^ _780478) ^ [_871481, _871483] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871481, _871483, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871481), tc_HOL_Obool))))], (19672 ^ _780478) ^ [_1147685] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1147685), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23585 ^ _780478) ^ [_1218859, _1218861] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218859), _1218861)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1218861), _1218859))], (1304 ^ _780478) ^ [_799642, _799644] : [-(class_Rings_Oring__1(_799642)), _799644 = _799642, class_Rings_Oring__1(_799644)], (39000 ^ _780478) ^ [_1536249, _1536251, _1536253, _1536255, _1536257, _1536259] : [class_Groups_Ocomm__monoid__mult(_1536249), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536251), _1536253)), 39010 ^ _780478 : [(39013 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1536255), hAPP(_1536257, 39009 ^ [_1536249, _1536251, _1536253, _1536255, _1536257, _1536259])))], (39011 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536251), 39009 ^ [_1536249, _1536251, _1536253, _1536255, _1536257, _1536259]), _1536253)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1536249, _1536251, c_Groups_Otimes__class_Otimes(_1536249)), hAPP(hAPP(c_COMBS(_1536251, tc_fun(_1536255, tc_HOL_Obool), _1536249), hAPP(hAPP(c_COMBC(_1536251, _1536249, tc_fun(tc_fun(_1536255, tc_HOL_Obool), _1536249)), hAPP(hAPP(c_COMBB(tc_fun(_1536255, _1536249), tc_fun(_1536249, tc_fun(tc_fun(_1536255, tc_HOL_Obool), _1536249)), _1536251), c_Finite__Set_Ofold__image(_1536249, _1536255, c_Groups_Otimes__class_Otimes(_1536249))), _1536259)), c_Groups_Oone__class_Oone(_1536249))), _1536257)), c_Groups_Oone__class_Oone(_1536249)), _1536253) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1536249, tc_prod(_1536251, _1536255), c_Groups_Otimes__class_Otimes(_1536249)), hAPP(c_Product__Type_Oprod_Oprod__case(_1536251, _1536255, _1536249), _1536259)), c_Groups_Oone__class_Oone(_1536249)), hAPP(hAPP(c_Product__Type_OSigma(_1536251, _1536255), _1536253), _1536257)))], (30348 ^ _780478) ^ [_1343538] : [class_Groups_Oordered__ab__group__add__abs(_1343538), -(hAPP(c_Groups_Oabs__class_Oabs(_1343538), c_Groups_Ozero__class_Ozero(_1343538)) = c_Groups_Ozero__class_Ozero(_1343538))], (19262 ^ _780478) ^ [_1141688, _1141690, _1141692] : [class_Rings_Ono__zero__divisors(_1141688), -(_1141690 = c_Groups_Ozero__class_Ozero(_1141688)), -(_1141692 = c_Groups_Ozero__class_Ozero(_1141688)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141688), _1141690), _1141692) = c_Groups_Ozero__class_Ozero(_1141688)], (40600 ^ _780478) ^ [_1574928, _1574930] : [-(c_Relation_Orefl__on(_1574928, c_Orderings_Otop__class_Otop(tc_fun(_1574928, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1574928, _1574930)))], (43317 ^ _780478) ^ [_1644580, _1644582, _1644584, _1644586, _1644588] : [_1644580 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1644582, _1644584, _1644586), _1644580), _1644588) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644584), _1644582), c_List_Olist_ONil(_1644584)), _1644588))], (45017 ^ _780478) ^ [_1682791, _1682793] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1682791), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1682793), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 45024 ^ _780478 : [(45031 ^ _780478) ^ [] : [_1682791 = _1682793, -(hAPP(c_Code__Numeral_Oof__nat, _1682791) = hAPP(c_Code__Numeral_Oof__nat, _1682793))], (45025 ^ _780478) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1682791) = hAPP(c_Code__Numeral_Oof__nat, _1682793), -(_1682791 = _1682793)]]], (48967 ^ _780478) ^ [_1768532, _1768534, _1768536, _1768538, _1768540, _1768542] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1768532, _1768534, _1768536, _1768538, c_Nitpick_Opair__box_OPairBox(_1768532, _1768534, _1768540, _1768542)) = hAPP(hAPP(_1768538, _1768540), _1768542))], (5857 ^ _780478) ^ [_873319, _873321, _873323, _873325, _873327] : [hBOOL(hAPP(hAPP(c_member(_873319), _873321), _873323)), -(hAPP(c_Set_Oimage(_873319, _873325, hAPP(c_COMBK(_873325, _873319), _873327)), _873323) = hAPP(hAPP(c_Set_Oinsert(_873325), _873327), c_Orderings_Obot__class_Obot(tc_fun(_873325, tc_HOL_Obool))))], (46139 ^ _780478) ^ [_1708068, _1708070, _1708072] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1708068, tc_HOL_Obool)), hAPP(c_List_Oset(_1708068), _1708070)), hAPP(hAPP(c_Set_Oinsert(_1708068), _1708072), c_Orderings_Obot__class_Obot(tc_fun(_1708068, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1708068), hAPP(c_List_Ofilter(_1708068, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1708068), c_fNot), hAPP(hAPP(c_COMBC(_1708068, _1708068, tc_HOL_Obool), c_fequal), _1708072))), _1708070)))], (40414 ^ _780478) ^ [_1570207, _1570209] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570207, _1570207)), c_Transitive__Closure_Otrancl(_1570207, _1570209))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570207, _1570207)), _1570209)))], (45131 ^ _780478) ^ [_1685233, _1685235] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1685233)), hAPP(c_Code__Numeral_Oof__nat, _1685235)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1685233), _1685235)))], (12496 ^ _780478) ^ [_1000960, _1000962, _1000964, _1000966] : [12497 ^ _780478 : [(12500 ^ _780478) ^ [] : [hBOOL(hAPP(_1000964, _1000962))], (12498 ^ _780478) ^ [] : [hBOOL(hAPP(_1000960, _1000962))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000966, tc_HOL_Obool)), _1000964), _1000960), _1000962)))], (51987 ^ _780478) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (43881 ^ _780478) ^ [_1658120, _1658122, _1658124, _1658126] : [hBOOL(hAPP(hAPP(c_member(_1658120), _1658122), hAPP(c_List_Oset(_1658120), hAPP(hAPP(c_List_Odrop(_1658120), _1658124), _1658126)))), -(hBOOL(hAPP(hAPP(c_member(_1658120), _1658122), hAPP(c_List_Oset(_1658120), _1658126))))], (47215 ^ _780478) ^ [_1730458, _1730460, _1730462] : [47217 ^ _780478 : [(47220 ^ _780478) ^ [] : [hBOOL(hAPP(_1730460, 47216 ^ [_1730458, _1730460, _1730462]))], (47218 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730458), 47216 ^ [_1730458, _1730460, _1730462]), hAPP(c_List_Oset(_1730458), _1730462))))]], -(c_List_OtakeWhile(_1730458, _1730460, _1730462) = _1730462)], (19528 ^ _780478) ^ [_1145528, _1145530] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1145528), _1145530) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145528 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1145530 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (34255 ^ _780478) ^ [_1426497, _1426499] : [class_Int_Onumber__ring(_1426497), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426497), hAPP(c_Int_Onumber__class_Onumber__of(_1426497), _1426499)), c_Groups_Oone__class_Oone(_1426497)) = hAPP(c_Int_Onumber__class_Onumber__of(_1426497), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1426499), c_Int_OBit1(c_Int_OPls))))], (3058 ^ _780478) ^ [_825874, _825876, _825878, _825880] : [-(c_Wellfounded_Oacc(_825880, _825876) = c_Wellfounded_Oacc(_825878, _825874)), _825880 = _825878, _825876 = _825874], (51765 ^ _780478) ^ [_1827633, _1827635] : [class_Lattices_Obounded__lattice(_1827633), -(class_Lattices_Obounded__lattice__top(tc_fun(_1827635, _1827633)))], (27778 ^ _780478) ^ [_1294093, _1294095, _1294097, _1294099] : [class_Groups_Oab__group__add(_1294093), 27781 ^ _780478 : [(27788 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1294095), _1294097))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1294093), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1294093, _1294093), hAPP(hAPP(c_COMBB(_1294093, tc_fun(_1294093, _1294093), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1294093)), _1294099)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1294093, tc_Nat_Onat), _1294099), 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, _1294095, _1294097)) = c_Groups_Ozero__class_Ozero(_1294093))], (27782 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1294095), _1294097)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1294093), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1294093, _1294093), hAPP(hAPP(c_COMBB(_1294093, tc_fun(_1294093, _1294093), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1294093)), _1294099)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1294093, tc_Nat_Onat), _1294099), 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, _1294095, _1294097)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1294093), hAPP(_1294099, _1294095)), hAPP(_1294099, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1294097), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (42912 ^ _780478) ^ [_1636533, _1636535] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1636533), _1636535))), -(c_Nitpick_Ocard_H(_1636533, _1636535) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23205 ^ _780478) ^ [_1212396] : [-(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), _1212396))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6105 ^ _780478) ^ [_877777, _877779, _877781, _877783, _877785] : [hBOOL(hAPP(hAPP(c_member(_877777), _877779), hAPP(c_Set_Oimage(_877781, _877777, _877783), _877785))), 6109 ^ _780478 : [(6112 ^ _780478) ^ [] : [-(_877779 = hAPP(_877783, 6108 ^ [_877777, _877779, _877781, _877783, _877785]))], (6110 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877781), 6108 ^ [_877777, _877779, _877781, _877783, _877785]), _877785)))]]], (42896 ^ _780478) ^ [_1636110, _1636112] : [class_Groups_Ocomm__monoid__add(_1636110), hBOOL(hAPP(c_List_Odistinct(_1636110), _1636112)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1636110), _1636112) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1636110, _1636110), c_COMBI(_1636110)), hAPP(c_List_Oset(_1636110), _1636112)))], (39771 ^ _780478) ^ [_1554928, _1554930, _1554932, _1554934, _1554936, _1554938] : [c_Fun_Oinj__on(_1554928, _1554930, _1554932, _1554934), c_Fun_Oinj__on(_1554930, _1554936, _1554938, hAPP(c_Set_Oimage(_1554928, _1554930, _1554932), _1554934)), -(c_Fun_Oinj__on(_1554928, _1554936, hAPP(c_Fun_Ocomp(_1554930, _1554936, _1554928, _1554938), _1554932), _1554934))], (27627 ^ _780478) ^ [_1291242, _1291244] : [c_Nat__Transfer_Onat__set(_1291242), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1291244), _1291242)), -(c_Nat__Transfer_Ois__nat(_1291244))], (23361 ^ _780478) ^ [_1215032] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215032), _1215032)))], (34799 ^ _780478) ^ [] : [-(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)))))], (26156 ^ _780478) ^ [_1265435, _1265437, _1265439] : [class_Fields_Ofield__inverse__zero(_1265435), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265435), hAPP(c_Groups_Ouminus__class_Ouminus(_1265435), _1265437)), hAPP(c_Groups_Ouminus__class_Ouminus(_1265435), _1265439)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265435), _1265437), _1265439))], (8515 ^ _780478) ^ [_927474, _927476, _927478, _927480, _927482, _927484, _927486] : [c_Finite__Set_Ofun__left__comm(_927474, _927476, _927478), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_927474, _927476, _927478, _927480, hAPP(hAPP(c_Set_Oinsert(_927474), _927482), _927484)), _927486)), -(hBOOL(hAPP(hAPP(c_member(_927474), _927482), _927484))), 8527 ^ _780478 : [(8530 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_927474, _927476, _927478, _927480, _927484), 8526 ^ [_927474, _927476, _927478, _927480, _927482, _927484, _927486])))], (8528 ^ _780478) ^ [] : [-(_927486 = hAPP(hAPP(_927478, _927482), 8526 ^ [_927474, _927476, _927478, _927480, _927482, _927484, _927486]))]]], (12776 ^ _780478) ^ [_1006774, _1006776, _1006778, _1006780] : [class_Lattices_Osemilattice__sup(_1006774), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006774), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006774), _1006776), _1006778)), _1006780) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006774), _1006776), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006774), _1006778), _1006780)))], (42304 ^ _780478) ^ [_1620846, _1620848, _1620850, _1620852] : [hBOOL(hAPP(hAPP(c_member(_1620846), _1620848), hAPP(c_List_Oset(_1620846), c_List_Osublist(_1620846, _1620850, _1620852)))), -(hBOOL(hAPP(hAPP(c_member(_1620846), _1620848), hAPP(c_List_Oset(_1620846), _1620850))))], (24032 ^ _780478) ^ [_1227371, _1227373] : [24034 ^ _780478 : [(24037 ^ _780478) ^ [] : [hBOOL(hAPP(_1227373, 24033 ^ [_1227371, _1227373]))], (24035 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 24033 ^ [_1227371, _1227373]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227371))))]], 24038 ^ _780478 : [(24039 ^ _780478) ^ [_1227524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1227524), _1227371)), -(hBOOL(hAPP(_1227373, _1227524)))]]], (18538 ^ _780478) ^ [_1128063, _1128065, _1128067] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1128063, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1128063, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1128063, tc_HOL_Obool), _1128065)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1128063, tc_HOL_Obool), _1128067))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1128063, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1128063, tc_HOL_Obool), tc_HOL_Obool)), _1128065), _1128067)))))], (9476 ^ _780478) ^ [_942923, _942925, _942927] : [9477 ^ _780478 : [(9480 ^ _780478) ^ [] : [_942925 = _942927], (9478 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942923, tc_HOL_Obool)), _942925), _942927))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942923, tc_HOL_Obool)), _942925), _942927)))], (39250 ^ _780478) ^ [_1542570, _1542572] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1542570, _1542572), 39251 ^ [_1542570, _1542572])), -(c_Wellfounded_OwfP(_1542570, _1542572))], (26808 ^ _780478) ^ [_1277136, _1277138, _1277140, _1277142] : [class_Fields_Olinordered__field(_1277136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277136), c_Groups_Ozero__class_Ozero(_1277136)), _1277138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277136), _1277140), _1277138)), _1277142)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277136), _1277140), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277136), _1277142), _1277138))))], (1374 ^ _780478) ^ [_800517, _800519] : [-(class_Lattices_Obounded__lattice__bot(_800517)), _800519 = _800517, class_Lattices_Obounded__lattice__bot(_800519)], (43879 ^ _780478) ^ [_1658080, _1658082] : [-(hAPP(c_List_Oset(_1658080), hAPP(c_List_Orotate1(_1658080), _1658082)) = hAPP(c_List_Oset(_1658080), _1658082))], (46115 ^ _780478) ^ [_1707357, _1707359, _1707361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707357), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1707359))), c_List_Otranspose(_1707359, _1707361)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1707359)), c_List_Otranspose(_1707359, _1707361)), _1707357) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707359), _1707359), hAPP(hAPP(c_COMBC(tc_List_Olist(_1707359), tc_Nat_Onat, _1707359), c_List_Onth(_1707359)), _1707357)), hAPP(c_List_Ofilter(tc_List_Olist(_1707359), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1707359)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707357)), c_Nat_Osize__class_Osize(tc_List_Olist(_1707359)))), _1707361)))], (15349 ^ _780478) ^ [_1056880, _1056882, _1056884, _1056886] : [class_Rings_Olinordered__semidom(_1056880), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056880), c_Groups_Oone__class_Oone(_1056880)), _1056882)), 15356 ^ _780478 : [(15363 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056884), _1056886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056880), hAPP(hAPP(c_Power_Opower__class_Opower(_1056880), _1056882), _1056884)), hAPP(hAPP(c_Power_Opower__class_Opower(_1056880), _1056882), _1056886))))], (15357 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056880), hAPP(hAPP(c_Power_Opower__class_Opower(_1056880), _1056882), _1056884)), hAPP(hAPP(c_Power_Opower__class_Opower(_1056880), _1056882), _1056886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056884), _1056886)))]]], (5670 ^ _780478) ^ [_867262, _867264] : [_867264 = _867262, -(c_Set_Oinsert(_867264) = c_Set_Oinsert(_867262))], (17430 ^ _780478) ^ [_1103326, _1103328, _1103330, _1103332, _1103334] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103326, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103328, tc_fun(_1103326, tc_HOL_Obool)), _1103330), _1103332)), _1103334) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103328, tc_fun(_1103326, tc_HOL_Obool)), _1103330), hAPP(hAPP(c_COMBC(_1103328, tc_fun(_1103326, tc_HOL_Obool), tc_fun(_1103326, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1103326, tc_HOL_Obool), tc_fun(tc_fun(_1103326, tc_HOL_Obool), tc_fun(_1103326, tc_HOL_Obool)), _1103328), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103326, tc_HOL_Obool))), _1103332)), _1103334)))], (24709 ^ _780478) ^ [_1239587, _1239589] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239587), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239589)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1239587), _1239589)))], (44819 ^ _780478) ^ [_1678420, _1678422, _1678424, _1678426, _1678428] : [-(hAPP(hAPP(c_List_Omap(_1678420, _1678422), _1678424), hAPP(hAPP(c_List_Olist_OCons(_1678420), _1678426), _1678428)) = hAPP(hAPP(c_List_Olist_OCons(_1678422), hAPP(_1678424, _1678426)), hAPP(hAPP(c_List_Omap(_1678420, _1678422), _1678424), _1678428)))], (306 ^ _780478) ^ [_785147, _785149] : [-(c_Nitpick_Ounknown(_785147)), _785149 = _785147, c_Nitpick_Ounknown(_785149)], (8386 ^ _780478) ^ [_924404, _924406, _924408, _924410] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_924404, _924406, hAPP(hAPP(c_Set_Oinsert(_924404), _924408), c_Orderings_Obot__class_Obot(tc_fun(_924404, tc_HOL_Obool)))), _924410)), -(_924408 = _924410)], (10287 ^ _780478) ^ [_959844, _959846, _959848] : [class_Orderings_Olinorder(_959844), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_959844), _959846), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959844), _959846), _959848)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_959844), _959846), _959848))], (50453 ^ _780478) ^ [_1801366, _1801368, _1801370, _1801372, _1801374] : [c_Fun_Obij__betw(_1801366, _1801368, _1801370, _1801372, _1801374), 50456 ^ _780478 : [(50459 ^ _780478) ^ [] : [-(hAPP(c_Set_Oimage(_1801366, _1801368, _1801370), _1801372) = _1801374)], (50457 ^ _780478) ^ [] : [-(c_Fun_Oinj__on(_1801366, _1801368, _1801370, _1801372))]]], (21506 ^ _780478) ^ [_1179859, _1179861, _1179863, _1179865, _1179867] : [class_Rings_Olinordered__semiring__strict(_1179859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179859), _1179861), _1179863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179859), _1179865), _1179867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179859), c_Groups_Ozero__class_Ozero(_1179859)), _1179861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179859), c_Groups_Ozero__class_Ozero(_1179859)), _1179865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179859), _1179861), _1179865)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179859), _1179863), _1179867))))], (9214 ^ _780478) ^ [_938480, _938482, _938484] : [class_Orderings_Oorder(_938480), 9217 ^ _780478 : [(9218 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938480), _938482), _938484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938480), _938482), _938484))), -(_938482 = _938484)], (9228 ^ _780478) ^ [] : [9229 ^ _780478 : [(9232 ^ _780478) ^ [] : [_938482 = _938484], (9230 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938480), _938482), _938484))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938480), _938482), _938484)))]]], (3278 ^ _780478) ^ [_829324, _829326, _829328, _829330] : [-(c_Random_Oselect(_829330, _829326) = c_Random_Oselect(_829328, _829324)), _829330 = _829328, _829326 = _829324], (37758 ^ _780478) ^ [_1501270] : [-(c_Relation_OId__on(_1501270, c_Orderings_Obot__class_Obot(tc_fun(_1501270, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1501270, _1501270), tc_HOL_Obool)))], (23319 ^ _780478) ^ [_1214286, _1214288] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214286), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214288)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1214286), _1214288))], (35786 ^ _780478) ^ [_1458874, _1458876, _1458878, _1458880, _1458882, _1458884] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1458876, _1458878)), hAPP(hAPP(c_Product__Type_OPair(_1458876, _1458878), _1458882), _1458884)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458874, tc_fun(tc_prod(_1458876, _1458878), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1458874, tc_HOL_Obool))), _1458880))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458874, tc_fun(_1458876, tc_fun(_1458878, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1458874, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1458876, _1458878), tc_HOL_Obool), tc_fun(_1458876, tc_fun(_1458878, tc_HOL_Obool)), _1458874), hAPP(c_COMBC(_1458876, tc_fun(tc_prod(_1458876, _1458878), tc_HOL_Obool), tc_fun(_1458878, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458878, tc_fun(tc_fun(tc_prod(_1458876, _1458878), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1458876, _1458878), tc_HOL_Obool), tc_fun(_1458878, tc_HOL_Obool)), _1458876), c_COMBC(_1458878, tc_fun(tc_prod(_1458876, _1458878), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458878, tc_prod(_1458876, _1458878)), tc_fun(_1458878, tc_fun(tc_fun(tc_prod(_1458876, _1458878), tc_HOL_Obool), tc_HOL_Obool)), _1458876), hAPP(c_COMBB(tc_prod(_1458876, _1458878), tc_fun(tc_fun(tc_prod(_1458876, _1458878), tc_HOL_Obool), tc_HOL_Obool), _1458878), c_member(tc_prod(_1458876, _1458878)))), c_Product__Type_OPair(_1458876, _1458878))))), _1458880)), _1458882), _1458884)))], (29261 ^ _780478) ^ [_1323715, _1323717, _1323719, _1323721] : [class_Divides_Osemiring__div(_1323715), -(c_Divides_Odiv__class_Omod(_1323715, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323715), _1323717), _1323719), _1323721) = c_Divides_Odiv__class_Omod(_1323715, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323715), c_Divides_Odiv__class_Omod(_1323715, _1323717, _1323721)), c_Divides_Odiv__class_Omod(_1323715, _1323719, _1323721)), _1323721))], (22610 ^ _780478) ^ [_1201506, _1201508] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1201506)), _1201508) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201506), _1201508)))], (39835 ^ _780478) ^ [_1556460, _1556462, _1556464] : [-(c_Hilbert__Choice_OEps(tc_prod(_1556460, _1556462), _1556464) = c_Hilbert__Choice_OEps(tc_prod(_1556460, _1556462), hAPP(c_Product__Type_Oprod_Oprod__case(_1556460, _1556462, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1556462, tc_prod(_1556460, _1556462)), tc_fun(_1556462, tc_HOL_Obool), _1556460), hAPP(c_COMBB(tc_prod(_1556460, _1556462), tc_HOL_Obool, _1556462), _1556464)), c_Product__Type_OPair(_1556460, _1556462)))))], (1224 ^ _780478) ^ [_798642, _798644] : [-(class_Rings_Ocomm__ring__1(_798642)), _798644 = _798642, class_Rings_Ocomm__ring__1(_798644)], (29209 ^ _780478) ^ [_1322593, _1322595, _1322597, _1322599] : [class_Divides_Oring__div(_1322593), -(c_Divides_Odiv__class_Omod(_1322593, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322593), _1322595), _1322597), _1322599) = c_Divides_Odiv__class_Omod(_1322593, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322593), c_Divides_Odiv__class_Omod(_1322593, _1322595, _1322599)), c_Divides_Odiv__class_Omod(_1322593, _1322597, _1322599)), _1322599))], (39893 ^ _780478) ^ [_1557762, _1557764, _1557766, _1557768, _1557770, _1557772] : [c_Finite__Set_Ofolding(_1557762, _1557764, _1557766, _1557768), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557762), _1557770)), hBOOL(hAPP(hAPP(c_member(_1557762), _1557772), _1557770)), -(hAPP(_1557768, _1557770) = hAPP(c_Fun_Ocomp(_1557764, _1557764, _1557764, hAPP(_1557768, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1557762, tc_HOL_Obool)), _1557770), hAPP(hAPP(c_Set_Oinsert(_1557762), _1557772), c_Orderings_Obot__class_Obot(tc_fun(_1557762, tc_HOL_Obool)))))), hAPP(_1557766, _1557772)))], (36327 ^ _780478) ^ [_1471418, _1471420, _1471422] : [hBOOL(hAPP(_1471418, hAPP(hAPP(c_Product__Type_OPair(_1471420, _1471422), 36328 ^ [_1471418, _1471420, _1471422]), 36329 ^ [_1471418, _1471420, _1471422]))), 36332 ^ _780478 : [(36333 ^ _780478) ^ [_1471565] : [-(hBOOL(hAPP(_1471418, _1471565)))]]], (14104 ^ _780478) ^ [_1032594] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032594), _1032594))))], (36186 ^ _780478) ^ [_1468420, _1468422, _1468424, _1468426, _1468428, _1468430] : [36187 ^ _780478 : [(36190 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1468426, _1468422), _1468424))], (36188 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1468420, _1468422), _1468424))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468428, tc_fun(_1468430, tc_HOL_Obool))), _1468426), _1468420), _1468422), _1468424)))], (18930 ^ _780478) ^ [_1135879, _1135881, _1135883] : [class_Lattices_Olattice(_1135879), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135879), _1135881)), -(_1135881 = c_Orderings_Obot__class_Obot(tc_fun(_1135879, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135879), _1135883)), -(_1135883 = c_Orderings_Obot__class_Obot(tc_fun(_1135879, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1135879, tc_HOL_Obool)), _1135881), _1135883) = c_Orderings_Obot__class_Obot(tc_fun(_1135879, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1135879, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1135879, tc_HOL_Obool)), _1135881), _1135883)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1135879), c_Big__Operators_Olattice__class_OInf__fin(_1135879, _1135881)), c_Big__Operators_Olattice__class_OInf__fin(_1135879, _1135883)))], (12623 ^ _780478) ^ [_1003635, _1003637, _1003639, _1003641] : [12625 ^ _780478 : [(12628 ^ _780478) ^ [] : [hBOOL(hAPP(_1003641, 12624 ^ [_1003635, _1003637, _1003639, _1003641]))], (12626 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1003635), 12624 ^ [_1003635, _1003637, _1003639, _1003641]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1003635, tc_HOL_Obool)), _1003637), _1003639))))]], 12629 ^ _780478 : [(12636 ^ _780478) ^ [_1003952] : [hBOOL(hAPP(hAPP(c_member(_1003635), _1003952), _1003639)), -(hBOOL(hAPP(_1003641, _1003952)))], (12630 ^ _780478) ^ [_1003855] : [hBOOL(hAPP(hAPP(c_member(_1003635), _1003855), _1003637)), -(hBOOL(hAPP(_1003641, _1003855)))]]], (40506 ^ _780478) ^ [_1572598, _1572600, _1572602, _1572604] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572598, _1572598)), hAPP(hAPP(c_Product__Type_OPair(_1572598, _1572598), _1572600), _1572602)), c_Transitive__Closure_Otrancl(_1572598, _1572604))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572598, _1572598)), hAPP(hAPP(c_Product__Type_OPair(_1572598, _1572598), _1572600), _1572602)), c_Transitive__Closure_Ortrancl(_1572598, _1572604))))], (45540 ^ _780478) ^ [_1694393, _1694395, _1694397, _1694399] : [_1694399 = c_List_Olist_ONil(_1694393), -(c_List_Olist__all2(_1694393, _1694395, _1694397, _1694399, c_List_Olist_ONil(_1694395)))], (21886 ^ _780478) ^ [_1186813, _1186815, _1186817] : [21887 ^ _780478 : [(21890 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186813), _1186817))], (21888 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186815)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186813), _1186815)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186817), _1186815))))], (19422 ^ _780478) ^ [_1144037] : [hAPP(c_Nat_OSuc, _1144037) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46708 ^ _780478) ^ [_1719823, _1719825, _1719827] : [class_Orderings_Olinorder(_1719823), 46711 ^ _780478 : [(46730 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1719823, hAPP(hAPP(c_List_Oappend(_1719823), _1719825), _1719827))), c_List_Olinorder__class_Osorted(_1719823, _1719825), c_List_Olinorder__class_Osorted(_1719823, _1719827), 46740 ^ _780478 : [(46746 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719823), 46739 ^ [_1719823, _1719825, _1719827]), 46742 ^ [_1719823, _1719825, _1719827]))], (46744 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1719823), 46742 ^ [_1719823, _1719825, _1719827]), hAPP(c_List_Oset(_1719823), _1719827))))], (46741 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1719823), 46739 ^ [_1719823, _1719825, _1719827]), hAPP(c_List_Oset(_1719823), _1719825))))]]], (46712 ^ _780478) ^ [] : [c_List_Olinorder__class_Osorted(_1719823, hAPP(hAPP(c_List_Oappend(_1719823), _1719825), _1719827)), 46715 ^ _780478 : [(46720 ^ _780478) ^ [_1720059] : [hBOOL(hAPP(hAPP(c_member(_1719823), _1720059), hAPP(c_List_Oset(_1719823), _1719825))), 46723 ^ _780478 : [(46724 ^ _780478) ^ [_1720169] : [hBOOL(hAPP(hAPP(c_member(_1719823), _1720169), hAPP(c_List_Oset(_1719823), _1719827))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719823), _1720059), _1720169)))]]], (46718 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1719823, _1719827))], (46716 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1719823, _1719825))]]]]], (10235 ^ _780478) ^ [_958713, _958715, _958717] : [class_Lattices_Oboolean__algebra(_958713), 10238 ^ _780478 : [(10245 ^ _780478) ^ [] : [_958715 = _958717, -(hAPP(c_Groups_Ouminus__class_Ouminus(_958713), _958715) = hAPP(c_Groups_Ouminus__class_Ouminus(_958713), _958717))], (10239 ^ _780478) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_958713), _958715) = hAPP(c_Groups_Ouminus__class_Ouminus(_958713), _958717), -(_958715 = _958717)]]], (41776 ^ _780478) ^ [_1605567, _1605569, _1605571, _1605573] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1605567), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1605569), _1605571))), -(hAPP(c_Random_Opick(_1605569, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1605569)), _1605571), _1605573)), _1605567) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1605569), _1605571))], (23221 ^ _780478) ^ [_1212687, _1212689] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212687) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212689), -(_1212687 = _1212689)], (51959 ^ _780478) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (38699 ^ _780478) ^ [_1526378, _1526380, _1526382, _1526384] : [hBOOL(hAPP(hAPP(c_member(_1526378), _1526380), hAPP(c_Relation_ODomain(_1526378, _1526382), _1526384))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1526378, _1526382)), hAPP(hAPP(c_Product__Type_OPair(_1526378, _1526382), _1526380), 38702 ^ [_1526378, _1526380, _1526382, _1526384])), _1526384)))], (33668 ^ _780478) ^ [_1415425, _1415427] : [hAPP(c_Nat_OSuc, _1415425) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415427), -(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(_1415427))), 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)), _1415425))))))], (48419 ^ _780478) ^ [_1756602, _1756604, _1756606, _1756608] : [-(c_New__Random__Sequence_Oneg__map(_1756602, _1756604, _1756606, _1756608) = c_New__Random__Sequence_Oneg__bind(_1756602, _1756604, _1756608, hAPP(c_Fun_Ocomp(_1756604, 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(_1756604)))))), _1756602, c_New__Random__Sequence_Oneg__single(_1756604)), _1756606)))], (41184 ^ _780478) ^ [_1589014, _1589016, _1589018] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589014, _1589014)), _1589016), c_Transitive__Closure_Ortrancl(_1589014, _1589018))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589014, _1589014)), _1589016), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1589014, _1589014), 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(_1589014, _1589014), tc_HOL_Obool), tc_fun(tc_prod(_1589014, _1589014), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1589014, _1589014), tc_HOL_Obool)), _1589018)))))], (924 ^ _780478) ^ [_794356, _794358, _794360, _794362] : [-(c_Equiv__Relations_Oequivp(_794360, _794356)), c_Equiv__Relations_Oequivp(_794362, _794358), _794362 = _794360, _794358 = _794356], (12782 ^ _780478) ^ [_1006917, _1006919, _1006921, _1006923, _1006925] : [class_Lattices_Olattice(_1006917), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006919, _1006917)), _1006921), _1006923), _1006925) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006917), hAPP(_1006921, _1006925)), hAPP(_1006923, _1006925)))], (44113 ^ _780478) ^ [_1663326, _1663328, _1663330] : [-(hAPP(hAPP(c_List_Odrop(_1663326), _1663328), hAPP(c_List_Otl(_1663326), _1663330)) = hAPP(c_List_Otl(_1663326), hAPP(hAPP(c_List_Odrop(_1663326), _1663328), _1663330)))], (24499 ^ _780478) ^ [_1235641, _1235643] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1235641)), _1235643) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1235641, _1235643))], (38830 ^ _780478) ^ [_1530561, _1530563, _1530565, _1530567] : [hBOOL(hAPP(c_Predicate_ODomainP(_1530561, _1530563, _1530565), _1530567)), -(hBOOL(hAPP(hAPP(_1530565, _1530567), 38833 ^ [_1530561, _1530563, _1530565, _1530567])))], (51911 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (41788 ^ _780478) ^ [_1605798, _1605800, _1605802] : [-(c_Random_Oselect__weight(_1605798, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1605798)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1605798), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1605800)), _1605802)) = c_Random_Oselect__weight(_1605798, _1605802))], (29842 ^ _780478) ^ [_1334588, _1334590] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334588))), -(c_SMT_Oz3mod(_1334590, _1334588) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1334590, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1334588)))], (49712 ^ _780478) ^ [_1786069] : [-(c_Relation_Osym(_1786069, c_Relation_OId(_1786069)))], (40049 ^ _780478) ^ [_1561348, _1561350, _1561352, _1561354, _1561356, _1561358] : [c_Finite__Set_Ofolding(_1561348, _1561350, _1561352, _1561354), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561348), _1561356)), -(hBOOL(hAPP(hAPP(c_member(_1561348), _1561358), _1561356))), -(hAPP(_1561354, hAPP(hAPP(c_Set_Oinsert(_1561348), _1561358), _1561356)) = hAPP(c_Fun_Ocomp(_1561350, _1561350, _1561350, hAPP(_1561354, _1561356)), hAPP(_1561352, _1561358)))], (35493 ^ _780478) ^ [_1448877, _1448879] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1448877), _1448879) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1448877 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1448877 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (13646 ^ _780478) ^ [_1024179, _1024181, _1024183, _1024185] : [class_Lattices_Osemilattice__sup(_1024179), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024179), _1024181)), hBOOL(hAPP(hAPP(c_member(_1024179), _1024183), _1024181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1024179), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1024179), _1024183), _1024185)), hAPP(hAPP(c_Finite__Set_Ofold(_1024179, _1024179, c_Lattices_Osemilattice__sup__class_Osup(_1024179)), _1024185), _1024181))))], (25787 ^ _780478) ^ [_1258709, _1258711] : [_1258709 = hAPP(c_Int_Onat, _1258711), 25790 ^ _780478 : [(25797 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258711))), -(_1258709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25791 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258711)), -(_1258711 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258709))]]], (38222 ^ _780478) ^ [_1514723, _1514725, _1514727] : [c_Wellfounded_Owf(_1514723, _1514725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1514723, _1514723), tc_HOL_Obool)), _1514727), _1514725)), -(c_Wellfounded_Owf(_1514723, _1514727))], (51871 ^ _780478) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (29948 ^ _780478) ^ [_1336282, _1336284] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336282, _1336284)) = _1336284, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1336282), _1336284) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25701 ^ _780478) ^ [_1257314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1257314))))], (31120 ^ _780478) ^ [_1359487, _1359489] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1359487)), -(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)), _1359487))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1359489))))) = 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)), _1359487))), 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, _1359489))))))], (29009 ^ _780478) ^ [_1318076, _1318078, _1318080, _1318082] : [-(hAPP(c_Set_OPow(_1318076), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1318078, tc_fun(_1318076, tc_HOL_Obool)), _1318080), _1318082)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1318078, tc_fun(tc_fun(_1318076, tc_HOL_Obool), tc_HOL_Obool)), _1318080), hAPP(hAPP(c_COMBB(tc_fun(_1318076, tc_HOL_Obool), tc_fun(tc_fun(_1318076, tc_HOL_Obool), tc_HOL_Obool), _1318078), c_Set_OPow(_1318076)), _1318082)))], (42172 ^ _780478) ^ [_1617431, _1617433, _1617435] : [_1617431 = _1617433, 42175 ^ _780478 : [(42178 ^ _780478) ^ [_1617579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1617579), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617435)), _1617431))), -(hAPP(hAPP(c_List_Onth(_1617435), _1617431), _1617579) = hAPP(hAPP(c_List_Onth(_1617435), _1617433), _1617579))], (42176 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617435)), _1617431) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617435)), _1617433))]]], (37175 ^ _780478) ^ [_1487734, _1487736] : [hAPP(c_Int_ORep__Integ, _1487734) = hAPP(c_Int_ORep__Integ, _1487736), -(_1487734 = _1487736)], (25130 ^ _780478) ^ [_1247297, _1247299, _1247301, _1247303] : [class_Orderings_Olinorder(_1247297), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247297), _1247299), _1247301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247297), _1247301), _1247303)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1247297, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1247297, _1247299, _1247301)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1247297, _1247301, _1247303)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1247297, _1247299, _1247303))], (49988 ^ _780478) ^ [_1790891, _1790893, _1790895] : [hAPP(c_Fun_Ocomp(_1790893, _1790891, _1790891, c_Hilbert__Choice_Oinv__into(_1790891, _1790893, c_Orderings_Otop__class_Otop(tc_fun(_1790891, tc_HOL_Obool)), _1790895)), _1790895) = c_Fun_Oid(_1790891), -(c_Fun_Oinj__on(_1790891, _1790893, _1790895, c_Orderings_Otop__class_Otop(tc_fun(_1790891, tc_HOL_Obool))))], (13126 ^ _780478) ^ [_1013183, _1013185, _1013187] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013183, tc_HOL_Obool)), _1013185), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013183, tc_HOL_Obool)), _1013187), _1013185))))], (47230 ^ _780478) ^ [_1730855, _1730857, _1730859, _1730861, _1730863] : [-(hBOOL(hAPP(_1730855, _1730857))), -(c_List_OtakeWhile(_1730859, _1730855, hAPP(hAPP(c_List_Oappend(_1730859), _1730861), hAPP(hAPP(c_List_Olist_OCons(_1730859), _1730857), _1730863))) = c_List_OtakeWhile(_1730859, _1730855, _1730861))], (44841 ^ _780478) ^ [_1679000] : [-(hAPP(c_List_Omap(_1679000, _1679000), c_Fun_Oid(_1679000)) = c_Fun_Oid(tc_List_Olist(_1679000)))], (32210 ^ _780478) ^ [_1388917, _1388919, _1388921] : [class_Int_Onumber__ring(_1388917), class_Rings_Olinordered__idom(_1388917), 32217 ^ _780478 : [(32224 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1388919), _1388921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388917), hAPP(c_Int_Onumber__class_Onumber__of(_1388917), _1388919)), hAPP(c_Int_Onumber__class_Onumber__of(_1388917), _1388921))))], (32218 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388917), hAPP(c_Int_Onumber__class_Onumber__of(_1388917), _1388919)), hAPP(c_Int_Onumber__class_Onumber__of(_1388917), _1388921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1388919), _1388921)))]]], (19796 ^ _780478) ^ [_1149940, _1149942, _1149944, _1149946] : [class_Groups_Oordered__comm__monoid__add(_1149940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149940), c_Groups_Ozero__class_Ozero(_1149940)), _1149942)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149940), _1149944), _1149946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149940), _1149944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149940), _1149946), _1149942))))], (51795 ^ _780478) ^ [_1828028, _1828030] : [class_Lattices_Oboolean__algebra(_1828028), -(class_Lattices_Oboolean__algebra(tc_fun(_1828030, _1828028)))], (41662 ^ _780478) ^ [_1601574] : [-(c_Nitpick_Odenom(_1601574) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1601574, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1601574)))], (17496 ^ _780478) ^ [_1105441, _1105443, _1105445, _1105447, _1105449] : [class_Complete__Lattice_Ocomplete__lattice(_1105441), 17499 ^ _780478 : [(17500 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105441), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105443, _1105441), _1105445), _1105447)), _1105449)), 17503 ^ _780478 : [(17504 ^ _780478) ^ [_1105622] : [hBOOL(hAPP(hAPP(c_member(_1105443), _1105622), _1105445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105441), hAPP(_1105447, _1105622)), _1105449)))]]], (17510 ^ _780478) ^ [] : [17512 ^ _780478 : [(17515 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105441), hAPP(_1105447, 17511 ^ [_1105441, _1105443, _1105445, _1105447, _1105449])), _1105449))], (17513 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1105443), 17511 ^ [_1105441, _1105443, _1105445, _1105447, _1105449]), _1105445)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105441), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105443, _1105441), _1105445), _1105447)), _1105449)))]]], (12093 ^ _780478) ^ [_992828, _992830, _992832] : [class_Orderings_Olinorder(_992828), hBOOL(hAPP(c_Finite__Set_Ofinite(_992828), _992830)), 12100 ^ _780478 : [(12107 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992828, tc_HOL_Obool)), _992830), hAPP(hAPP(c_Set_Oinsert(_992828), _992832), c_Orderings_Obot__class_Obot(tc_fun(_992828, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992828, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_992828, c_Orderings_Oord__class_Omin(_992828), hAPP(hAPP(c_Set_Oinsert(_992828), _992832), _992830)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_992828), _992832), c_Big__Operators_Olattice_OInf__fin(_992828, c_Orderings_Oord__class_Omin(_992828), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992828, tc_HOL_Obool)), _992830), hAPP(hAPP(c_Set_Oinsert(_992828), _992832), c_Orderings_Obot__class_Obot(tc_fun(_992828, tc_HOL_Obool)))))))], (12101 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_992828, tc_HOL_Obool)), _992830), hAPP(hAPP(c_Set_Oinsert(_992828), _992832), c_Orderings_Obot__class_Obot(tc_fun(_992828, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_992828, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_992828, c_Orderings_Oord__class_Omin(_992828), hAPP(hAPP(c_Set_Oinsert(_992828), _992832), _992830)) = _992832)]]], (21179 ^ _780478) ^ [_1174115, _1174117, _1174119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174115), _1174117)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174115), _1174119)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174117), _1174119))))], (19700 ^ _780478) ^ [_1148144, _1148146, _1148148] : [class_Groups_Ocomm__monoid__add(_1148144), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1148146, _1148144), hAPP(c_COMBK(_1148144, _1148146), c_Groups_Ozero__class_Ozero(_1148144))), _1148148) = c_Groups_Ozero__class_Ozero(_1148144))], (36302 ^ _780478) ^ [_1470927, _1470929, _1470931, _1470933, _1470935, _1470937] : [hAPP(hAPP(c_Product__Type_OPair(_1470927, _1470929), _1470931), _1470933) = hAPP(hAPP(c_Product__Type_OPair(_1470927, _1470929), _1470935), _1470937), 36305 ^ _780478 : [(36308 ^ _780478) ^ [] : [-(_1470933 = _1470937)], (36306 ^ _780478) ^ [] : [-(_1470931 = _1470935)]]], (31526 ^ _780478) ^ [_1372521, _1372523, _1372525] : [class_Lattices_Odistrib__lattice(_1372521), hBOOL(hAPP(c_Finite__Set_Ofinite(_1372521), _1372523)), -(_1372523 = c_Orderings_Obot__class_Obot(tc_fun(_1372521, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1372521), _1372525), c_Big__Operators_Olattice__class_OInf__fin(_1372521, _1372523)) = c_Big__Operators_Olattice__class_OInf__fin(_1372521, hAPP(c_Set_OCollect(_1372521), hAPP(hAPP(c_COMBB(tc_fun(_1372521, tc_HOL_Obool), tc_HOL_Obool, _1372521), c_HOL_OEx(_1372521)), hAPP(hAPP(c_COMBC(_1372521, tc_fun(_1372521, tc_HOL_Obool), tc_fun(_1372521, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372521, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1372521, tc_HOL_Obool), tc_fun(_1372521, tc_HOL_Obool)), _1372521), c_COMBS(_1372521, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372521, tc_HOL_Obool), tc_fun(_1372521, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1372521), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1372521), c_fconj)), hAPP(hAPP(c_COMBC(_1372521, tc_fun(_1372521, _1372521), tc_fun(_1372521, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372521, tc_HOL_Obool), tc_fun(tc_fun(_1372521, _1372521), tc_fun(_1372521, tc_HOL_Obool)), _1372521), c_COMBB(_1372521, tc_HOL_Obool, _1372521)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1372521), _1372525))))), hAPP(hAPP(c_COMBC(_1372521, tc_fun(_1372521, tc_HOL_Obool), tc_HOL_Obool), c_member(_1372521)), _1372523))))))], (13908 ^ _780478) ^ [_1029122, _1029124, _1029126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029122), _1029124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029122), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029126), _1029124))))], (8970 ^ _780478) ^ [_934799, _934801] : [class_Orderings_Opreorder(_934799), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934799), _934801), _934801))], (13538 ^ _780478) ^ [_1021961, _1021963, _1021965, _1021967, _1021969] : [c_Fun_Oinj__on(_1021961, _1021963, _1021965, c_Orderings_Otop__class_Otop(tc_fun(_1021961, tc_HOL_Obool))), 13541 ^ _780478 : [(13548 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1021961), _1021967), _1021969)), -(hBOOL(hAPP(hAPP(c_member(_1021963), hAPP(_1021965, _1021967)), hAPP(c_Set_Oimage(_1021961, _1021963, _1021965), _1021969))))], (13542 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1021963), hAPP(_1021965, _1021967)), hAPP(c_Set_Oimage(_1021961, _1021963, _1021965), _1021969))), -(hBOOL(hAPP(hAPP(c_member(_1021961), _1021967), _1021969)))]]], (12578 ^ _780478) ^ [_1002585, _1002587, _1002589] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002585, tc_HOL_Obool)), _1002587), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002585, tc_HOL_Obool)), _1002587), _1002589)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002585, tc_HOL_Obool)), _1002587), _1002589))], (24855 ^ _780478) ^ [_1242087, _1242089, _1242091, _1242093] : [class_Orderings_Olinorder(_1242087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242087), _1242089), _1242091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242087), _1242091), _1242093)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1242087, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1242087, _1242089, _1242091)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1242087, _1242091, _1242093)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1242087, _1242089, _1242093))], (6996 ^ _780478) ^ [_897342, _897344, _897346, _897348, _897350, _897352] : [-(hBOOL(hAPP(hAPP(c_member(_897342), _897344), _897346))), -(hAPP(c_Fun_Ooverride__on(_897342, _897348, _897350, _897352, _897346), _897344) = hAPP(_897350, _897344))], (34573 ^ _780478) ^ [_1432357] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1432357)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1432357)))], (47292 ^ _780478) ^ [_1732012, _1732014, _1732016, _1732018, _1732020] : [class_Orderings_Olinorder(_1732012), c_List_Olinorder__class_Osorted(_1732012, hAPP(c_List_Orev(_1732012), hAPP(hAPP(c_List_Omap(_1732014, _1732012), _1732016), _1732018))), -(hAPP(c_List_Ofilter(_1732014, hAPP(hAPP(c_COMBB(_1732012, tc_HOL_Obool, _1732014), hAPP(c_Orderings_Oord__class_Oless(_1732012), _1732020)), _1732016)), _1732018) = c_List_OtakeWhile(_1732014, hAPP(hAPP(c_COMBB(_1732012, tc_HOL_Obool, _1732014), hAPP(c_Orderings_Oord__class_Oless(_1732012), _1732020)), _1732016), _1732018))], (5847 ^ _780478) ^ [_873105, _873107, _873109, _873111] : [5848 ^ _780478 : [(5851 ^ _780478) ^ [] : [_873107 = _873111], (5849 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873105), _873107), _873109))]], -(hBOOL(hAPP(hAPP(c_member(_873105), _873107), hAPP(hAPP(c_Set_Oinsert(_873105), _873111), _873109))))], (31670 ^ _780478) ^ [_1377907, _1377909, _1377911] : [_1377909 = c_Orderings_Obot__class_Obot(tc_fun(_1377907, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377907, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377907), _1377909), _1377911))], (4234 ^ _780478) ^ [_844542, _844544, _844546, _844548] : [-(c_List_Olast(_844548, _844544) = c_List_Olast(_844546, _844542)), _844548 = _844546, _844544 = _844542], (2154 ^ _780478) ^ [_811884, _811886, _811888, _811890, _811892, _811894, _811896, _811898] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_811898, _811894, _811890, _811886) = c_Nat_Osemiring__1__class_Oof__nat__aux(_811896, _811892, _811888, _811884)), _811898 = _811896, _811894 = _811892, _811890 = _811888, _811886 = _811884], (52005 ^ _780478) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (18171 ^ _780478) ^ [_1119727, _1119729, _1119731, _1119733, _1119735] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119727, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119729, tc_fun(_1119727, tc_HOL_Obool)), _1119731), _1119733)), _1119735) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119729, tc_fun(_1119727, tc_HOL_Obool)), _1119731), hAPP(hAPP(c_COMBC(_1119729, tc_fun(_1119727, tc_HOL_Obool), tc_fun(_1119727, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1119727, tc_HOL_Obool), tc_fun(tc_fun(_1119727, tc_HOL_Obool), tc_fun(_1119727, tc_HOL_Obool)), _1119729), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119727, tc_HOL_Obool))), _1119733)), _1119735)))], (5997 ^ _780478) ^ [_875803, _875805, _875807, _875809] : [-(hAPP(hAPP(c_Set_Oinsert(_875803), _875805), hAPP(hAPP(c_Set_Oinsert(_875803), _875807), _875809)) = hAPP(hAPP(c_Set_Oinsert(_875803), _875807), hAPP(hAPP(c_Set_Oinsert(_875803), _875805), _875809)))], (2918 ^ _780478) ^ [_823692, _823694] : [_823694 = _823692, -(c_Int_Oring__1__class_Oof__int(_823694) = c_Int_Oring__1__class_Oof__int(_823692))], (30278 ^ _780478) ^ [_1342247, _1342249] : [class_Groups_Oordered__ab__group__add__abs(_1342247), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342247), _1342249), hAPP(c_Groups_Oabs__class_Oabs(_1342247), _1342249))))], (1464 ^ _780478) ^ [_801642, _801644] : [-(class_Lazy__Sequence_Osmall__lazy(_801642)), _801644 = _801642, class_Lazy__Sequence_Osmall__lazy(_801644)], (28540 ^ _780478) ^ [_1308823, _1308825, _1308827] : [class_Orderings_Olinorder(_1308823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1308823), _1308825), _1308827)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308823, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1308823), _1308825)), c_SetInterval_Oord__class_OatLeastAtMost(_1308823, _1308825, _1308827)) = hAPP(c_SetInterval_Oord__class_OatMost(_1308823), _1308827))], (32270 ^ _780478) ^ [_1390032, _1390034, _1390036, _1390038] : [class_Int_Onumber__ring(_1390032), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1390032), hAPP(c_Int_Onumber__class_Onumber__of(_1390032), _1390034)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1390032), hAPP(c_Int_Onumber__class_Onumber__of(_1390032), _1390036)), _1390038)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1390032), hAPP(c_Int_Onumber__class_Onumber__of(_1390032), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1390034), _1390036))), _1390038))], (19182 ^ _780478) ^ [_1140468, _1140470] : [class_Groups_Ocomm__monoid__add(_1140468), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140468), _1140470), c_Groups_Ozero__class_Ozero(_1140468)) = _1140470)], (52437 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(t_a), v_F)))], (23299 ^ _780478) ^ [_1214025, _1214027] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214025), _1214027))), -(_1214025 = _1214027), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214027), _1214025)))], (44831 ^ _780478) ^ [_1678687, _1678689, _1678691, _1678693, _1678695] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1678687), tc_List_Olist(_1678689), tc_List_Olist(_1678691), hAPP(c_List_Omap(_1678687, _1678689), _1678693)), hAPP(c_List_Omap(_1678691, _1678687), _1678695)) = hAPP(c_List_Omap(_1678691, _1678689), hAPP(c_Fun_Ocomp(_1678687, _1678689, _1678691, _1678693), _1678695)))], (6746 ^ _780478) ^ [_892122, _892124, _892126, _892128, _892130] : [c_Fun_Ofun__upd(_892122, _892124, _892126, _892128, _892130) = _892126, -(hAPP(_892126, _892128) = _892130)], (42489 ^ _780478) ^ [_1626761, _1626763, _1626765] : [-(_1626761 = _1626763), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626765)), _1626761) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626765)), _1626763), 42495 ^ _780478 : [(42498 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1626765, _1626765, tc_HOL_Obool), c_fequal), 42494 ^ [_1626761, _1626763, _1626765]))], (42496 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1626765, _1626765)), 42494 ^ [_1626761, _1626763, _1626765]), hAPP(c_List_Oset(tc_prod(_1626765, _1626765)), hAPP(hAPP(c_List_Ozip(_1626765, _1626765), _1626761), _1626763)))))]]], (14381 ^ _780478) ^ [_1037314, _1037316, _1037318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037316), _1037318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037314), _1037316)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037314), _1037318))))], (40280 ^ _780478) ^ [_1567009, _1567011, _1567013, _1567015] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1567009, tc_HOL_Obool), tc_fun(_1567009, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1567009, tc_HOL_Obool), tc_fun(_1567009, tc_HOL_Obool)), _1567011), _1567013)), c_Wellfounded_Omax__ext(_1567009, _1567015)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1567009), _1567011)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1567009), _1567013)), -(_1567013 = c_Orderings_Obot__class_Obot(tc_fun(_1567009, tc_HOL_Obool))), 40294 ^ _780478 : [(40297 ^ _780478) ^ [_1567414] : [hBOOL(hAPP(hAPP(c_member(_1567009), _1567414), _1567013)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567009, _1567009)), hAPP(hAPP(c_Product__Type_OPair(_1567009, _1567009), 40293 ^ [_1567009, _1567011, _1567013, _1567015]), _1567414)), _1567015))], (40295 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1567009), 40293 ^ [_1567009, _1567011, _1567013, _1567015]), _1567011)))]]], (45458 ^ _780478) ^ [_1692820, _1692822, _1692824, _1692826, _1692828, _1692830, _1692832] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692820)), _1692822) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692824)), _1692826), 45461 ^ _780478 : [(45470 ^ _780478) ^ [] : [-(c_List_Olist__all2(_1692820, _1692824, _1692828, hAPP(hAPP(c_List_Oappend(_1692820), _1692822), _1692830), hAPP(hAPP(c_List_Oappend(_1692824), _1692826), _1692832))), c_List_Olist__all2(_1692820, _1692824, _1692828, _1692822, _1692826), c_List_Olist__all2(_1692820, _1692824, _1692828, _1692830, _1692832)], (45462 ^ _780478) ^ [] : [c_List_Olist__all2(_1692820, _1692824, _1692828, hAPP(hAPP(c_List_Oappend(_1692820), _1692822), _1692830), hAPP(hAPP(c_List_Oappend(_1692824), _1692826), _1692832)), 45465 ^ _780478 : [(45468 ^ _780478) ^ [] : [-(c_List_Olist__all2(_1692820, _1692824, _1692828, _1692830, _1692832))], (45466 ^ _780478) ^ [] : [-(c_List_Olist__all2(_1692820, _1692824, _1692828, _1692822, _1692826))]]]]], (23207 ^ _780478) ^ [_1212445, _1212447] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212445) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212447), -(_1212445 = _1212447)], (31278 ^ _780478) ^ [_1363060, _1363062, _1363064] : [-(hBOOL(hAPP(_1363060, _1363062))), -(hAPP(c_Set_OCollect(_1363064), hAPP(hAPP(c_COMBS(_1363064, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1363064), c_fconj), hAPP(hAPP(c_COMBC(_1363064, _1363064, tc_HOL_Obool), c_fequal), _1363062))), _1363060)) = c_Orderings_Obot__class_Obot(tc_fun(_1363064, tc_HOL_Obool)))], (30384 ^ _780478) ^ [_1344513, _1344515, _1344517] : [class_Complete__Lattice_Ocomplete__lattice(_1344513), 30387 ^ _780478 : [(30388 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344513), c_Complete__Lattice_OSup__class_OSup(_1344513, _1344515)), _1344517)), 30391 ^ _780478 : [(30392 ^ _780478) ^ [_1344671] : [hBOOL(hAPP(hAPP(c_member(_1344513), _1344671), _1344515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344513), _1344671), _1344517)))]]], (30398 ^ _780478) ^ [] : [30400 ^ _780478 : [(30403 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344513), 30399 ^ [_1344513, _1344515, _1344517]), _1344517))], (30401 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344513), 30399 ^ [_1344513, _1344515, _1344517]), _1344515)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344513), c_Complete__Lattice_OSup__class_OSup(_1344513, _1344515)), _1344517)))]]], (10371 ^ _780478) ^ [_961392, _961394, _961396, _961398] : [class_Groups_Ouminus(_961392), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961394, _961392)), _961396), _961398) = hAPP(c_Groups_Ouminus__class_Ouminus(_961392), hAPP(_961396, _961398)))], (50421 ^ _780478) ^ [_1800648, _1800650, _1800652, _1800654] : [c_Fun_Obij__betw(_1800648, _1800650, _1800652, c_Orderings_Otop__class_Otop(tc_fun(_1800648, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1800650, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1800648, _1800650, _1800652), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1800648, tc_HOL_Obool)), _1800654)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1800650, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1800648, _1800650, _1800652), _1800654)))], (34629 ^ _780478) ^ [_1433347, _1433349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1433347)), c_Int_OBit0(_1433349))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433347), _1433349)))], (43269 ^ _780478) ^ [_1643151] : [-(c_List_Olistset(_1643151, c_List_Olist_ONil(tc_fun(_1643151, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1643151)), c_List_Olist_ONil(_1643151)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1643151), tc_HOL_Obool))))], (47236 ^ _780478) ^ [_1730938, _1730940, _1730942, _1730944] : [hBOOL(hAPP(_1730938, _1730940)), -(c_List_OtakeWhile(_1730942, _1730938, hAPP(hAPP(c_List_Olist_OCons(_1730942), _1730940), _1730944)) = hAPP(hAPP(c_List_Olist_OCons(_1730942), _1730940), c_List_OtakeWhile(_1730942, _1730938, _1730944)))], (2574 ^ _780478) ^ [_818380, _818382] : [_818382 = _818380, -(c_Int_Oint__ge__less__than2(_818382) = c_Int_Oint__ge__less__than2(_818380))], (29999 ^ _780478) ^ [_1337004, _1337006, _1337008] : [-(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), _1337004), _1337006)), _1337008), _1337006) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337008, _1337006))], (43871 ^ _780478) ^ [_1657846, _1657848, _1657850, _1657852] : [-(hAPP(hAPP(c_List_Odrop(_1657846), _1657848), hAPP(hAPP(c_List_Odrop(_1657846), _1657850), _1657852)) = hAPP(hAPP(c_List_Odrop(_1657846), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657848), _1657850)), _1657852))], (2332 ^ _780478) ^ [_814633, _814635] : [_814635 = _814633, -(c_Nat_Osemiring__1__class_ONats(_814635) = c_Nat_Osemiring__1__class_ONats(_814633))], (40371 ^ _780478) ^ [_1569240, _1569242] : [c_Wellfounded_Oacyclic(_1569240, _1569242), 40374 ^ _780478 : [(40375 ^ _780478) ^ [_1569325] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569240, _1569240)), hAPP(hAPP(c_Product__Type_OPair(_1569240, _1569240), _1569325), _1569325)), c_Transitive__Closure_Otrancl(_1569240, _1569242)))]]], (47421 ^ _780478) ^ [_1734730, _1734732, _1734734] : [-(c_List_OdropWhile(_1734730, _1734732, _1734734) = hAPP(hAPP(c_List_Odrop(_1734730), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734730)), c_List_OtakeWhile(_1734730, _1734732, _1734734))), _1734734))], (29506 ^ _780478) ^ [_1328356, _1328358, _1328360] : [class_Divides_Osemiring__div(_1328356), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328356), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328356), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1328356), _1328358), _1328360)), _1328360)), c_Divides_Odiv__class_Omod(_1328356, _1328358, _1328360)) = _1328358)], (52449 ^ _780478) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P_H)), v_c0)), v_Q_H)), v_F)))], (33306 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (49901 ^ _780478) ^ [_1788974, _1788976] : [c_Equiv__Relations_Opart__equivp(_1788974, _1788976), 49905 ^ _780478 : [(49918 ^ _780478) ^ [_1789316, _1789318] : [-(hBOOL(hAPP(hAPP(_1788976, _1789318), _1789316))), hBOOL(hAPP(hAPP(_1788976, _1789318), _1789318)), hBOOL(hAPP(hAPP(_1788976, _1789316), _1789316)), hAPP(_1788976, _1789318) = hAPP(_1788976, _1789316)], (49908 ^ _780478) ^ [_1789147, _1789149] : [hBOOL(hAPP(hAPP(_1788976, _1789149), _1789147)), 49911 ^ _780478 : [(49916 ^ _780478) ^ [] : [-(hAPP(_1788976, _1789149) = hAPP(_1788976, _1789147))], (49914 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1788976, _1789147), _1789147)))], (49912 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1788976, _1789149), _1789149)))]]], (49906 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1788976, 49904 ^ [_1788974, _1788976]), 49904 ^ [_1788974, _1788976])))]]], (15661 ^ _780478) ^ [_1063348, _1063350, _1063352] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063348, tc_HOL_Obool)), _1063350), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063348, tc_HOL_Obool)), _1063350), _1063352)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063348, tc_HOL_Obool)), _1063350), _1063352))], (16230 ^ _780478) ^ [_1074869, _1074871, _1074873, _1074875] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074869, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074869, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074869, tc_HOL_Obool)), _1074871), _1074873)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074869, tc_HOL_Obool)), _1074873), _1074875))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074869, tc_HOL_Obool)), _1074875), _1074871)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074869, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074869, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074869, tc_HOL_Obool)), _1074871), _1074873)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074869, tc_HOL_Obool)), _1074873), _1074875))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074869, tc_HOL_Obool)), _1074875), _1074871)))], (51589 ^ _780478) ^ [_1824720, _1824722, _1824724] : [class_Divides_Osemiring__div(_1824720), 51592 ^ _780478 : [(51599 ^ _780478) ^ [] : [c_Divides_Odiv__class_Omod(_1824720, _1824724, _1824722) = c_Groups_Ozero__class_Ozero(_1824720), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824720), _1824722), _1824724)))], (51593 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824720), _1824722), _1824724)), -(c_Divides_Odiv__class_Omod(_1824720, _1824724, _1824722) = c_Groups_Ozero__class_Ozero(_1824720))]]], (35439 ^ _780478) ^ [_1448077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1448077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1448077))))], (46310 ^ _780478) ^ [_1712625, _1712627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712625), _1712627)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1712625, _1712627)) = _1712625)], (7870 ^ _780478) ^ [_914004, _914006, _914008, _914010, _914012, _914014] : [hBOOL(hAPP(hAPP(c_member(_914004), _914006), _914008)), -(hAPP(c_Fun_Ooverride__on(_914004, _914010, _914012, _914014, _914008), _914006) = hAPP(_914014, _914006))], (18183 ^ _780478) ^ [_1120336, _1120338, _1120340, _1120342, _1120344, _1120346] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120336, tc_fun(_1120338, tc_HOL_Obool)), _1120340), hAPP(hAPP(c_COMBC(_1120336, tc_fun(_1120342, tc_fun(_1120338, tc_HOL_Obool)), tc_fun(_1120338, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1120342, tc_HOL_Obool), tc_fun(tc_fun(_1120342, tc_fun(_1120338, tc_HOL_Obool)), tc_fun(_1120338, tc_HOL_Obool)), _1120336), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120342, tc_fun(_1120338, tc_HOL_Obool))), _1120344)), _1120346)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120342, tc_fun(_1120338, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1120336, tc_fun(_1120342, tc_HOL_Obool)), _1120340), _1120344)), _1120346))], (38937 ^ _780478) ^ [_1533259, _1533261, _1533263, _1533265] : [-(_1533259 = c_Orderings_Obot__class_Obot(tc_fun(_1533261, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1533263, _1533261), _1533263, c_Product__Type_Ofst(_1533263, _1533261)), hAPP(hAPP(c_Product__Type_OSigma(_1533263, _1533261), _1533265), hAPP(c_COMBK(tc_fun(_1533261, tc_HOL_Obool), _1533263), _1533259))) = _1533265)], (31827 ^ _780478) ^ [_1381592] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1381592))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1381592)) = _1381592)], (22271 ^ _780478) ^ [_1194571, _1194573, _1194575, _1194577, _1194579] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_1194571, _1194573, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1194571), _1194575), _1194577), _1194579)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30007 ^ _780478) ^ [_1337166, _1337168] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1337166), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1337168)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337166, _1337168)))], (9332 ^ _780478) ^ [_940192, _940194, _940196, _940198] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_940192), 9335 ^ _780478 : [(9342 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940192), _940194), _940198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940192), _940194), _940196)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940192), _940198), _940196))))], (9336 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940192), _940194), _940196)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940192), _940198), _940196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940192), _940194), _940198)))]]], (27389 ^ _780478) ^ [_1287391, _1287393, _1287395] : [class_Int_Oring__char__0(_1287391), 27392 ^ _780478 : [(27399 ^ _780478) ^ [] : [_1287393 = _1287395, -(hAPP(c_Int_Oring__1__class_Oof__int(_1287391), _1287393) = hAPP(c_Int_Oring__1__class_Oof__int(_1287391), _1287395))], (27393 ^ _780478) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1287391), _1287393) = hAPP(c_Int_Oring__1__class_Oof__int(_1287391), _1287395), -(_1287393 = _1287395)]]], (6856 ^ _780478) ^ [_893859, _893861, _893863, _893865, _893867, _893869, _893871] : [hBOOL(hAPP(hAPP(c_member(_893859), _893861), _893863)), c_Nitpick_Ofold__graph_H(_893859, _893865, _893867, _893869, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893859, tc_HOL_Obool)), _893863), hAPP(hAPP(c_Set_Oinsert(_893859), _893861), c_Orderings_Obot__class_Obot(tc_fun(_893859, tc_HOL_Obool)))), _893871), -(c_Nitpick_Ofold__graph_H(_893859, _893865, _893867, _893869, _893863, hAPP(hAPP(_893867, _893861), _893871)))], (37092 ^ _780478) ^ [_1486083, _1486085, _1486087] : [37094 ^ _780478 : [(37097 ^ _780478) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1486083, _1486085), 37093 ^ [_1486083, _1486085, _1486087]))], (37095 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1486085, 37093 ^ [_1486083, _1486085, _1486087]), _1486087)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1486083, _1486085), _1486087)))], (15665 ^ _780478) ^ [_1063481, _1063483, _1063485, _1063487, _1063489] : [-(hAPP(c_Set_Ovimage(_1063481, _1063483, _1063485), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063483, tc_HOL_Obool)), _1063487), _1063489)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063481, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1063481, _1063483, _1063485), _1063487)), hAPP(c_Set_Ovimage(_1063481, _1063483, _1063485), _1063489)))], (29824 ^ _780478) ^ [_1334278, _1334280] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1334278)), _1334280)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1334278), _1334280)))], (43329 ^ _780478) ^ [_1644997, _1644999, _1645001, _1645003] : [-(c_List_Osublist(_1644997, hAPP(hAPP(c_List_Olist_OCons(_1644997), _1644999), _1645001), _1645003) = hAPP(hAPP(c_List_Oappend(_1644997), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1644997)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1645003)), hAPP(hAPP(c_List_Olist_OCons(_1644997), _1644999), c_List_Olist_ONil(_1644997))), c_List_Olist_ONil(_1644997))), c_List_Osublist(_1644997, _1645001, 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)), _1645003)))))], (40570 ^ _780478) ^ [_1574121, _1574123, _1574125, _1574127, _1574129] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574121, _1574121)), hAPP(hAPP(c_Product__Type_OPair(_1574121, _1574121), _1574123), _1574125)), c_Transitive__Closure_Ortrancl(_1574121, _1574127))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574121, _1574121)), hAPP(hAPP(c_Product__Type_OPair(_1574121, _1574121), _1574125), _1574129)), c_Transitive__Closure_Ortrancl(_1574121, _1574127))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574121, _1574121)), hAPP(hAPP(c_Product__Type_OPair(_1574121, _1574121), _1574123), _1574129)), c_Transitive__Closure_Ortrancl(_1574121, _1574127))))], (47197 ^ _780478) ^ [_1730077, _1730079, _1730081, _1730083] : [hBOOL(hAPP(hAPP(c_member(_1730077), _1730079), hAPP(c_List_Oset(_1730077), c_List_OtakeWhile(_1730077, _1730081, _1730083)))), 47200 ^ _780478 : [(47203 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1730081, _1730079)))], (47201 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730077), _1730079), hAPP(c_List_Oset(_1730077), _1730083))))]]], (34341 ^ _780478) ^ [_1428242, _1428244] : [-(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), _1428242)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1428244)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1428242))) = 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), _1428244)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428242)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23170 ^ _780478) ^ [_1211818] : [hBOOL(hAPP(_1211818, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23171 ^ [_1211818]))), 23174 ^ _780478 : [(23175 ^ _780478) ^ [_1211918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1211918)), -(hBOOL(hAPP(_1211818, _1211918)))]]], (23975 ^ _780478) ^ [_1226245, _1226247, _1226249, _1226251, _1226253, _1226255] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226245), _1226247)), _1226249) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1226251), _1226253)), _1226255), 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), _1226251), _1226253)), _1226255)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226249), _1226245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226251), _1226245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226253), _1226247)))], (42985 ^ _780478) ^ [_1638000] : [-(c_List_Obutlast(_1638000, c_List_Olist_ONil(_1638000)) = c_List_Olist_ONil(_1638000))], (16224 ^ _780478) ^ [_1074617, _1074619, _1074621, _1074623] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074617, tc_HOL_Obool)), _1074619), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074617, tc_HOL_Obool)), _1074621), _1074623)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074617, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074617, tc_HOL_Obool)), _1074619), _1074621)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074617, tc_HOL_Obool)), _1074619), _1074623)))], (13456 ^ _780478) ^ [_1020316, _1020318, _1020320, _1020322] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1020316), _1020318)), hAPP(c_Finite__Set_Ocard(_1020320), hAPP(c_Set_Oimage(_1020316, _1020320, _1020322), _1020318)) = hAPP(c_Finite__Set_Ocard(_1020316), _1020318), -(c_Fun_Oinj__on(_1020316, _1020320, _1020322, _1020318))], (33348 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10317 ^ _780478) ^ [_960453, _960455, _960457] : [class_Orderings_Olinorder(_960453), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_960453), _960455), hAPP(hAPP(c_Orderings_Oord__class_Omin(_960453), _960455), _960457)) = _960455)], (37022 ^ _780478) ^ [_1484636, _1484638] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1484636, _1484638) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1484636, _1484638)))], (11601 ^ _780478) ^ [_983883, _983885, _983887] : [class_Lattices_Oab__semigroup__idem__mult(_983883), hBOOL(hAPP(c_Finite__Set_Ofinite(_983883), _983885)), -(hAPP(c_Finite__Set_Ofold1(_983883, c_Groups_Otimes__class_Otimes(_983883)), hAPP(hAPP(c_Set_Oinsert(_983883), _983887), _983885)) = hAPP(hAPP(c_Finite__Set_Ofold(_983883, _983883, c_Groups_Otimes__class_Otimes(_983883)), _983887), _983885))], (6786 ^ _780478) ^ [_892707, _892709, _892711, _892713, _892715] : [hAPP(_892707, _892709) = _892711, -(c_Fun_Ofun__upd(_892713, _892715, _892707, _892709, _892711) = _892707)], (23867 ^ _780478) ^ [_1224332, _1224334, _1224336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224332)), _1224332 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224334), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224332), _1224336)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224336), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (40103 ^ _780478) ^ [_1562744, _1562746, _1562748, _1562750, _1562752, _1562754] : [class_Groups_Ocomm__monoid__add(_1562744), hBOOL(hAPP(c_Finite__Set_Ofinite(_1562746), _1562748)), 40113 ^ _780478 : [(40114 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562746), 40112 ^ [_1562744, _1562746, _1562748, _1562750, _1562752, _1562754]), _1562748)))], (40119 ^ _780478) ^ [] : [40112 ^ [_1562744, _1562746, _1562748, _1562750, _1562752, _1562754] = 40115 ^ [_1562744, _1562746, _1562748, _1562750, _1562752, _1562754]], (40123 ^ _780478) ^ [] : [hAPP(_1562752, hAPP(_1562750, 40112 ^ [_1562744, _1562746, _1562748, _1562750, _1562752, _1562754])) = c_Groups_Ozero__class_Ozero(_1562744)], (40121 ^ _780478) ^ [] : [-(hAPP(_1562750, 40112 ^ [_1562744, _1562746, _1562748, _1562750, _1562752, _1562754]) = hAPP(_1562750, 40115 ^ [_1562744, _1562746, _1562748, _1562750, _1562752, _1562754]))], (40117 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562746), 40115 ^ [_1562744, _1562746, _1562748, _1562750, _1562752, _1562754]), _1562748)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1562754, _1562744), _1562752), hAPP(c_Set_Oimage(_1562746, _1562754, _1562750), _1562748)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1562746, _1562744), hAPP(c_Fun_Ocomp(_1562754, _1562744, _1562746, _1562752), _1562750)), _1562748))], (15982 ^ _780478) ^ [_1069600, _1069602, _1069604, _1069606] : [class_Lattices_Osemilattice__inf(_1069600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069600), _1069602), _1069604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069600), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069600), _1069606), _1069602)), _1069604)))], (23219 ^ _780478) ^ [_1212633, _1212635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212633)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212635))))], (13564 ^ _780478) ^ [_1022467, _1022469] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1022467), c_Orderings_Otop__class_Otop(tc_fun(_1022467, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1022467, _1022467, _1022469), c_Orderings_Otop__class_Otop(tc_fun(_1022467, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1022467, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1022467, _1022467, _1022469, c_Orderings_Otop__class_Otop(tc_fun(_1022467, tc_HOL_Obool))))], (4104 ^ _780478) ^ [_842541, _842543, _842545, _842547] : [-(c_New__DSequence_Oneg__single(_842547, _842543) = c_New__DSequence_Oneg__single(_842545, _842541)), _842547 = _842545, _842543 = _842541], (15699 ^ _780478) ^ [_1064185, _1064187] : [class_Lattices_Osemilattice__inf(_1064185), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064185), _1064187), _1064187) = _1064187)], (15093 ^ _780478) ^ [_1052220, _1052222, _1052224, _1052226] : [class_Rings_Ocomm__semiring__1(_1052220), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1052220), hAPP(hAPP(c_Power_Opower__class_Opower(_1052220), _1052222), _1052224)), _1052226) = hAPP(hAPP(c_Power_Opower__class_Opower(_1052220), _1052222), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1052224), _1052226)))], (7986 ^ _780478) ^ [_916276, _916278, _916280] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916276, tc_HOL_Obool)), _916278), hAPP(hAPP(c_Set_Oinsert(_916276), _916280), c_Orderings_Obot__class_Obot(tc_fun(_916276, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_916276, _916280, _916278) = c_HOL_OThe(_916276, hAPP(hAPP(c_COMBC(_916276, tc_fun(_916276, tc_HOL_Obool), tc_HOL_Obool), c_member(_916276)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916276, tc_HOL_Obool)), _916278), hAPP(hAPP(c_Set_Oinsert(_916276), _916280), c_Orderings_Obot__class_Obot(tc_fun(_916276, tc_HOL_Obool)))))))], (7672 ^ _780478) ^ [_909863, _909865, _909867, _909869, _909871] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909863, tc_HOL_Obool)), _909865), hAPP(c_Set_Oimage(_909867, _909863, _909869), _909871)))), 7673 ^ _780478 : [(7674 ^ _780478) ^ [_909943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909867, tc_HOL_Obool)), _909943), _909871)), _909865 = hAPP(c_Set_Oimage(_909867, _909863, _909869), _909943)]]], (20484 ^ _780478) ^ [_1162443, _1162445, _1162447, _1162449] : [class_Rings_Olinordered__semiring__strict(_1162443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162443), _1162445), _1162447)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162443), c_Groups_Ozero__class_Ozero(_1162443)), _1162449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162443), _1162445), _1162449)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162443), _1162447), _1162449))))], (20366 ^ _780478) ^ [_1160277, _1160279, _1160281] : [class_Rings_Olinordered__semiring__strict(_1160277), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160277), c_Groups_Ozero__class_Ozero(_1160277)), _1160279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160277), c_Groups_Ozero__class_Ozero(_1160277)), _1160281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160277), c_Groups_Ozero__class_Ozero(_1160277)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160277), _1160279), _1160281))))], (37780 ^ _780478) ^ [_1501734, _1501736, _1501738, _1501740] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1501734, _1501734)), hAPP(hAPP(c_Product__Type_OPair(_1501734, _1501734), _1501736), _1501738)), c_Relation_OId__on(_1501734, _1501740)))), _1501736 = _1501738, hBOOL(hAPP(hAPP(c_member(_1501734), _1501736), _1501740))], (13596 ^ _780478) ^ [_1023186, _1023188, _1023190, _1023192] : [hAPP(c_Set_Oimage(_1023186, _1023188, _1023190), c_Orderings_Otop__class_Otop(tc_fun(_1023186, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1023188, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1023188, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1023188, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1023186, _1023188, _1023190), _1023192))), hAPP(c_Set_Oimage(_1023186, _1023188, _1023190), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1023186, tc_HOL_Obool)), _1023192)))))], (29235 ^ _780478) ^ [_1323162, _1323164, _1323166, _1323168, _1323170, _1323172] : [class_Divides_Osemiring__div(_1323162), c_Divides_Odiv__class_Omod(_1323162, _1323164, _1323166) = c_Divides_Odiv__class_Omod(_1323162, _1323168, _1323166), c_Divides_Odiv__class_Omod(_1323162, _1323170, _1323166) = c_Divides_Odiv__class_Omod(_1323162, _1323172, _1323166), -(c_Divides_Odiv__class_Omod(_1323162, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323162), _1323164), _1323170), _1323166) = c_Divides_Odiv__class_Omod(_1323162, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323162), _1323168), _1323172), _1323166))], (46302 ^ _780478) ^ [_1712451, _1712453, _1712455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1712451), _1712453)), _1712455)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1712453), c_List_Oupt(_1712451, _1712455)) = c_List_Oupt(_1712451, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1712451), _1712453)))], (34997 ^ _780478) ^ [_1439837, _1439839, _1439841] : [class_Rings_Olinordered__semidom(_1439837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439837), hAPP(hAPP(c_Power_Opower__class_Opower(_1439837), _1439839), 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(_1439837), _1439841), 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(_1439837), c_Groups_Ozero__class_Ozero(_1439837)), _1439841)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439837), _1439839), _1439841)))], (6220 ^ _780478) ^ [_880162, _880164] : [hBOOL(hAPP(hAPP(c_member(_880162), _880164), c_Orderings_Obot__class_Obot(tc_fun(_880162, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_880162, tc_HOL_Obool)), _880164)))], (27407 ^ _780478) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (21712 ^ _780478) ^ [_1183703, _1183705] : [hAPP(c_Finite__Set_Ocard(_1183703), _1183705) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1183705 = c_Orderings_Obot__class_Obot(tc_fun(_1183703, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1183703), _1183705))], (8074 ^ _780478) ^ [_918251, _918253, _918255, _918257, _918259, _918261] : [c_Finite__Set_Ofun__left__comm(_918251, _918253, _918255), hBOOL(hAPP(c_Finite__Set_Ofinite(_918251), _918257)), -(hBOOL(hAPP(hAPP(c_member(_918251), _918259), _918257))), -(hAPP(hAPP(c_Finite__Set_Ofold(_918251, _918253, _918255), _918261), hAPP(hAPP(c_Set_Oinsert(_918251), _918259), _918257)) = hAPP(hAPP(_918255, _918259), hAPP(hAPP(c_Finite__Set_Ofold(_918251, _918253, _918255), _918261), _918257)))], (30376 ^ _780478) ^ [_1344183, _1344185, _1344187] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1344183, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1344183, tc_HOL_Obool), _1344185)), _1344187) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1344183, tc_HOL_Obool), tc_fun(_1344183, tc_HOL_Obool)), _1344185), hAPP(hAPP(c_COMBC(tc_fun(_1344183, tc_HOL_Obool), tc_fun(_1344183, tc_HOL_Obool), tc_fun(_1344183, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1344183, tc_HOL_Obool))), _1344187)))], (44089 ^ _780478) ^ [_1663091, _1663093] : [-(_1663091 = c_List_Olist_ONil(_1663093)), -(hBOOL(hAPP(hAPP(c_member(_1663093), hAPP(c_List_Ohd(_1663093), _1663091)), hAPP(c_List_Oset(_1663093), _1663091))))], (41210 ^ _780478) ^ [_1589656, _1589658, _1589660] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589656, _1589656, _1589656), _1589658), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589656, _1589656), tc_HOL_Obool), _1589660), _1589658)) = hAPP(hAPP(c_Relation_Orel__comp(_1589656, _1589656, _1589656), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589656, _1589656), tc_HOL_Obool), _1589660), _1589658)), _1589658))], (15992 ^ _780478) ^ [_1069779, _1069781] : [class_Lattices_Obounded__lattice__bot(_1069779), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069779), c_Orderings_Obot__class_Obot(_1069779)), _1069781) = c_Orderings_Obot__class_Obot(_1069779))], (21065 ^ _780478) ^ [_1172211, _1172213] : [class_Power_Opower(_1172211), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1172211), _1172213), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1172211))], (48965 ^ _780478) ^ [_1768482, _1768484, _1768486, _1768488, _1768490, _1768492] : [-(c_Nitpick_Opair__box_Opair__box__case(_1768482, _1768484, _1768486, _1768488, c_Nitpick_Opair__box_OPairBox(_1768482, _1768484, _1768490, _1768492)) = hAPP(hAPP(_1768488, _1768490), _1768492))], (36548 ^ _780478) ^ [_1475699, _1475701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475699)), 36551 ^ _780478 : [(36558 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1475701), _1475699))), -(c_Divides_OposDivAlg(_1475701, _1475699) = hAPP(c_Divides_Oadjust(_1475699), c_Divides_OposDivAlg(_1475701, 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)))), _1475699))))], (36552 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1475701), _1475699)), -(c_Divides_OposDivAlg(_1475701, _1475699) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475701))]]], (31576 ^ _780478) ^ [_1374592, _1374594, _1374596] : [class_Orderings_Olinorder(_1374592), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374592), _1374594)), -(_1374594 = c_Orderings_Obot__class_Obot(tc_fun(_1374592, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374592), _1374596)), -(_1374596 = c_Orderings_Obot__class_Obot(tc_fun(_1374592, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1374592), c_Big__Operators_Olattice_OSup__fin(_1374592, c_Orderings_Oord__class_Omax(_1374592), _1374594)), c_Big__Operators_Olattice_OSup__fin(_1374592, c_Orderings_Oord__class_Omax(_1374592), _1374596)) = c_Big__Operators_Olattice_OSup__fin(_1374592, c_Orderings_Oord__class_Omax(_1374592), hAPP(c_Set_OCollect(_1374592), hAPP(hAPP(c_COMBB(tc_fun(_1374592, tc_HOL_Obool), tc_HOL_Obool, _1374592), c_HOL_OEx(_1374592)), hAPP(hAPP(c_COMBB(tc_fun(_1374592, tc_fun(_1374592, tc_HOL_Obool)), tc_fun(_1374592, tc_HOL_Obool), _1374592), hAPP(c_COMBB(tc_fun(_1374592, tc_HOL_Obool), tc_HOL_Obool, _1374592), c_HOL_OEx(_1374592))), hAPP(hAPP(c_COMBC(_1374592, tc_fun(_1374592, tc_fun(_1374592, tc_HOL_Obool)), tc_fun(_1374592, tc_fun(_1374592, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1374592, tc_fun(tc_fun(_1374592, tc_HOL_Obool), tc_fun(_1374592, tc_HOL_Obool))), tc_fun(tc_fun(_1374592, tc_fun(_1374592, tc_HOL_Obool)), tc_fun(_1374592, tc_fun(_1374592, tc_HOL_Obool))), _1374592), c_COMBS(_1374592, tc_fun(_1374592, tc_HOL_Obool), tc_fun(_1374592, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1374592, tc_fun(_1374592, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1374592, tc_fun(tc_fun(_1374592, tc_HOL_Obool), tc_fun(_1374592, tc_HOL_Obool))), _1374592), hAPP(c_COMBB(tc_fun(_1374592, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1374592, tc_HOL_Obool), tc_fun(_1374592, tc_HOL_Obool)), _1374592), c_COMBS(_1374592, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1374592, tc_fun(_1374592, tc_HOL_Obool)), tc_fun(_1374592, tc_fun(_1374592, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1374592), hAPP(c_COMBB(tc_fun(_1374592, tc_HOL_Obool), tc_fun(_1374592, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1374592), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1374592), c_fconj))), hAPP(hAPP(c_COMBC(_1374592, tc_fun(_1374592, tc_fun(_1374592, _1374592)), tc_fun(_1374592, tc_fun(_1374592, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1374592, _1374592), tc_fun(_1374592, tc_HOL_Obool)), tc_fun(tc_fun(_1374592, tc_fun(_1374592, _1374592)), tc_fun(_1374592, tc_fun(_1374592, tc_HOL_Obool))), _1374592), c_COMBB(tc_fun(_1374592, _1374592), tc_fun(_1374592, tc_HOL_Obool), _1374592)), hAPP(hAPP(c_COMBB(tc_fun(_1374592, tc_HOL_Obool), tc_fun(tc_fun(_1374592, _1374592), tc_fun(_1374592, tc_HOL_Obool)), _1374592), c_COMBB(_1374592, tc_HOL_Obool, _1374592)), c_fequal))), c_Orderings_Oord__class_Omin(_1374592)))))), hAPP(hAPP(c_COMBC(_1374592, tc_fun(_1374592, tc_HOL_Obool), tc_fun(_1374592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1374592, tc_HOL_Obool), tc_fun(_1374592, tc_HOL_Obool)), _1374592), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1374592)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1374592), c_fconj), hAPP(hAPP(c_COMBC(_1374592, tc_fun(_1374592, tc_HOL_Obool), tc_HOL_Obool), c_member(_1374592)), _1374594)))), hAPP(hAPP(c_COMBC(_1374592, tc_fun(_1374592, tc_HOL_Obool), tc_HOL_Obool), c_member(_1374592)), _1374596))))))))], (14411 ^ _780478) ^ [_1037764, _1037766] : [-(_1037764 = _1037766), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037764), _1037766))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037766), _1037764)))], (48276 ^ _780478) ^ [_1753506, _1753508, _1753510] : [c_List_Olist__all(_1753506, _1753510, _1753508), 48279 ^ _780478 : [(48280 ^ _780478) ^ [_1753587] : [hBOOL(hAPP(hAPP(c_member(_1753506), _1753587), hAPP(c_List_Oset(_1753506), _1753508))), -(hBOOL(hAPP(_1753510, _1753587)))]]], (34353 ^ _780478) ^ [_1428475, _1428477, _1428479] : [-(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), _1428475)), 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))), _1428477))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1428479))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1428479)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428475), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428475), 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), _1428479), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1428477)))))], (35569 ^ _780478) ^ [_1450032] : [-(c_Int_Oint__ge__less__than(_1450032) = 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), _1450032)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (34273 ^ _780478) ^ [_1426888, _1426890] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426888)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426890)) = 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)))), _1426888)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426890)))], (5664 ^ _780478) ^ [_867177, _867179] : [_867179 = _867177, -(c_Orderings_Obot__class_Obot(_867179) = c_Orderings_Obot__class_Obot(_867177))], (39025 ^ _780478) ^ [_1536933, _1536935] : [-(hAPP(c_Fun_Oid(_1536933), _1536935) = _1536935)], (17374 ^ _780478) ^ [_1101495, _1101497, _1101499, _1101501] : [c_Orderings_Obot__class_Obot(tc_fun(_1101495, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101497, tc_fun(_1101495, tc_HOL_Obool)), _1101499), _1101501), 17377 ^ _780478 : [(17378 ^ _780478) ^ [_1101611] : [hBOOL(hAPP(hAPP(c_member(_1101497), _1101611), _1101499)), -(hAPP(_1101501, _1101611) = c_Orderings_Obot__class_Obot(tc_fun(_1101495, tc_HOL_Obool)))]]], (22525 ^ _780478) ^ [_1199952, _1199954, _1199956, _1199958, _1199960] : [class_Groups_Ocomm__monoid__add(_1199952), class_Groups_Oordered__ab__semigroup__add(_1199952), hBOOL(hAPP(c_Finite__Set_Ofinite(_1199954), _1199956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1199954, tc_HOL_Obool)), _1199958), _1199956)), 22543 ^ _780478 : [(22546 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1199952), c_Groups_Ozero__class_Ozero(_1199952)), hAPP(_1199960, 22542 ^ [_1199952, _1199954, _1199956, _1199958, _1199960])))], (22544 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1199954), 22542 ^ [_1199952, _1199954, _1199956, _1199958, _1199960]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1199954, tc_HOL_Obool)), _1199956), _1199958))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1199952), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1199954, _1199952), _1199960), _1199958)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1199954, _1199952), _1199960), _1199956))))], (50167 ^ _780478) ^ [_1795010, _1795012, _1795014] : [hAPP(c_Set_Oimage(_1795010, _1795012, _1795014), c_Orderings_Otop__class_Otop(tc_fun(_1795010, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1795012, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1795010, _1795012, _1795012, _1795014), c_Hilbert__Choice_Oinv__into(_1795010, _1795012, c_Orderings_Otop__class_Otop(tc_fun(_1795010, tc_HOL_Obool)), _1795014)) = c_Fun_Oid(_1795012))], (42710 ^ _780478) ^ [_1631827, _1631829, _1631831, _1631833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631827), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631829)), _1631831))), 42713 ^ _780478 : [(42720 ^ _780478) ^ [] : [hAPP(hAPP(c_List_Onth(_1631829), _1631831), _1631827) = _1631833, -(hAPP(hAPP(c_List_Olist__update(_1631829, _1631831), _1631827), _1631833) = _1631831)], (42714 ^ _780478) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1631829, _1631831), _1631827), _1631833) = _1631831, -(hAPP(hAPP(c_List_Onth(_1631829), _1631831), _1631827) = _1631833)]]], (16651 ^ _780478) ^ [_1084880, _1084882, _1084884, _1084886, _1084888] : [class_Groups_Ocomm__monoid__mult(_1084880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084882), _1084884)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084882), _1084886)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084880), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084882, _1084880), _1084888), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1084882, tc_HOL_Obool)), _1084884), _1084886))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084882, _1084880), _1084888), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1084882, tc_HOL_Obool)), _1084884), _1084886))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084880), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084882, _1084880), _1084888), _1084884)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1084882, _1084880), _1084888), _1084886)))], (30998 ^ _780478) ^ [_1356810, _1356812, _1356814] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1356810, tc_HOL_Obool)), _1356812)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356810), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1356810, tc_HOL_Obool), _1356812))), 31008 ^ _780478 : [(31011 ^ _780478) ^ [] : [hAPP(c_Finite__Set_Ocard(_1356810), 31007 ^ [_1356810, _1356812, _1356814]) = _1356814], (31009 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1356810, tc_HOL_Obool)), 31007 ^ [_1356810, _1356812, _1356814]), _1356812)))]], 31015 ^ _780478 : [(31019 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1356810, tc_HOL_Obool)), 31017 ^ [_1356810, _1356812, _1356814]), _1356812)))], (31021 ^ _780478) ^ [] : [31014 ^ [_1356810, _1356812, _1356814] = 31017 ^ [_1356810, _1356812, _1356814]], (31023 ^ _780478) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1356810, tc_HOL_Obool)), 31014 ^ [_1356810, _1356812, _1356814]), 31017 ^ [_1356810, _1356812, _1356814]) = c_Orderings_Obot__class_Obot(tc_fun(_1356810, tc_HOL_Obool))], (31016 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1356810, tc_HOL_Obool)), 31014 ^ [_1356810, _1356812, _1356814]), _1356812)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1356814), hAPP(c_Finite__Set_Ocard(tc_fun(_1356810, tc_HOL_Obool)), _1356812)) = hAPP(c_Finite__Set_Ocard(_1356810), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1356810, tc_HOL_Obool), _1356812)))], (14118 ^ _780478) ^ [_1032818, _1032820] : [class_Groups_Ocomm__monoid__mult(_1032818), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032818), c_Groups_Oone__class_Oone(_1032818)), _1032820) = _1032820)], (51697 ^ _780478) ^ [_1826562, _1826564, _1826566, _1826568] : [class_Rings_Ocomm__semiring__1(_1826562), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826562), _1826564), _1826566)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826562), _1826566), _1826568)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826562), _1826564), _1826568)))], (25241 ^ _780478) ^ [_1249533, _1249535, _1249537] : [class_Rings_Odivision__ring(_1249533), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1249533), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249533), _1249535), _1249537)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249533), hAPP(c_Groups_Ouminus__class_Ouminus(_1249533), _1249535)), _1249537))], (20644 ^ _780478) ^ [_1165348, _1165350] : [class_Groups_Olinordered__ab__group__add(_1165348), 20647 ^ _780478 : [(20654 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165348), _1165350), c_Groups_Ozero__class_Ozero(_1165348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165348), _1165350), hAPP(c_Groups_Ouminus__class_Ouminus(_1165348), _1165350))))], (20648 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165348), _1165350), hAPP(c_Groups_Ouminus__class_Ouminus(_1165348), _1165350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165348), _1165350), c_Groups_Ozero__class_Ozero(_1165348))))]]], (5210 ^ _780478) ^ [_860082, _860084, _860086, _860088, _860090, _860092, _860094, _860096] : [-(c_Quotient_OBabs(_860096, _860092, _860088, _860084) = c_Quotient_OBabs(_860094, _860090, _860086, _860082)), _860096 = _860094, _860092 = _860090, _860088 = _860086, _860084 = _860082], (15517 ^ _780478) ^ [_1060359, _1060361, _1060363, _1060365, _1060367] : [class_Groups_Ocomm__monoid__mult(_1060359), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060361), _1060363)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1060361, tc_HOL_Obool)), _1060365), _1060363)), 15531 ^ _780478 : [(15534 ^ _780478) ^ [] : [hAPP(_1060367, 15530 ^ [_1060359, _1060361, _1060363, _1060365, _1060367]) = c_Groups_Oone__class_Oone(_1060359)], (15532 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1060361), 15530 ^ [_1060359, _1060361, _1060363, _1060365, _1060367]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1060361, tc_HOL_Obool)), _1060363), _1060365))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1060361, _1060359), _1060367), _1060363) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1060361, _1060359), _1060367), _1060365))], (34653 ^ _780478) ^ [_1433793, _1433795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1433793)), c_Int_OBit1(_1433795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433793), _1433795)))], (46046 ^ _780478) ^ [_1706155, _1706157, _1706159, _1706161] : [-(hBOOL(hAPP(_1706155, _1706157))), -(c_List_Oremove1(_1706159, _1706157, hAPP(c_List_Ofilter(_1706159, _1706155), _1706161)) = hAPP(c_List_Ofilter(_1706159, _1706155), _1706161))], (15681 ^ _780478) ^ [_1063872, _1063874, _1063876, _1063878] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063872, tc_HOL_Obool)), _1063874), _1063876), _1063878)), -(hBOOL(hAPP(_1063874, _1063878)))], (10365 ^ _780478) ^ [_961297, _961299] : [class_Lattices_Oboolean__algebra(_961297), -(hAPP(c_Groups_Ouminus__class_Ouminus(_961297), hAPP(c_Groups_Ouminus__class_Ouminus(_961297), _961299)) = _961299)], (1114 ^ _780478) ^ [_797267, _797269] : [-(class_Groups_Olinordered__ab__group__add(_797267)), _797269 = _797267, class_Groups_Olinordered__ab__group__add(_797269)], (36240 ^ _780478) ^ [_1469584, _1469586, _1469588, _1469590] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1469584, tc_fun(_1469586, tc_HOL_Obool))), _1469588), _1469590))], (41632 ^ _780478) ^ [_1600951, _1600953] : [-(c_Nitpick_Oinverse__frac(_1600951, _1600953) = hAPP(hAPP(c_Nitpick_Ofrac(_1600951), hAPP(c_Nitpick_Odenom(_1600951), _1600953)), hAPP(c_Nitpick_Onum(_1600951), _1600953)))], (45671 ^ _780478) ^ [_1697429, _1697431, _1697433] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1697429))), c_Enum_On__lists(_1697429, _1697431, _1697433)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697429)), _1697433)), _1697431))], (4862 ^ _780478) ^ [_854626, _854628] : [_854628 = _854626, -(c_Wellfounded_Ofinite__psubset(_854628) = c_Wellfounded_Ofinite__psubset(_854626))], (37423 ^ _780478) ^ [_1492962] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1492962)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1492962)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (51771 ^ _780478) ^ [_1827712, _1827714] : [class_Lattices_Obounded__lattice(_1827712), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1827714, _1827712)))], (29279 ^ _780478) ^ [_1324128, _1324130, _1324132] : [class_Divides_Osemiring__div(_1324128), -(c_Divides_Odiv__class_Omod(_1324128, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1324128), _1324130), _1324132), _1324130) = c_Divides_Odiv__class_Omod(_1324128, _1324132, _1324130))], (37937 ^ _780478) ^ [_1506930, _1506932, _1506934, _1506936, _1506938, _1506940, _1506942, _1506944] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1506930, _1506932)), hAPP(hAPP(c_Product__Type_OPair(_1506930, _1506932), _1506934), _1506936)), _1506938)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1506932, _1506940)), hAPP(hAPP(c_Product__Type_OPair(_1506932, _1506940), _1506936), _1506942)), _1506944)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1506930, _1506940)), hAPP(hAPP(c_Product__Type_OPair(_1506930, _1506940), _1506934), _1506942)), hAPP(hAPP(c_Relation_Orel__comp(_1506930, _1506932, _1506940), _1506938), _1506944))))], (19612 ^ _780478) ^ [_1146756, _1146758, _1146760] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146756), _1146758) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146756), _1146760), -(_1146758 = _1146760), -(_1146756 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1844 ^ _780478) ^ [_806392, _806394] : [-(class_Groups_Ominus(_806392)), _806394 = _806392, class_Groups_Ominus(_806394)], (28144 ^ _780478) ^ [_1301233, _1301235, _1301237, _1301239] : [class_Groups_Ocomm__monoid__add(_1301233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1301235), _1301237)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1301233), _1301239), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1301235, _1301237)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1301233), hAPP(_1301239, _1301235)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1301233), _1301239), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1301235, _1301237))))], (46234 ^ _780478) ^ [_1711346, _1711348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711346), _1711348)), -(c_List_Oupt(_1711346, hAPP(c_Nat_OSuc, _1711348)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1711346, _1711348)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1711348), c_List_Olist_ONil(tc_Nat_Onat))))], (44071 ^ _780478) ^ [_1662852, _1662854, _1662856] : [-(_1662852 = c_List_Olist_ONil(_1662854)), -(hAPP(c_List_Ohd(_1662854), hAPP(hAPP(c_List_Oappend(_1662854), _1662852), _1662856)) = hAPP(c_List_Ohd(_1662854), _1662852))], (6192 ^ _780478) ^ [_879606, _879608, _879610, _879612] : [c_Orderings_Obot__class_Obot(tc_fun(_879606, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_879608, _879606, _879610), _879612), -(_879612 = c_Orderings_Obot__class_Obot(tc_fun(_879608, tc_HOL_Obool)))], (8248 ^ _780478) ^ [_921658, _921660, _921662, _921664] : [class_Groups_Oordered__ab__semigroup__add(_921658), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921658), _921660), _921662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921658), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921658), _921660), _921664)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921658), _921662), _921664))))], (42792 ^ _780478) ^ [_1633806, _1633808, _1633810] : [hBOOL(hAPP(c_List_Odistinct(_1633806), _1633808)), -(hBOOL(hAPP(c_List_Odistinct(_1633806), c_List_Osublist(_1633806, _1633808, _1633810))))], (11857 ^ _780478) ^ [_988869, _988871, _988873] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_988869, tc_HOL_Obool)), _988871) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_988869, tc_HOL_Obool)), _988873), -(_988871 = _988873)], (880 ^ _780478) ^ [_793642, _793644, _793646, _793648, _793650, _793652, _793654, _793656, _793658, _793660] : [-(c_Fun_Obij__betw(_793658, _793654, _793650, _793646, _793642)), c_Fun_Obij__betw(_793660, _793656, _793652, _793648, _793644), _793660 = _793658, _793656 = _793654, _793652 = _793650, _793648 = _793646, _793644 = _793642], (7273 ^ _780478) ^ [_901752, _901754, _901756, _901758, _901760, _901762] : [class_Groups_Ocomm__monoid__add(_901752), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_901754, _901752), hAPP(hAPP(c_COMBC(_901754, tc_fun(_901756, tc_HOL_Obool), _901752), hAPP(hAPP(c_COMBB(tc_fun(_901756, _901752), tc_fun(tc_fun(_901756, tc_HOL_Obool), _901752), _901754), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_901756, _901752)), _901758)), _901760)), _901762) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_901756, _901752), hAPP(hAPP(c_COMBC(_901756, tc_fun(_901754, tc_HOL_Obool), _901752), hAPP(hAPP(c_COMBB(tc_fun(_901754, _901752), tc_fun(tc_fun(_901754, tc_HOL_Obool), _901752), _901756), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_901754, _901752)), hAPP(c_COMBC(_901754, _901756, _901752), _901758))), _901762)), _901760))], (34497 ^ _780478) ^ [_1431002, _1431004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1431002)), c_Int_OBit1(_1431004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431002), _1431004)))], (38996 ^ _780478) ^ [_1536109, _1536111, _1536113, _1536115] : [-(c_Fun_Oinj__on(_1536109, tc_prod(_1536111, _1536109), 38994 ^ [_1536109, _1536111, _1536113, _1536115], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536111, tc_fun(_1536109, tc_HOL_Obool)), _1536113), _1536115)))], (37802 ^ _780478) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (42047 ^ _780478) ^ [_1614041, _1614043, _1614045, _1614047, _1614049, _1614051] : [-(c_List_Olistrelp(_1614041, _1614043, hAPP(hAPP(c_List_Olist_OCons(_1614041), _1614045), _1614047), hAPP(hAPP(c_List_Olist_OCons(_1614041), _1614049), _1614051))), hBOOL(hAPP(hAPP(_1614043, _1614045), _1614049)), c_List_Olistrelp(_1614041, _1614043, _1614047, _1614051)], (32412 ^ _780478) ^ [_1392684, _1392686, _1392688, _1392690] : [class_Fields_Ofield__inverse__zero(_1392684), class_Int_Onumber(_1392684), 32419 ^ _780478 : [(32420 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1392684), _1392686) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392684), _1392688), _1392690), 32423 ^ _780478 : [(32430 ^ _780478) ^ [] : [_1392690 = c_Groups_Ozero__class_Ozero(_1392684), -(hAPP(c_Int_Onumber__class_Onumber__of(_1392684), _1392686) = c_Groups_Ozero__class_Ozero(_1392684))], (32424 ^ _780478) ^ [] : [-(_1392690 = c_Groups_Ozero__class_Ozero(_1392684)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392684), hAPP(c_Int_Onumber__class_Onumber__of(_1392684), _1392686)), _1392690) = _1392688)]]], (32436 ^ _780478) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1392684), _1392686) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392684), _1392688), _1392690)), 32439 ^ _780478 : [(32442 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392684), hAPP(c_Int_Onumber__class_Onumber__of(_1392684), _1392686)), _1392690) = _1392688], (32440 ^ _780478) ^ [] : [_1392690 = c_Groups_Ozero__class_Ozero(_1392684)]], 32443 ^ _780478 : [(32446 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1392684), _1392686) = c_Groups_Ozero__class_Ozero(_1392684)], (32444 ^ _780478) ^ [] : [-(_1392690 = c_Groups_Ozero__class_Ozero(_1392684))]]]]], (19430 ^ _780478) ^ [_1144174, _1144176] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1144174), _1144176) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1144176 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1144174 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21143 ^ _780478) ^ [_1173433, _1173435, _1173437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173433), _1173435)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173433), _1173437))), 21146 ^ _780478 : [(21149 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173435), _1173437)))], (21147 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173433)))]]], (31722 ^ _780478) ^ [_1379510, _1379512, _1379514, _1379516, _1379518, _1379520] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379510, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379512, _1379510, _1379514), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1379516, tc_fun(_1379512, tc_HOL_Obool)), _1379518), _1379520))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1379516, tc_fun(_1379510, tc_HOL_Obool)), _1379518), hAPP(hAPP(c_COMBB(tc_fun(_1379512, tc_HOL_Obool), tc_fun(_1379510, tc_HOL_Obool), _1379516), c_Relation_OImage(_1379512, _1379510, _1379514)), _1379520)))))], (48267 ^ _780478) ^ [_1753330, _1753332, _1753334] : [48269 ^ _780478 : [(48272 ^ _780478) ^ [] : [hBOOL(hAPP(_1753334, 48268 ^ [_1753330, _1753332, _1753334]))], (48270 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753330), 48268 ^ [_1753330, _1753332, _1753334]), hAPP(c_List_Oset(_1753330), _1753332))))]], -(c_List_Olist__all(_1753330, _1753334, _1753332))], (33554 ^ _780478) ^ [_1413421, _1413423] : [class_Int_Onumber__ring(_1413421), class_Rings_Olinordered__idom(_1413421), 33561 ^ _780478 : [(33568 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1413423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413421), c_Groups_Ozero__class_Ozero(_1413421)), hAPP(c_Int_Onumber__class_Onumber__of(_1413421), _1413423))))], (33562 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413421), c_Groups_Ozero__class_Ozero(_1413421)), hAPP(c_Int_Onumber__class_Onumber__of(_1413421), _1413423))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1413423)))]]], (35085 ^ _780478) ^ [_1441643, _1441645, _1441647] : [class_Rings_Ocomm__semiring__1(_1441643), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1441643), _1441645), 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)))), _1441647))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1441643), _1441645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1441643), hAPP(hAPP(c_Power_Opower__class_Opower(_1441643), _1441645), _1441647)), hAPP(hAPP(c_Power_Opower__class_Opower(_1441643), _1441645), _1441647))))], (10211 ^ _780478) ^ [_958141, _958143, _958145, _958147] : [class_Orderings_Olinorder(_958141), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_958141), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958141), _958143), _958145)), _958147) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_958141), _958143), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958141), _958145), _958147)))], (41025 ^ _780478) ^ [_1585417] : [-(hAPP(c_Relation_Oconverse(_1585417, _1585417), c_Relation_OId(_1585417)) = c_Relation_OId(_1585417))], (27665 ^ _780478) ^ [_1291851, _1291853] : [class_Rings_Olinordered__idom(_1291851), 27668 ^ _780478 : [(27675 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1291853), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291851), hAPP(c_Int_Oring__1__class_Oof__int(_1291851), _1291853)), c_Groups_Ozero__class_Ozero(_1291851))))], (27669 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291851), hAPP(c_Int_Oring__1__class_Oof__int(_1291851), _1291853)), c_Groups_Ozero__class_Ozero(_1291851))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1291853), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (5704 ^ _780478) ^ [_867789, _867791, _867793, _867795] : [-(hAPP(_867795, _867791) = hAPP(_867793, _867789)), _867795 = _867793, _867791 = _867789], (15335 ^ _780478) ^ [_1056615, _1056617, _1056619, _1056621] : [class_Rings_Olinordered__semidom(_1056615), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056615), c_Groups_Oone__class_Oone(_1056615)), _1056617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056615), hAPP(hAPP(c_Power_Opower__class_Opower(_1056615), _1056617), _1056619)), hAPP(hAPP(c_Power_Opower__class_Opower(_1056615), _1056617), _1056621))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056619), _1056621)))], (16350 ^ _780478) ^ [_1077762, _1077764, _1077766, _1077768] : [hBOOL(hAPP(hAPP(c_member(_1077762), _1077764), _1077766)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077762, tc_HOL_Obool)), _1077766), hAPP(hAPP(c_Set_Oinsert(_1077762), _1077764), _1077768)) = hAPP(hAPP(c_Set_Oinsert(_1077762), _1077764), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077762, tc_HOL_Obool)), _1077766), _1077768)))], (22759 ^ _780478) ^ [] : [-(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))))], (52311 ^ _780478) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (52103 ^ _780478) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (33474 ^ _780478) ^ [_1412166, _1412168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412166)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412168))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412166), _1412168))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412166), c_Int_OPls)))], (6230 ^ _780478) ^ [_880395, _880397, _880399, _880401, _880403] : [c_Finite__Set_Ofolding__one(_880395, _880397, _880399), hBOOL(hAPP(c_Finite__Set_Ofinite(_880395), _880401)), -(hBOOL(hAPP(hAPP(c_member(_880395), _880403), _880401))), -(_880401 = c_Orderings_Obot__class_Obot(tc_fun(_880395, tc_HOL_Obool))), -(hAPP(_880399, hAPP(hAPP(c_Set_Oinsert(_880395), _880403), _880401)) = hAPP(hAPP(_880397, _880403), hAPP(_880399, _880401)))], (7441 ^ _780478) ^ [_905387, _905389, _905391] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_905387), _905389)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905387, tc_HOL_Obool)), hAPP(c_Set_Oimage(_905387, _905387, _905391), _905389)), _905389)), c_Fun_Oinj__on(_905387, _905387, _905391, _905389), -(hAPP(c_Set_Oimage(_905387, _905387, _905391), _905389) = _905389)], (14921 ^ _780478) ^ [_1048539, _1048541, _1048543, _1048545] : [hBOOL(hAPP(hAPP(_1048543, _1048541), _1048545)), -(hBOOL(hAPP(hAPP(c_member(_1048539), _1048541), c_SetInterval_Oord_OlessThan(_1048539, _1048543, _1048545))))], (44534 ^ _780478) ^ [_1672047, _1672049] : [-(_1672047 = c_List_Olist_ONil(_1672049)), -(c_List_Olast(_1672049, _1672047) = hAPP(hAPP(c_List_Onth(_1672049), _1672047), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672049)), _1672047)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (24409 ^ _780478) ^ [_1234126, _1234128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1234126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234128), 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), _1234126), _1234128)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12147 ^ _780478) ^ [_994024, _994026, _994028] : [class_Orderings_Olinorder(_994024), hBOOL(hAPP(c_Finite__Set_Ofinite(_994024), _994026)), -(hBOOL(hAPP(hAPP(c_member(_994024), _994028), _994026))), -(c_Big__Operators_Olattice_OSup__fin(_994024, c_Orderings_Oord__class_Omax(_994024), hAPP(hAPP(c_Set_Oinsert(_994024), _994028), _994026)) = hAPP(hAPP(c_Finite__Set_Ofold(_994024, _994024, c_Orderings_Oord__class_Omax(_994024)), _994028), _994026))], (30861 ^ _780478) ^ [_1353765, _1353767, _1353769] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1353765, tc_HOL_Obool)), _1353767), _1353769) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353765, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1353765, tc_HOL_Obool)), _1353767), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1353765, tc_HOL_Obool)), _1353769), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1353765, tc_HOL_Obool), tc_HOL_Obool))))))], (20981 ^ _780478) ^ [_1171013, _1171015] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1171013), _1171015), 20986 ^ _780478 : [(20989 ^ _780478) ^ [] : [-(_1171015 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20987 ^ _780478) ^ [] : [-(_1171013 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20990 ^ _780478 : [(20993 ^ _780478) ^ [] : [-(_1171015 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20991 ^ _780478) ^ [] : [-(_1171013 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (17450 ^ _780478) ^ [_1104216, _1104218, _1104220, _1104222, _1104224, _1104226] : [-(hAPP(c_Set_Ovimage(_1104216, _1104218, _1104220), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104222, tc_fun(_1104218, tc_HOL_Obool)), _1104224), _1104226)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104222, tc_fun(_1104216, tc_HOL_Obool)), _1104224), hAPP(hAPP(c_COMBB(tc_fun(_1104218, tc_HOL_Obool), tc_fun(_1104216, tc_HOL_Obool), _1104222), c_Set_Ovimage(_1104216, _1104218, _1104220)), _1104226)))], (29981 ^ _780478) ^ [_1336807, _1336809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1336807), _1336809)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336807, _1336809) = _1336807)], (41063 ^ _780478) ^ [_1586086, _1586088, _1586090] : [_1586088 = _1586090, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586086, _1586086)), hAPP(hAPP(c_Product__Type_OPair(_1586086, _1586086), _1586088), _1586090)), c_Relation_OId(_1586086))))], (35369 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (7682 ^ _780478) ^ [_910108, _910110, _910112, _910114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910108, tc_HOL_Obool)), _910110), _910112)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910108, tc_HOL_Obool)), _910112), _910114)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910108, tc_HOL_Obool)), _910112), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910108, tc_HOL_Obool)), _910114), _910110)) = _910110)], (15233 ^ _780478) ^ [_1054596, _1054598, _1054600] : [class_Lattices_Olattice(_1054596), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054596), _1054598)), 15240 ^ _780478 : [(15247 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054596, tc_HOL_Obool)), _1054598), hAPP(hAPP(c_Set_Oinsert(_1054596), _1054600), c_Orderings_Obot__class_Obot(tc_fun(_1054596, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1054596, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1054596, hAPP(hAPP(c_Set_Oinsert(_1054596), _1054600), _1054598)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1054596), _1054600), c_Big__Operators_Olattice__class_OSup__fin(_1054596, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054596, tc_HOL_Obool)), _1054598), hAPP(hAPP(c_Set_Oinsert(_1054596), _1054600), c_Orderings_Obot__class_Obot(tc_fun(_1054596, tc_HOL_Obool)))))))], (15241 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054596, tc_HOL_Obool)), _1054598), hAPP(hAPP(c_Set_Oinsert(_1054596), _1054600), c_Orderings_Obot__class_Obot(tc_fun(_1054596, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1054596, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1054596, hAPP(hAPP(c_Set_Oinsert(_1054596), _1054600), _1054598)) = _1054600)]]], (19514 ^ _780478) ^ [_1145313, _1145315] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1145313), _1145315) = _1145313, -(_1145315 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46447 ^ _780478) ^ [_1715516, _1715518] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1715516, _1715518)))], (20422 ^ _780478) ^ [_1161297, _1161299, _1161301] : [class_Rings_Olinordered__semiring__strict(_1161297), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161297), c_Groups_Ozero__class_Ozero(_1161297)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161297), _1161299), _1161301))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161297), c_Groups_Ozero__class_Ozero(_1161297)), _1161301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161297), c_Groups_Ozero__class_Ozero(_1161297)), _1161299)))], (21666 ^ _780478) ^ [_1182811, _1182813, _1182815, _1182817] : [class_Rings_Olinordered__semidom(_1182811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182811), hAPP(hAPP(c_Power_Opower__class_Opower(_1182811), _1182813), _1182815)), hAPP(hAPP(c_Power_Opower__class_Opower(_1182811), _1182817), _1182815))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182811), c_Groups_Ozero__class_Ozero(_1182811)), _1182817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182811), _1182813), _1182817)))], (43441 ^ _780478) ^ [_1647537, _1647539, _1647541, _1647543, _1647545, _1647547] : [hAPP(hAPP(c_List_Oappend(_1647537), _1647539), _1647541) = _1647543, _1647545 = hAPP(hAPP(c_List_Oappend(_1647537), _1647541), _1647547), -(hAPP(hAPP(c_List_Oappend(_1647537), _1647539), _1647545) = hAPP(hAPP(c_List_Oappend(_1647537), _1647543), _1647547))], (1644 ^ _780478) ^ [_803892, _803894] : [-(class_Groups_Oab__semigroup__add(_803892)), _803894 = _803892, class_Groups_Oab__semigroup__add(_803894)], (38509 ^ _780478) ^ [_1520960] : [-(c_Nitpick_Ozero__frac(_1520960) = c_Nitpick_OAbs__Frac(_1520960, 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))))], (14357 ^ _780478) ^ [_1036832, _1036834, _1036836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036832), _1036834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036832), _1036836)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036834), _1036836))))], (11437 ^ _780478) ^ [_980896, _980898, _980900, _980902, _980904] : [class_Groups_Ocomm__monoid__mult(_980896), hBOOL(hAPP(c_Finite__Set_Ofinite(_980898), _980900)), -(hBOOL(hAPP(hAPP(c_member(_980898), _980902), _980900))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_980898, _980896), _980904), hAPP(hAPP(c_Set_Oinsert(_980898), _980902), _980900)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980896), hAPP(_980904, _980902)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_980898, _980896), _980904), _980900)))], (24987 ^ _780478) ^ [_1244495, _1244497, _1244499, _1244501, _1244503] : [class_Orderings_Olinorder(_1244495), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1244495, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1244495, _1244497, _1244499)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1244495, _1244501, _1244503)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1244495, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1244495), _1244497), _1244501), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1244495), _1244499), _1244503)))], (30001 ^ _780478) ^ [_1337051, _1337053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1337051), _1337053)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337053, _1337051) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1337053), _1337051), _1337051))], (40612 ^ _780478) ^ [_1575235, _1575237, _1575239, _1575241, _1575243] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575235, _1575235)), hAPP(hAPP(c_Product__Type_OPair(_1575235, _1575235), _1575237), _1575239)), c_Transitive__Closure_Otrancl(_1575235, _1575241))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575235, _1575235)), hAPP(hAPP(c_Product__Type_OPair(_1575235, _1575235), _1575239), _1575243)), c_Transitive__Closure_Ortrancl(_1575235, _1575241))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575235, _1575235)), hAPP(hAPP(c_Product__Type_OPair(_1575235, _1575235), _1575237), _1575243)), c_Transitive__Closure_Otrancl(_1575235, _1575241))))], (47582 ^ _780478) ^ [_1738111, _1738113, _1738115] : [-(c_List_Omaps(_1738111, _1738113, _1738115, c_List_Olist_ONil(_1738111)) = c_List_Olist_ONil(_1738113))], (31302 ^ _780478) ^ [_1363554, _1363556, _1363558] : [-(hAPP(hAPP(c_Set_Oinsert(_1363554), _1363556), _1363558) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1363554, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1363554), hAPP(hAPP(c_COMBC(_1363554, _1363554, tc_HOL_Obool), c_fequal), _1363556))), _1363558))], (1294 ^ _780478) ^ [_799517, _799519] : [-(class_Groups_Oabs__if(_799517)), _799519 = _799517, class_Groups_Oabs__if(_799519)], (31041 ^ _780478) ^ [_1357775, _1357777, _1357779] : [31043 ^ _780478 : [(31046 ^ _780478) ^ [] : [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(_1357777, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 31042 ^ [_1357775, _1357777, _1357779]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1357777, 31042 ^ [_1357775, _1357777, _1357779])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31044 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31042 ^ [_1357775, _1357777, _1357779]), _1357775)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1357777, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1357779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1357779), hAPP(_1357777, _1357775))), 31056 ^ _780478 : [(31059 ^ _780478) ^ [] : [-(hAPP(_1357777, 31055 ^ [_1357775, _1357777, _1357779]) = _1357779)], (31057 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 31055 ^ [_1357775, _1357777, _1357779]), _1357775)))]]], (14171 ^ _780478) ^ [_1033733, _1033735] : [class_Rings_Olinordered__semidom(_1033733), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033733), _1033735), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1033733), _1033735), c_Groups_Oone__class_Oone(_1033733)))))], (23845 ^ _780478) ^ [_1223911] : [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)), _1223911))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1223911)))], (2610 ^ _780478) ^ [_818936, _818938] : [_818938 = _818936, -(c_Nitpick_Oone__frac(_818938) = c_Nitpick_Oone__frac(_818936))], (35261 ^ _780478) ^ [_1445398] : [_1445398 = c_Int_OMin, -(c_Int_OBit1(_1445398) = c_Int_OMin)], (9236 ^ _780478) ^ [_938778, _938780, _938782] : [class_Orderings_Opreorder(_938778), 9239 ^ _780478 : [(9248 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938778), _938780), _938782))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938778), _938780), _938782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938778), _938782), _938780)))], (9240 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_938778), _938780), _938782)), 9243 ^ _780478 : [(9246 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938778), _938782), _938780))], (9244 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_938778), _938780), _938782)))]]]]], (6792 ^ _780478) ^ [_892808, _892810, _892812, _892814, _892816] : [c_Finite__Set_Ofun__left__comm__idem(_892808, _892810, _892812), -(hAPP(hAPP(_892812, _892814), hAPP(hAPP(_892812, _892814), _892816)) = hAPP(hAPP(_892812, _892814), _892816))], (43610 ^ _780478) ^ [_1651056, _1651058, _1651060] : [_1651058 = c_List_Olist_ONil(_1651056), -(hAPP(hAPP(c_List_Oappend(_1651056), _1651058), _1651060) = _1651060)], (45185 ^ _780478) ^ [_1686139, _1686141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1686139), _1686141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686139)), hAPP(c_Code__Numeral_Onat__of, _1686141))))], (39644 ^ _780478) ^ [_1552309, _1552311, _1552313, _1552315, _1552317, _1552319] : [-(hAPP(hAPP(c_Fun_Ocomp(_1552309, _1552311, _1552313, _1552315), _1552317), _1552319) = hAPP(_1552315, hAPP(_1552317, _1552319)))], (2488 ^ _780478) ^ [_817001, _817003] : [_817003 = _817001, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_817003) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_817001))], (31206 ^ _780478) ^ [_1361147, _1361149, _1361151] : [-(hAPP(hAPP(c_Set_Oinsert(_1361147), _1361149), hAPP(c_Set_OCollect(_1361147), _1361151)) = hAPP(c_Set_OCollect(_1361147), hAPP(hAPP(c_COMBS(_1361147, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361147), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1361147), c_fNot), hAPP(hAPP(c_COMBC(_1361147, _1361147, tc_HOL_Obool), c_fequal), _1361149)))), _1361151)))], (47224 ^ _780478) ^ [_1730646, _1730648, _1730650, _1730652, _1730654] : [-(hAPP(hAPP(c_List_Ozip(_1730646, _1730648), _1730650), c_List_OtakeWhile(_1730648, _1730652, _1730654)) = c_List_OtakeWhile(tc_prod(_1730646, _1730648), hAPP(c_Fun_Ocomp(_1730648, tc_HOL_Obool, tc_prod(_1730646, _1730648), _1730652), c_Product__Type_Osnd(_1730646, _1730648)), hAPP(hAPP(c_List_Ozip(_1730646, _1730648), _1730650), _1730654)))], (45480 ^ _780478) ^ [_1693272, _1693274, _1693276, _1693278, _1693280, _1693282, _1693284] : [c_List_Olist__all2(_1693272, _1693274, _1693276, hAPP(hAPP(c_List_Olist_OCons(_1693272), _1693278), _1693280), hAPP(hAPP(c_List_Olist_OCons(_1693274), _1693282), _1693284)), 45483 ^ _780478 : [(45486 ^ _780478) ^ [] : [-(c_List_Olist__all2(_1693272, _1693274, _1693276, _1693280, _1693284))], (45484 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1693276, _1693278), _1693282)))]]], (6043 ^ _780478) ^ [_876598, _876600, _876602, _876604] : [hBOOL(hAPP(hAPP(c_member(_876598), _876600), _876602)), -(hBOOL(hAPP(hAPP(c_member(_876598), _876600), hAPP(hAPP(c_Set_Oinsert(_876598), _876604), _876602))))], (31202 ^ _780478) ^ [_1361078, _1361080] : [-(hAPP(c_Set_OCollect(_1361078), _1361080) = _1361080)], (22445 ^ _780478) ^ [_1198104, _1198106, _1198108, _1198110, _1198112] : [class_Groups_Ocomm__monoid__add(_1198104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1198106), _1198108)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1198106), _1198110)), 22459 ^ _780478 : [(22462 ^ _780478) ^ [] : [hAPP(_1198112, 22458 ^ [_1198104, _1198106, _1198108, _1198110, _1198112]) = c_Groups_Ozero__class_Ozero(_1198104)], (22460 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1198106), 22458 ^ [_1198104, _1198106, _1198108, _1198110, _1198112]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1198106, tc_HOL_Obool)), _1198108), _1198110))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198106, _1198104), _1198112), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1198106, tc_HOL_Obool)), _1198108), _1198110)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198104), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198106, _1198104), _1198112), _1198108)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198106, _1198104), _1198112), _1198110)))], (12554 ^ _780478) ^ [_1002122, _1002124] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1002122), c_Orderings_Otop__class_Otop(tc_fun(_1002122, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002124), c_Orderings_Otop__class_Otop(tc_fun(_1002124, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1002122, _1002124)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1002122, _1002124), tc_HOL_Obool)))))], (28510 ^ _780478) ^ [_1308220, _1308222, _1308224] : [class_Orderings_Oorder(_1308220), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308220, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1308220), _1308222)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1308220, _1308222, _1308224)) = c_Orderings_Obot__class_Obot(tc_fun(_1308220, tc_HOL_Obool)))], (46523 ^ _780478) ^ [_1716625, _1716627] : [class_Orderings_Olinorder(_1716625), -(_1716627 = c_List_Olist_ONil(_1716625)), c_List_Olinorder__class_Osorted(_1716625, _1716627), -(c_List_Olinorder__class_Osorted(_1716625, c_List_Obutlast(_1716625, _1716627)))], (39951 ^ _780478) ^ [_1559045, _1559047, _1559049, _1559051, _1559053, _1559055, _1559057, _1559059] : [c_Finite__Set_Ofolding(_1559045, _1559047, _1559049, _1559051), -(hAPP(c_Fun_Ocomp(_1559047, _1559047, _1559053, hAPP(_1559049, _1559055)), hAPP(c_Fun_Ocomp(_1559047, _1559047, _1559053, hAPP(_1559049, _1559057)), _1559059)) = hAPP(c_Fun_Ocomp(_1559047, _1559047, _1559053, hAPP(_1559049, _1559057)), hAPP(c_Fun_Ocomp(_1559047, _1559047, _1559053, hAPP(_1559049, _1559055)), _1559059)))], (3078 ^ _780478) ^ [_826172, _826174, _826176, _826178, _826180, _826182] : [-(c_List_Oset__Cons(_826182, _826178, _826174) = c_List_Oset__Cons(_826180, _826176, _826172)), _826182 = _826180, _826178 = _826176, _826174 = _826172], (10263 ^ _780478) ^ [_959272, _959274, _959276, _959278] : [class_Orderings_Olinorder(_959272), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_959272), _959274), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959272), _959276), _959278)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_959272), _959276), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959272), _959274), _959278)))], (18271 ^ _780478) ^ [_1122253, _1122255, _1122257] : [class_Power_Opower(_1122253), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1122253), _1122255), hAPP(c_Nat_OSuc, _1122257)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122253), _1122255), hAPP(hAPP(c_Power_Opower__class_Opower(_1122253), _1122255), _1122257)))], (40436 ^ _780478) ^ [_1570700, _1570702, _1570704, _1570706, _1570708] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570700, _1570700)), hAPP(hAPP(c_Product__Type_OPair(_1570700, _1570700), _1570702), _1570704)), c_Transitive__Closure_Otrancl(_1570700, _1570706))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570700, _1570700)), hAPP(hAPP(c_Product__Type_OPair(_1570700, _1570700), _1570704), _1570708)), _1570706)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570700, _1570700)), hAPP(hAPP(c_Product__Type_OPair(_1570700, _1570700), _1570702), _1570708)), c_Transitive__Closure_Otrancl(_1570700, _1570706))))], (31437 ^ _780478) ^ [_1368992, _1368994] : [-(hAPP(c_Set_OPow(_1368992), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1368992, tc_HOL_Obool)), _1368994)) = hAPP(c_Set_OCollect(tc_fun(_1368992, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1368992, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1368992, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1368992, tc_HOL_Obool), tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1368992, tc_HOL_Obool)), c_COMBS(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1368992, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1368992, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1368992, tc_HOL_Obool), tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_fun(_1368992, tc_HOL_Obool)), tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_fun(_1368992, tc_HOL_Obool)), tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1368992, tc_HOL_Obool)), c_COMBB(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1368992, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1368992, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1368992, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1368992, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1368992, tc_HOL_Obool)), _1368994)), c_Set_OPow(_1368992))))))], (5548 ^ _780478) ^ [_865459, _865461] : [_865461 = _865459, -(c_Groups_Ozero__class_Ozero(_865461) = c_Groups_Ozero__class_Ozero(_865459))], (2950 ^ _780478) ^ [_824160, _824162, _824164, _824166, _824168, _824170] : [-(c_Nitpick_Oplus__frac(_824170, _824166, _824162) = c_Nitpick_Oplus__frac(_824168, _824164, _824160)), _824170 = _824168, _824166 = _824164, _824162 = _824160], (39139 ^ _780478) ^ [_1539691, _1539693, _1539695, _1539697, _1539699, _1539701, _1539703, _1539705, _1539707] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539691, _1539693)), hAPP(hAPP(c_Product__Type_OPair(_1539691, _1539693), _1539695), _1539697)), _1539699)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1539701, _1539703)), hAPP(hAPP(c_Product__Type_OPair(_1539701, _1539703), hAPP(_1539705, _1539695)), hAPP(_1539707, _1539697))), hAPP(c_Set_Oimage(tc_prod(_1539691, _1539693), tc_prod(_1539701, _1539703), c_Product__Type_Omap__pair(_1539691, _1539701, _1539693, _1539703, _1539705, _1539707)), _1539699))))], (7822 ^ _780478) ^ [_912979, _912981, _912983, _912985, _912987] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912979, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912979, tc_HOL_Obool)), hAPP(c_Set_Oimage(_912981, _912979, _912983), _912985)), hAPP(c_Set_Oimage(_912981, _912979, _912983), _912987))), hAPP(c_Set_Oimage(_912981, _912979, _912983), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912981, tc_HOL_Obool)), _912985), _912987)))))], (23797 ^ _780478) ^ [_1223061, _1223063, _1223065] : [class_Groups_Ocomm__monoid__add(_1223061), hAPP(_1223063, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1223061), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223061), _1223063), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1223065)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1223061), _1223063), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1223065)))], (48766 ^ _780478) ^ [_1764234, _1764236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1764234), _1764236)), -(c_Lazy__Sequence_Osmall__lazy_H(_1764234, _1764236) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (49367 ^ _780478) ^ [_1777803, _1777805, _1777807] : [-(c_List_Olist__ex(_1777803, _1777805, _1777807)), 49368 ^ _780478 : [(49369 ^ _780478) ^ [_1777860] : [hBOOL(hAPP(hAPP(c_member(_1777803), _1777860), hAPP(c_List_Oset(_1777803), _1777807))), hBOOL(hAPP(_1777805, _1777860))]]], (31990 ^ _780478) ^ [_1384861, _1384863, _1384865, _1384867, _1384869] : [c_Equiv__Relations_Oequiv(_1384861, _1384863, _1384865), hBOOL(hAPP(hAPP(c_member(tc_fun(_1384861, tc_HOL_Obool)), _1384867), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1384861), _1384863), _1384865))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1384861, tc_HOL_Obool)), _1384869), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1384861), _1384863), _1384865))), -(_1384867 = _1384869), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1384861, tc_HOL_Obool)), _1384867), _1384869) = c_Orderings_Obot__class_Obot(tc_fun(_1384861, tc_HOL_Obool)))], (38096 ^ _780478) ^ [_1511241, _1511243, _1511245, _1511247, _1511249, _1511251] : [c_Typedef_Otype__definition(_1511241, _1511243, _1511245, _1511247, _1511249), -(hBOOL(hAPP(hAPP(c_member(_1511243), hAPP(_1511245, _1511251)), _1511249)))], (8436 ^ _780478) ^ [_925409, _925411, _925413, _925415, _925417] : [c_Finite__Set_Ofun__left__comm(_925409, _925411, _925413), hBOOL(hAPP(c_Finite__Set_Ofinite(_925409), _925415)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_925409, _925411, _925413, _925417, _925415), hAPP(hAPP(c_Finite__Set_Ofold(_925409, _925411, _925413), _925417), _925415))))], (14759 ^ _780478) ^ [_1044750, _1044752, _1044754, _1044756] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044750), _1044752)), hBOOL(hAPP(hAPP(c_member(_1044750), _1044754), _1044752)), -(hBOOL(hAPP(hAPP(c_member(_1044750), _1044754), _1044756))), -(hAPP(c_Finite__Set_Ocard(_1044750), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044750, tc_HOL_Obool)), _1044752), hAPP(hAPP(c_Set_Oinsert(_1044750), _1044754), _1044756))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1044750), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044750, tc_HOL_Obool)), _1044752), _1044756))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12504 ^ _780478) ^ [_1001115, _1001117] : [-(hBOOL(hAPP(hAPP(c_member(_1001115), _1001117), c_Orderings_Otop__class_Otop(tc_fun(_1001115, tc_HOL_Obool)))))], (50907 ^ _780478) ^ [_1812321, _1812323, _1812325] : [50909 ^ _780478 : [(50912 ^ _780478) ^ [] : [hBOOL(hAPP(_1812321, 50908 ^ [_1812321, _1812323, _1812325]))], (50910 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50908 ^ [_1812321, _1812323, _1812325]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1812323), _1812325))))]], -(c_List_Oall__interval__nat(_1812321, _1812323, _1812325))], (33534 ^ _780478) ^ [_1413107, _1413109] : [class_Int_Onumber__ring(_1413107), class_Rings_Olinordered__idom(_1413107), 33541 ^ _780478 : [(33548 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413109), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413107), hAPP(c_Int_Onumber__class_Onumber__of(_1413107), _1413109)), c_Groups_Ozero__class_Ozero(_1413107))))], (33542 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1413107), hAPP(c_Int_Onumber__class_Onumber__of(_1413107), _1413109)), c_Groups_Ozero__class_Ozero(_1413107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413109), c_Int_OPls)))]]], (4576 ^ _780478) ^ [_850063, _850065, _850067, _850069, _850071, _850073, _850075, _850077] : [-(c_Nitpick_Opair__box_OPairBox(_850077, _850073, _850069, _850065) = c_Nitpick_Opair__box_OPairBox(_850075, _850071, _850067, _850063)), _850077 = _850075, _850073 = _850071, _850069 = _850067, _850065 = _850063], (8116 ^ _780478) ^ [_919168, _919170, _919172, _919174, _919176] : [class_Groups_Ocomm__monoid__add(_919168), hBOOL(hAPP(c_Finite__Set_Ofinite(_919170), _919172)), hBOOL(hAPP(hAPP(c_member(_919170), _919174), _919172)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_919170, _919168), _919176), _919172) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919168), hAPP(_919176, _919174)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_919170, _919168), _919176), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919170, tc_HOL_Obool)), _919172), hAPP(hAPP(c_Set_Oinsert(_919170), _919174), c_Orderings_Obot__class_Obot(tc_fun(_919170, tc_HOL_Obool)))))))], (7214 ^ _780478) ^ [_900796, _900798, _900800, _900802] : [hBOOL(hAPP(_900796, _900798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900800, tc_HOL_Obool)), _900796), _900802)), -(hBOOL(hAPP(_900802, _900798)))], (51937 ^ _780478) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (41037 ^ _780478) ^ [_1585617, _1585619, _1585621, _1585623, _1585625] : [c_Relation_Osingle__valued(_1585617, _1585619, _1585621), c_Relation_Osingle__valued(_1585619, _1585623, _1585625), -(c_Relation_Osingle__valued(_1585617, _1585623, hAPP(hAPP(c_Relation_Orel__comp(_1585617, _1585619, _1585623), _1585621), _1585625)))], (44428 ^ _780478) ^ [_1670155, _1670157, _1670159] : [class_Orderings_Olinorder(_1670155), -(c_List_Oremove1(_1670155, _1670157, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1670155, _1670155, c_COMBI(_1670155)), _1670157), _1670159)) = _1670159)], (35333 ^ _780478) ^ [_1446462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1446462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1446462))))], (22753 ^ _780478) ^ [_1204068, _1204070] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1204068), _1204070)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204068)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204070)))], (49121 ^ _780478) ^ [_1771981, _1771983, _1771985, _1771987] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1771981), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1771983, _1771985, _1771981, _1771987) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1771983, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm)), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1771985, _1771987)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1771983, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1771983, _1771985, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1771981), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1771987))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1771983, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983))))), tc_prod(_1771983, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1771983)), hAPP(hAPP(c_COMBB(_1771983, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771983)))), tc_prod(_1771983, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1771983)), c_Product__Type_Ofst(_1771983, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (32374 ^ _780478) ^ [_1392089, _1392091, _1392093, _1392095] : [class_Fields_Ofield__inverse__zero(_1392089), class_Int_Onumber(_1392089), 32381 ^ _780478 : [(32382 ^ _780478) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392089), _1392091), _1392093) = hAPP(c_Int_Onumber__class_Onumber__of(_1392089), _1392095), 32385 ^ _780478 : [(32392 ^ _780478) ^ [] : [_1392093 = c_Groups_Ozero__class_Ozero(_1392089), -(hAPP(c_Int_Onumber__class_Onumber__of(_1392089), _1392095) = c_Groups_Ozero__class_Ozero(_1392089))], (32386 ^ _780478) ^ [] : [-(_1392093 = c_Groups_Ozero__class_Ozero(_1392089)), -(_1392091 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392089), hAPP(c_Int_Onumber__class_Onumber__of(_1392089), _1392095)), _1392093))]]], (32398 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1392089), _1392091), _1392093) = hAPP(c_Int_Onumber__class_Onumber__of(_1392089), _1392095)), 32401 ^ _780478 : [(32404 ^ _780478) ^ [] : [_1392091 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1392089), hAPP(c_Int_Onumber__class_Onumber__of(_1392089), _1392095)), _1392093)], (32402 ^ _780478) ^ [] : [_1392093 = c_Groups_Ozero__class_Ozero(_1392089)]], 32405 ^ _780478 : [(32408 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1392089), _1392095) = c_Groups_Ozero__class_Ozero(_1392089)], (32406 ^ _780478) ^ [] : [-(_1392093 = c_Groups_Ozero__class_Ozero(_1392089))]]]]], (3414 ^ _780478) ^ [_831378, _831380, _831382, _831384, _831386, _831388] : [-(c_Enum_On__lists(_831388, _831384, _831380) = c_Enum_On__lists(_831386, _831382, _831378)), _831388 = _831386, _831384 = _831382, _831380 = _831378], (47444 ^ _780478) ^ [_1735358, _1735360] : [class_Orderings_Olinorder(_1735358), 47451 ^ _780478 : [(47456 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1735358), hAPP(hAPP(c_List_Onth(_1735358), _1735360), 47449 ^ [_1735358, _1735360])), hAPP(hAPP(c_List_Onth(_1735358), _1735360), 47450 ^ [_1735358, _1735360])))], (47454 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47450 ^ [_1735358, _1735360]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735358)), _1735360))))], (47452 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47449 ^ [_1735358, _1735360]), 47450 ^ [_1735358, _1735360])))]], -(c_List_Olinorder__class_Osorted(_1735358, _1735360))], (30382 ^ _780478) ^ [_1344423, _1344425, _1344427, _1344429] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1344423, tc_fun(_1344425, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1344423, tc_HOL_Obool), _1344427)), _1344429) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1344423, tc_HOL_Obool), tc_fun(_1344425, tc_HOL_Obool)), _1344427), hAPP(hAPP(c_COMBC(tc_fun(_1344423, tc_HOL_Obool), tc_fun(_1344423, tc_fun(_1344425, tc_HOL_Obool)), tc_fun(_1344425, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1344423, tc_fun(_1344425, tc_HOL_Obool))), _1344429)))], (35653 ^ _780478) ^ [_1453903, _1453905, _1453907, _1453909] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1453903, _1453905)), hAPP(hAPP(c_Product__Type_OPair(_1453903, _1453905), _1453907), _1453909)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1453903, _1453905), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1453903, tc_fun(_1453905, tc_HOL_Obool))), _1453907), _1453909)))], (50695 ^ _780478) ^ [_1806063, _1806065, _1806067] : [c_Equiv__Relations_Oequivp(_1806063, _1806065), 50698 ^ _780478 : [(50699 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1806067, 50706 ^ [_1806063, _1806065, _1806067]))), 50700 ^ _780478 : [(50701 ^ _780478) ^ [_1806185] : [hBOOL(hAPP(hAPP(c_member(_1806063), _1806185), c_Quotient_ORespects(_1806063, _1806065))), hBOOL(hAPP(_1806067, _1806185))]]], (50710 ^ _780478) ^ [] : [50711 ^ _780478 : [(50712 ^ _780478) ^ [_1806352] : [hBOOL(hAPP(_1806067, _1806352))]], 50714 ^ _780478 : [(50717 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1806067, 50713 ^ [_1806063, _1806065, _1806067])))], (50715 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806063), 50713 ^ [_1806063, _1806065, _1806067]), c_Quotient_ORespects(_1806063, _1806065))))]]]]], (39837 ^ _780478) ^ [_1556538, _1556540, _1556542, _1556544, _1556546] : [class_Groups_Ocomm__monoid__add(_1556538), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556540), _1556542)), c_Fun_Oinj__on(_1556540, _1556540, _1556544, _1556542), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1556540, _1556538), _1556546), hAPP(c_Set_Oimage(_1556540, _1556540, _1556544), _1556542)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1556540, _1556538), hAPP(c_Fun_Ocomp(_1556540, _1556538, _1556540, _1556546), _1556544)), _1556542))], (48749 ^ _780478) ^ [_1763839, _1763841, _1763843, _1763845] : [-(hAPP(c_New__DSequence_Opos__union(_1763839, _1763841, _1763843), _1763845) = c_Lazy__Sequence_Oappend(_1763839, hAPP(_1763841, _1763845), hAPP(_1763843, _1763845)))], (11375 ^ _780478) ^ [_979729, _979731, _979733] : [-(hAPP(c_Finite__Set_Ofold1(_979729, _979731), hAPP(hAPP(c_Set_Oinsert(_979729), _979733), c_Orderings_Obot__class_Obot(tc_fun(_979729, tc_HOL_Obool)))) = _979733)], (35629 ^ _780478) ^ [_1451833, _1451835, _1451837, _1451839, _1451841, _1451843] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1451833, _1451835)), hAPP(hAPP(c_Product__Type_OPair(_1451833, _1451835), _1451841), _1451843)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool)), _1451837), _1451839))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451833, tc_fun(_1451835, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1451833, tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_fun(_1451835, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451835, tc_fun(tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_fun(_1451835, tc_HOL_Obool)), _1451833), c_COMBC(_1451835, tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451835, tc_prod(_1451833, _1451835)), tc_fun(_1451835, tc_fun(tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_HOL_Obool)), _1451833), hAPP(c_COMBB(tc_prod(_1451833, _1451835), tc_fun(tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_HOL_Obool), _1451835), c_member(tc_prod(_1451833, _1451835)))), c_Product__Type_OPair(_1451833, _1451835)))), _1451837)), hAPP(hAPP(c_COMBC(_1451833, tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_fun(_1451835, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451835, tc_fun(tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_fun(_1451835, tc_HOL_Obool)), _1451833), c_COMBC(_1451835, tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451835, tc_prod(_1451833, _1451835)), tc_fun(_1451835, tc_fun(tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_HOL_Obool)), _1451833), hAPP(c_COMBB(tc_prod(_1451833, _1451835), tc_fun(tc_fun(tc_prod(_1451833, _1451835), tc_HOL_Obool), tc_HOL_Obool), _1451835), c_member(tc_prod(_1451833, _1451835)))), c_Product__Type_OPair(_1451833, _1451835)))), _1451839)), _1451841), _1451843)))], (43413 ^ _780478) ^ [_1646889, _1646891, _1646893, _1646895, _1646897, _1646899] : [hAPP(hAPP(c_List_Olist_OCons(_1646889), _1646891), _1646893) = _1646895, _1646897 = hAPP(hAPP(c_List_Oappend(_1646889), _1646893), _1646899), -(hAPP(hAPP(c_List_Olist_OCons(_1646889), _1646891), _1646897) = hAPP(hAPP(c_List_Oappend(_1646889), _1646895), _1646899))], (45213 ^ _780478) ^ [_1686644, _1686646] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1686644), _1686646) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686644)), hAPP(c_Code__Numeral_Onat__of, _1686646))))], (20628 ^ _780478) ^ [_1165074, _1165076] : [class_Groups_Oordered__ab__group__add(_1165074), 20631 ^ _780478 : [(20638 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165074), _1165076), c_Groups_Ozero__class_Ozero(_1165074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165074), c_Groups_Ozero__class_Ozero(_1165074)), hAPP(c_Groups_Ouminus__class_Ouminus(_1165074), _1165076))))], (20632 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165074), c_Groups_Ozero__class_Ozero(_1165074)), hAPP(c_Groups_Ouminus__class_Ouminus(_1165074), _1165076))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165074), _1165076), c_Groups_Ozero__class_Ozero(_1165074))))]]], (13122 ^ _780478) ^ [_1013068, _1013070, _1013072, _1013074] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013068, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1013068), _1013070), _1013072)), _1013074) = hAPP(hAPP(c_Set_Oinsert(_1013068), _1013070), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013068, tc_HOL_Obool)), _1013072), _1013074)))], (51365 ^ _780478) ^ [_1820959, _1820961] : [_1820959 = _1820961, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820959, _1820961) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1820959), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (30009 ^ _780478) ^ [_1337208, _1337210] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337208, _1337210)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1337208), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1337210)))], (35241 ^ _780478) ^ [_1445144] : [c_Int_OBit0(_1445144) = c_Int_OMin], (34709 ^ _780478) ^ [_1434897, _1434899, _1434901] : [class_Int_Onumber__ring(_1434897), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1434897), hAPP(c_Int_Onumber__class_Onumber__of(_1434897), _1434899)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1434901))) = hAPP(hAPP(c_HOL_OLet(_1434897, _1434897), hAPP(hAPP(c_Power_Opower__class_Opower(_1434897), hAPP(c_Int_Onumber__class_Onumber__of(_1434897), _1434899)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434901))), hAPP(hAPP(c_COMBS(_1434897, _1434897, _1434897), c_Groups_Otimes__class_Otimes(_1434897)), c_COMBI(_1434897))))], (23347 ^ _780478) ^ [_1214828, _1214830] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214828), _1214830))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214828), _1214830)), -(_1214828 = _1214830)], (18484 ^ _780478) ^ [_1126742, _1126744, _1126746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126744), _1126746)), -(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, _1126742)), _1126744)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126742)), _1126746))))], (36654 ^ _780478) ^ [_1477499, _1477501, _1477503] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1477499), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1477501)), _1477503)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1477499, _1477501), hAPP(c_Divides_OnegateSnd, _1477503))))], (12564 ^ _780478) ^ [_1002317, _1002319] : [class_Lattices_Olattice(_1002317), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1002317), _1002319), _1002319) = _1002319)], (5444 ^ _780478) ^ [_863739, _863741] : [_863741 = _863739, -(c_Groups_Otimes__class_Otimes(_863741) = c_Groups_Otimes__class_Otimes(_863739))], (27565 ^ _780478) ^ [_1290141, _1290143] : [class_Rings_Oring__1(_1290141), -(hBOOL(hAPP(hAPP(c_member(_1290141), hAPP(c_Int_Oring__1__class_Oof__int(_1290141), _1290143)), c_Int_Oring__1__class_OInts(_1290141))))], (31310 ^ _780478) ^ [_1363831, _1363833] : [-(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), _1363831)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1363833))))))], (21462 ^ _780478) ^ [_1179013, _1179015, _1179017, _1179019, _1179021] : [class_Rings_Olinordered__semiring__strict(_1179013), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179013), _1179015), _1179017)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179013), _1179019), _1179021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179013), c_Groups_Ozero__class_Ozero(_1179013)), _1179015)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179013), c_Groups_Ozero__class_Ozero(_1179013)), _1179019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179013), _1179015), _1179019)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179013), _1179017), _1179021))))], (11274 ^ _780478) ^ [_977704, _977706, _977708] : [class_Orderings_Olinorder(_977704), hBOOL(hAPP(c_Finite__Set_Ofinite(_977704), _977706)), -(_977706 = c_Orderings_Obot__class_Obot(tc_fun(_977704, tc_HOL_Obool))), 11285 ^ _780478 : [(11286 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977704), _977708), hAPP(c_Finite__Set_Ofold1(_977704, c_Orderings_Oord__class_Omin(_977704)), _977706))), 11289 ^ _780478 : [(11290 ^ _780478) ^ [_977997] : [hBOOL(hAPP(hAPP(c_member(_977704), _977997), _977706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977704), _977708), _977997)))]]], (11296 ^ _780478) ^ [] : [11298 ^ _780478 : [(11301 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977704), _977708), 11297 ^ [_977704, _977706, _977708]))], (11299 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_977704), 11297 ^ [_977704, _977706, _977708]), _977706)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977704), _977708), hAPP(c_Finite__Set_Ofold1(_977704, c_Orderings_Oord__class_Omin(_977704)), _977706))))]]], (23773 ^ _780478) ^ [] : [-(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)))], (23435 ^ _780478) ^ [_1216197, _1216199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216197), _1216199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216197), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1216199), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50253 ^ _780478) ^ [_1797117, _1797119, _1797121, _1797123] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1797117, _1797119, _1797121, _1797123, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1797119)) = _1797121)], (16458 ^ _780478) ^ [_1080779, _1080781, _1080783, _1080785, _1080787] : [-(hAPP(c_Set_Ovimage(_1080779, _1080781, _1080783), hAPP(hAPP(c_Set_Oinsert(_1080781), _1080785), _1080787)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1080779, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1080779, _1080781, _1080783), hAPP(hAPP(c_Set_Oinsert(_1080781), _1080785), c_Orderings_Obot__class_Obot(tc_fun(_1080781, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1080779, _1080781, _1080783), _1080787)))], (10353 ^ _780478) ^ [_961115, _961117] : [class_Orderings_Olinorder(_961115), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_961115), _961117), _961117) = _961117)], (36248 ^ _780478) ^ [_1469777, _1469779, _1469781] : [-(c_Fun_Oinj__on(tc_prod(_1469777, _1469779), tc_prod(_1469779, _1469777), hAPP(c_Product__Type_Oprod_Oprod__case(_1469777, _1469779, tc_prod(_1469779, _1469777)), hAPP(c_COMBC(_1469779, _1469777, tc_prod(_1469779, _1469777)), c_Product__Type_OPair(_1469779, _1469777))), _1469781))], (30197 ^ _780478) ^ [_1340635, _1340637, _1340639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1340635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1340637), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1340639), 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), _1340639), _1340637))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1340635)))))], (37293 ^ _780478) ^ [_1490152, _1490154, _1490156, _1490158, _1490160, _1490162] : [hBOOL(hAPP(_1490152, _1490154)), hBOOL(hAPP(_1490156, _1490158)), 37300 ^ _780478 : [(37303 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1490156, hAPP(c_Product__Type_Osnd(_1490160, _1490162), hAPP(hAPP(c_Product__Type_OPair(_1490160, _1490162), _1490154), _1490158)))))], (37301 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1490152, hAPP(c_Product__Type_Ofst(_1490160, _1490162), hAPP(hAPP(c_Product__Type_OPair(_1490160, _1490162), _1490154), _1490158)))))]]], (52075 ^ _780478) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (39396 ^ _780478) ^ [_1545702, _1545704] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1545702, _1545702)), _1545704)), 39399 ^ _780478 : [(39406 ^ _780478) ^ [] : [c_Wellfounded_Oacyclic(_1545702, _1545704), -(c_Wellfounded_Owf(_1545702, _1545704))], (39400 ^ _780478) ^ [] : [c_Wellfounded_Owf(_1545702, _1545704), -(c_Wellfounded_Oacyclic(_1545702, _1545704))]]], (18363 ^ _780478) ^ [_1123988, _1123990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123988), hAPP(c_Nat_OSuc, _1123990))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123988), _1123990)))], (15369 ^ _780478) ^ [_1057255, _1057257, _1057259] : [class_Rings_Olinordered__semidom(_1057255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057255), c_Groups_Oone__class_Oone(_1057255)), _1057257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057255), hAPP(hAPP(c_Power_Opower__class_Opower(_1057255), _1057257), _1057259)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057255), _1057257), hAPP(hAPP(c_Power_Opower__class_Opower(_1057255), _1057257), _1057259)))))], (37917 ^ _780478) ^ [_1505695] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1505695)), c_Int_OInteg)))], (19560 ^ _780478) ^ [_1145986] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1145986), _1145986) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14843 ^ _780478) ^ [_1046765, _1046767, _1046769, _1046771, _1046773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046765), _1046767)), 14846 ^ _780478 : [(14853 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046771), 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), _1046767), _1046765)), _1046769)), _1046773))), -(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), _1046765), _1046769)), _1046771)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046767), _1046769)), _1046773))))], (14847 ^ _780478) ^ [] : [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), _1046765), _1046769)), _1046771)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1046767), _1046769)), _1046773))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1046771), 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), _1046767), _1046765)), _1046769)), _1046773))))]]], (31306 ^ _780478) ^ [_1363678, _1363680, _1363682, _1363684] : [-(hAPP(c_Set_Ovimage(_1363678, _1363680, _1363682), _1363684) = hAPP(c_Set_OCollect(_1363678), hAPP(hAPP(c_COMBC(_1363678, tc_fun(_1363680, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1363680, tc_fun(tc_fun(_1363680, tc_HOL_Obool), tc_HOL_Obool), _1363678), c_member(_1363680)), _1363682)), _1363684)))], (51903 ^ _780478) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (38531 ^ _780478) ^ [_1521520, _1521522, _1521524] : [_1521524 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521520, _1521522), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1521520, _1521522), _1521524) = c_Orderings_Obot__class_Obot(tc_fun(_1521522, tc_HOL_Obool)))], (50997 ^ _780478) ^ [_1813947, _1813949, _1813951] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1813947), _1813949)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1813947), _1813951))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1813947)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813949), _1813951)))], (25423 ^ _780478) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35287 ^ _780478) ^ [_1445737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1445737)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1445737), c_Int_OMin)))], (14525 ^ _780478) ^ [_1040053, _1040055] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040053), _1040055)), _1040053) = _1040055)], (33336 ^ _780478) ^ [_1410024, _1410026] : [class_Int_Onumber__ring(_1410024), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1410024), hAPP(c_Int_Onumber__class_Onumber__of(_1410024), c_Int_OPls)), _1410026) = _1410026)], (31984 ^ _780478) ^ [_1384746] : [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), _1384746))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1384746) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1384746)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (38562 ^ _780478) ^ [_1522252, _1522254, _1522256, _1522258, _1522260] : [-(hAPP(c_Relation_ORange(_1522252, _1522254), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1522252, _1522254)), hAPP(hAPP(c_Product__Type_OPair(_1522252, _1522254), _1522256), _1522258)), _1522260)) = hAPP(hAPP(c_Set_Oinsert(_1522254), _1522258), hAPP(c_Relation_ORange(_1522252, _1522254), _1522260)))], (51777 ^ _780478) ^ [_1827791, _1827793] : [class_Lattices_Olattice(_1827791), -(class_Lattices_Osemilattice__sup(tc_fun(_1827793, _1827791)))], (51887 ^ _780478) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (25916 ^ _780478) ^ [_1260916, _1260918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260916)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1260916)), _1260918) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1260916), _1260918)))], (24581 ^ _780478) ^ [_1237192, _1237194, _1237196] : [hBOOL(hAPP(_1237192, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1237194), _1237196))), 24584 ^ _780478 : [(24609 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237196), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24612 ^ _780478 : [(24613 ^ _780478) ^ [_1237856] : [-(hBOOL(hAPP(_1237192, _1237856))), 24614 ^ _780478 : [(24615 ^ _780478) ^ [_1237930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237196), _1237930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237930), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1237194 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237196), _1237856)), _1237930)]]]]], (24591 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237196)), 24594 ^ _780478 : [(24595 ^ _780478) ^ [_1237526] : [-(hBOOL(hAPP(_1237192, _1237526))), 24596 ^ _780478 : [(24597 ^ _780478) ^ [_1237597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237597)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237597), _1237196)), _1237194 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237196), _1237526)), _1237597)]]]]], (24585 ^ _780478) ^ [] : [_1237196 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1237192, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37181 ^ _780478) ^ [_1487819, _1487821] : [_1487819 = _1487821, -(hAPP(c_Int_ORep__Integ, _1487819) = hAPP(c_Int_ORep__Integ, _1487821))], (11149 ^ _780478) ^ [_975482] : [class_Orderings_Olinorder(_975482), -(c_Finite__Set_Ofun__left__comm__idem(_975482, _975482, c_Orderings_Oord__class_Omax(_975482)))], (28858 ^ _780478) ^ [_1314959, _1314961, _1314963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1314959)), 28861 ^ _780478 : [(28862 ^ _780478) ^ [_1315093] : [28864 ^ _780478 : [(28870 ^ _780478) ^ [] : [-(_1315093 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28866 ^ [_1314959, _1314961, _1314963, _1315093]), 28863 ^ [_1314959, _1314961, _1314963, _1315093]))], (28868 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28866 ^ [_1314959, _1314961, _1314963, _1315093]), _1314961)))], (28865 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28863 ^ [_1314959, _1314961, _1314963, _1315093]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1314959))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1314963), _1315093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1314963), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1315093), _1314959))))]]], (37614 ^ _780478) ^ [_1498357] : [-(c_Wellfounded_Omeasure(_1498357) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1498357), c_Wellfounded_Oless__than))], (28899 ^ _780478) ^ [_1315778, _1315780] : [-(hBOOL(hAPP(_1315778, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1315778, _1315780)), 28907 ^ _780478 : [(28910 ^ _780478) ^ [_1316016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1316016), 28906 ^ [_1315778, _1315780])), hBOOL(hAPP(_1315778, _1316016))], (28916 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1315778, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 28906 ^ [_1315778, _1315780]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (28908 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 28906 ^ [_1315778, _1315780]), _1315780)))]]], (15693 ^ _780478) ^ [_1064094, _1064096] : [class_Lattices_Osemilattice__inf(_1064094), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064094), _1064096), _1064096) = _1064096)], (12261 ^ _780478) ^ [_996377, _996379, _996381] : [class_Orderings_Olinorder(_996377), hAPP(_996379, hAPP(hAPP(c_Orderings_Oord__class_Omin(_996377), 12266 ^ [_996377, _996379, _996381]), 12267 ^ [_996377, _996379, _996381])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_996377), hAPP(_996379, 12266 ^ [_996377, _996379, _996381])), hAPP(_996379, 12267 ^ [_996377, _996379, _996381])), hBOOL(hAPP(c_Finite__Set_Ofinite(_996377), _996381)), -(_996381 = c_Orderings_Obot__class_Obot(tc_fun(_996377, tc_HOL_Obool))), -(hAPP(_996379, c_Big__Operators_Olinorder__class_OMin(_996377, _996381)) = c_Big__Operators_Olinorder__class_OMin(_996377, hAPP(c_Set_Oimage(_996377, _996377, _996379), _996381)))], (30795 ^ _780478) ^ [_1352582, _1352584, _1352586] : [class_Complete__Lattice_Ocomplete__lattice(_1352582), hBOOL(hAPP(hAPP(c_member(_1352582), _1352584), _1352586)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1352582), _1352584), c_Complete__Lattice_OSup__class_OSup(_1352582, _1352586))))], (6278 ^ _780478) ^ [_881375, _881377, _881379] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_881375, _881377, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_881375)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_881375), _881379), c_Com_Ocom_OSKIP), _881379)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_881375), tc_HOL_Obool)))))], (7846 ^ _780478) ^ [_913573, _913575, _913577, _913579, _913581, _913583, _913585, _913587] : [c_Finite__Set_Ofolding__image__simple__idem(_913573, _913575, _913577, _913579, _913581, _913583), hBOOL(hAPP(c_Finite__Set_Ofinite(_913575), _913585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913575, tc_HOL_Obool)), _913587), _913585)), -(hAPP(hAPP(_913577, hAPP(_913583, _913587)), hAPP(_913583, _913585)) = hAPP(_913583, _913585))], (4554 ^ _780478) ^ [_849674, _849676, _849678, _849680, _849682, _849684, _849686, _849688, _849690, _849692] : [-(c_Nitpick_Opair__box_Opair__box__rec(_849692, _849688, _849684, _849680, _849676) = c_Nitpick_Opair__box_Opair__box__rec(_849690, _849686, _849682, _849678, _849674)), _849692 = _849690, _849688 = _849686, _849684 = _849682, _849680 = _849678, _849676 = _849674], (6009 ^ _780478) ^ [_876095, _876097] : [hBOOL(hAPP(hAPP(c_member(_876095), _876097), c_Orderings_Obot__class_Obot(tc_fun(_876095, tc_HOL_Obool))))], (46441 ^ _780478) ^ [_1715421, _1715423] : [class_Orderings_Olinorder(_1715421), -(c_List_Olinorder__class_Osorted(_1715421, hAPP(hAPP(c_List_Olist_OCons(_1715421), _1715423), c_List_Olist_ONil(_1715421))))], (10060 ^ _780478) ^ [_955470, _955472, _955474] : [class_Orderings_Olinorder(_955470), hBOOL(hAPP(c_Finite__Set_Ofinite(_955470), _955472)), 10070 ^ _780478 : [(10073 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955470), 10069 ^ [_955470, _955472, _955474]), _955474))], (10071 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_955470), 10069 ^ [_955470, _955472, _955474]), _955472)))]], hBOOL(hAPP(hAPP(c_member(_955470), _955474), _955472)), -(c_Big__Operators_Olinorder__class_OMax(_955470, _955472) = _955474)], (38038 ^ _780478) ^ [_1510238, _1510240, _1510242, _1510244, _1510246] : [c_Typedef_Otype__definition(_1510238, _1510240, _1510242, _1510244, _1510246), -(hAPP(c_Set_Oimage(_1510240, _1510238, _1510244), _1510246) = c_Orderings_Otop__class_Otop(tc_fun(_1510238, tc_HOL_Obool)))], (41758 ^ _780478) ^ [_1604561, _1604563, _1604565, _1604567, _1604569, _1604571] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604561), tc_List_Olist(_1604561))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604561), tc_List_Olist(_1604561)), hAPP(hAPP(c_List_Olist_OCons(_1604561), _1604563), _1604565)), hAPP(hAPP(c_List_Olist_OCons(_1604561), _1604567), _1604569))), c_List_Olex(_1604561, _1604571)))), 41759 ^ _780478 : [(41766 ^ _780478) ^ [] : [_1604563 = _1604567, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604561), tc_List_Olist(_1604561))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604561), tc_List_Olist(_1604561)), _1604565), _1604569)), c_List_Olex(_1604561, _1604571)))], (41760 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604561, _1604561)), hAPP(hAPP(c_Product__Type_OPair(_1604561, _1604561), _1604563), _1604567)), _1604571)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604561)), _1604565) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604561)), _1604569)]]], (2416 ^ _780478) ^ [_815867, _815869, _815871, _815873] : [-(c_Divides_Odivmod__int(_815873, _815869) = c_Divides_Odivmod__int(_815871, _815867)), _815873 = _815871, _815869 = _815867], (44115 ^ _780478) ^ [_1663379, _1663381, _1663383] : [-(hAPP(c_List_Otl(_1663379), hAPP(hAPP(c_List_Odrop(_1663379), _1663381), _1663383)) = hAPP(hAPP(c_List_Odrop(_1663379), _1663381), hAPP(c_List_Otl(_1663379), _1663383)))], (906 ^ _780478) ^ [_794087, _794089, _794091, _794093, _794095, _794097] : [-(c_Relation_Orefl__on(_794095, _794091, _794087)), c_Relation_Orefl__on(_794097, _794093, _794089), _794097 = _794095, _794093 = _794091, _794089 = _794087], (6742 ^ _780478) ^ [_892029, _892031] : [-(c_HOL_OThe(_892029, hAPP(c_fequal, _892031)) = _892031)], (31797 ^ _780478) ^ [_1381203] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1381203))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1381203)))], (44813 ^ _780478) ^ [_1678247, _1678249, _1678251, _1678253, _1678255] : [-(hAPP(hAPP(c_List_Otake(_1678247), _1678249), hAPP(hAPP(c_List_Omap(_1678251, _1678247), _1678253), _1678255)) = hAPP(hAPP(c_List_Omap(_1678251, _1678247), _1678253), hAPP(hAPP(c_List_Otake(_1678251), _1678249), _1678255)))], (48056 ^ _780478) ^ [_1749136, _1749138, _1749140, _1749142] : [48057 ^ _780478 : [(48060 ^ _780478) ^ [] : [c_List_Olist__ex(_1749136, _1749138, _1749142)], (48058 ^ _780478) ^ [] : [c_List_Olist__ex(_1749136, _1749138, _1749140)]], -(c_List_Olist__ex(_1749136, _1749138, hAPP(hAPP(c_List_Oappend(_1749136), _1749140), _1749142)))], (14565 ^ _780478) ^ [_1040848, _1040850, _1040852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040848), _1040850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040848), _1040852)), 14572 ^ _780478 : [(14579 ^ _780478) ^ [] : [_1040850 = _1040852, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040850), _1040848) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040852), _1040848))], (14573 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040850), _1040848) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040852), _1040848), -(_1040850 = _1040852)]]], (25968 ^ _780478) ^ [_1261828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1261828)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1261828)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1261828)))], (44728 ^ _780478) ^ [_1676050, _1676052, _1676054, _1676056, _1676058] : [hAPP(hAPP(c_List_Omap(_1676050, _1676052), _1676054), _1676056) = hAPP(hAPP(c_List_Omap(_1676050, _1676052), _1676058), _1676056), 44731 ^ _780478 : [(44732 ^ _780478) ^ [_1676173] : [hBOOL(hAPP(hAPP(c_member(_1676050), _1676173), hAPP(c_List_Oset(_1676050), _1676056))), -(hAPP(_1676054, _1676173) = hAPP(_1676058, _1676173))]]], (35840 ^ _780478) ^ [_1460829, _1460831] : [-(c_Divides_Odivmod__int(_1460829, _1460831) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1460829), _1460831)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1460829, _1460831)))], (45165 ^ _780478) ^ [] : [-(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))))], (45861 ^ _780478) ^ [_1701231, _1701233] : [-(c_List_Oconcat(_1701231, _1701233) = hAPP(c_List_Ofoldl(tc_List_Olist(_1701231), tc_List_Olist(_1701231), c_List_Oappend(_1701231), c_List_Olist_ONil(_1701231)), _1701233))], (19810 ^ _780478) ^ [_1150193, _1150195, _1150197, _1150199] : [class_Groups_Oordered__comm__monoid__add(_1150193), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150193), c_Groups_Ozero__class_Ozero(_1150193)), _1150195)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150193), _1150197), _1150199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1150193), _1150197), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1150193), _1150195), _1150199))))], (36294 ^ _780478) ^ [_1470749, _1470751, _1470753, _1470755, _1470757, _1470759] : [hAPP(hAPP(c_Product__Type_OPair(_1470749, _1470751), _1470753), _1470755) = hAPP(hAPP(c_Product__Type_OPair(_1470749, _1470751), _1470757), _1470759), 36297 ^ _780478 : [(36300 ^ _780478) ^ [] : [-(_1470755 = _1470759)], (36298 ^ _780478) ^ [] : [-(_1470753 = _1470757)]]], (4504 ^ _780478) ^ [_848811, _848813] : [_848813 = _848811, -(c_List_Omember(_848813) = c_List_Omember(_848811))], (42199 ^ _780478) ^ [_1618076, _1618078, _1618080, _1618082] : [-(hAPP(hAPP(c_List_Onth(_1618076), hAPP(hAPP(c_List_Olist_OCons(_1618076), _1618078), _1618080)), hAPP(c_Nat_OSuc, _1618082)) = hAPP(hAPP(c_List_Onth(_1618076), _1618080), _1618082))], (14064 ^ _780478) ^ [_1031834, _1031836] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031834), _1031836)), _1031834 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1031836 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (45631 ^ _780478) ^ [_1696438, _1696440, _1696442, _1696444] : [-(hAPP(c_List_Oset(tc_prod(_1696438, _1696440)), c_Enum_Oproduct(_1696438, _1696440, _1696442, _1696444)) = hAPP(hAPP(c_Product__Type_OSigma(_1696438, _1696440), hAPP(c_List_Oset(_1696438), _1696442)), hAPP(c_COMBK(tc_fun(_1696440, tc_HOL_Obool), _1696438), hAPP(c_List_Oset(_1696440), _1696444))))], (45859 ^ _780478) ^ [_1701179, _1701181, _1701183] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1701179), tc_List_Olist(_1701179), c_List_Oappend(_1701179), _1701181), _1701183) = hAPP(hAPP(c_List_Oappend(_1701179), _1701181), c_List_Oconcat(_1701179, _1701183)))], (38683 ^ _780478) ^ [_1525518, _1525520, _1525522] : [-(hAPP(c_Relation_ODomain(_1525518, _1525520), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1525518, _1525520), tc_HOL_Obool), _1525522)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1525518, _1525520), tc_HOL_Obool), tc_fun(_1525518, tc_HOL_Obool)), _1525522), c_Relation_ODomain(_1525518, _1525520)))], (45560 ^ _780478) ^ [_1694869, _1694871, _1694873, _1694875, _1694877] : [-(c_List_Olist__all2(_1694869, _1694871, _1694873, _1694875, _1694877)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694869)), _1694875) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694871)), _1694877), 45566 ^ _780478 : [(45569 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1694873, hAPP(hAPP(c_List_Onth(_1694869), _1694875), 45565 ^ [_1694869, _1694871, _1694873, _1694875, _1694877])), hAPP(hAPP(c_List_Onth(_1694871), _1694877), 45565 ^ [_1694869, _1694871, _1694873, _1694875, _1694877])))], (45567 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45565 ^ [_1694869, _1694871, _1694873, _1694875, _1694877]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1694869)), _1694875))))]]], (6190 ^ _780478) ^ [_879541, _879543, _879545] : [-(hAPP(c_Set_Oimage(_879541, _879543, _879545), c_Orderings_Obot__class_Obot(tc_fun(_879541, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_879543, tc_HOL_Obool)))], (12462 ^ _780478) ^ [_1000449, _1000451, _1000453] : [class_Orderings_Olinorder(_1000449), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000449), _1000451)), -(_1000451 = c_Orderings_Obot__class_Obot(tc_fun(_1000449, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1000449), _1000453)), -(_1000453 = c_Orderings_Obot__class_Obot(tc_fun(_1000449, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1000449, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000449, tc_HOL_Obool)), _1000451), _1000453)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1000449), c_Big__Operators_Olinorder__class_OMin(_1000449, _1000451)), c_Big__Operators_Olinorder__class_OMin(_1000449, _1000453)))], (17320 ^ _780478) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (22423 ^ _780478) ^ [_1197540, _1197542] : [class_Groups_Olinordered__ab__group__add(_1197540), 22426 ^ _780478 : [(22433 ^ _780478) ^ [] : [_1197542 = c_Groups_Ozero__class_Ozero(_1197540), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197540), _1197542), _1197542) = c_Groups_Ozero__class_Ozero(_1197540))], (22427 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197540), _1197542), _1197542) = c_Groups_Ozero__class_Ozero(_1197540), -(_1197542 = c_Groups_Ozero__class_Ozero(_1197540))]]], (5939 ^ _780478) ^ [_874886, _874888, _874890, _874892] : [_874886 = _874888, 5942 ^ _780478 : [(5949 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874890), _874892), _874888)), -(hBOOL(hAPP(hAPP(c_member(_874890), _874892), _874886)))], (5943 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874890), _874892), _874886)), -(hBOOL(hAPP(hAPP(c_member(_874890), _874892), _874888)))]]], (23017 ^ _780478) ^ [_1208918, _1208920] : [class_Rings_Olinordered__semidom(_1208918), 23020 ^ _780478 : [(23027 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1208920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208918), c_Groups_Ozero__class_Ozero(_1208918)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208918), _1208920))))], (23021 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208918), c_Groups_Ozero__class_Ozero(_1208918)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208918), _1208920))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1208920)))]]], (40512 ^ _780478) ^ [_1572767, _1572769] : [-(c_Transitive__Closure_Ortrancl(_1572767, c_Transitive__Closure_Otrancl(_1572767, _1572769)) = c_Transitive__Closure_Ortrancl(_1572767, _1572769))], (49724 ^ _780478) ^ [_1786255, _1786257] : [c_Relation_Osym(_1786255, _1786257), -(c_Relation_Osym(_1786255, c_Transitive__Closure_Otrancl(_1786255, _1786257)))], (5126 ^ _780478) ^ [_858786, _858788] : [_858788 = _858786, -(c_Lattices_Osemilattice__sup__class_Osup(_858788) = c_Lattices_Osemilattice__sup__class_Osup(_858786))], (48174 ^ _780478) ^ [_1751688, _1751690] : [-(c_List_Olist__all(_1751688, _1751690, c_List_Olist_ONil(_1751688)))], (47099 ^ _780478) ^ [_1727958, _1727960, _1727962] : [-(hAPP(c_List_Orotate(_1727958, _1727960), hAPP(c_List_Orev(_1727958), _1727962)) = hAPP(c_List_Orev(_1727958), hAPP(c_List_Orotate(_1727958, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727958)), _1727962)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1727960, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727958)), _1727962)))), _1727962)))], (30057 ^ _780478) ^ [_1338157, _1338159] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1338157), _1338159)), _1338159) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1338157), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338157, _1338159)))], (20660 ^ _780478) ^ [_1165616, _1165618] : [class_Groups_Oordered__ab__group__add(_1165616), 20663 ^ _780478 : [(20670 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165616), c_Groups_Ozero__class_Ozero(_1165616)), _1165618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165616), hAPP(c_Groups_Ouminus__class_Ouminus(_1165616), _1165618)), c_Groups_Ozero__class_Ozero(_1165616))))], (20664 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165616), hAPP(c_Groups_Ouminus__class_Ouminus(_1165616), _1165618)), c_Groups_Ozero__class_Ozero(_1165616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165616), c_Groups_Ozero__class_Ozero(_1165616)), _1165618)))]]], (9850 ^ _780478) ^ [_951085, _951087, _951089, _951091, _951093] : [class_Rings_Ocomm__semiring__1(_951085), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951085), _951087), _951089)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951085), _951091), _951093)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951085), _951087), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951085), _951089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951085), _951091), _951093))))], (7279 ^ _780478) ^ [_902025, _902027, _902029] : [_902025 = _902027, 7282 ^ _780478 : [(7285 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902029, tc_HOL_Obool)), _902027), _902025)))], (7283 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902029, tc_HOL_Obool)), _902025), _902027)))]]], (17420 ^ _780478) ^ [_1102858, _1102860, _1102862, _1102864, _1102866] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102858, tc_fun(_1102860, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102858, tc_HOL_Obool)), _1102862), _1102864)), _1102866) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102860, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102858, tc_fun(_1102860, tc_HOL_Obool)), _1102862), _1102866)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102858, tc_fun(_1102860, tc_HOL_Obool)), _1102864), _1102866)))], (38853 ^ _780478) ^ [_1531079, _1531081, _1531083, _1531085, _1531087, _1531089] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531079, _1531081)), hAPP(hAPP(c_Product__Type_OPair(_1531079, _1531081), _1531083), _1531085)), hAPP(hAPP(c_Product__Type_OSigma(_1531079, _1531081), _1531087), _1531089)))), hBOOL(hAPP(hAPP(c_member(_1531079), _1531083), _1531087)), hBOOL(hAPP(hAPP(c_member(_1531081), _1531085), hAPP(_1531089, _1531083)))], (22945 ^ _780478) ^ [_1207544, _1207546, _1207548] : [class_Rings_Oring__1(_1207544), hBOOL(hAPP(hAPP(c_member(_1207544), _1207546), c_Int_Oring__1__class_OInts(_1207544))), hBOOL(hAPP(hAPP(c_member(_1207544), _1207548), c_Int_Oring__1__class_OInts(_1207544))), -(hBOOL(hAPP(hAPP(c_member(_1207544), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1207544), _1207546), _1207548)), c_Int_Oring__1__class_OInts(_1207544))))], (29055 ^ _780478) ^ [_1319305] : [-(hAPP(c_Set_OPow(_1319305), c_Orderings_Obot__class_Obot(tc_fun(_1319305, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1319305, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1319305, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1319305, tc_HOL_Obool), tc_HOL_Obool))))], (18216 ^ _780478) ^ [_1121184, _1121186, _1121188] : [class_Complete__Lattice_Ocomplete__lattice(_1121184), class_Orderings_Olinorder(_1121184), 18223 ^ _780478 : [(18233 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121184), c_Complete__Lattice_OInf__class_OInf(_1121184, _1121186)), _1121188))), 18234 ^ _780478 : [(18235 ^ _780478) ^ [_1121490] : [hBOOL(hAPP(hAPP(c_member(_1121184), _1121490), _1121186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121184), _1121490), _1121188))]]], (18224 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121184), c_Complete__Lattice_OInf__class_OInf(_1121184, _1121186)), _1121188)), 18228 ^ _780478 : [(18231 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121184), 18227 ^ [_1121184, _1121186, _1121188]), _1121188)))], (18229 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1121184), 18227 ^ [_1121184, _1121186, _1121188]), _1121186)))]]]]], (48184 ^ _780478) ^ [_1751862, _1751864, _1751866, _1751868] : [-(c_List_Olist__all(_1751862, _1751864, hAPP(hAPP(c_List_Oappend(_1751862), _1751866), _1751868))), c_List_Olist__all(_1751862, _1751864, _1751866), c_List_Olist__all(_1751862, _1751864, _1751868)], (11023 ^ _780478) ^ [_972879, _972881, _972883] : [class_Rings_Oring(_972879), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972879), hAPP(c_Groups_Ouminus__class_Ouminus(_972879), _972881)), _972883) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972879), _972881), hAPP(c_Groups_Ouminus__class_Ouminus(_972879), _972883)))], (2436 ^ _780478) ^ [_816165, _816167, _816169, _816171] : [-(c_Divides_OposDivAlg(_816171, _816167) = c_Divides_OposDivAlg(_816169, _816165)), _816171 = _816169, _816167 = _816165], (38706 ^ _780478) ^ [_1526543, _1526545, _1526547, _1526549, _1526551, _1526553] : [-(hAPP(c_Set_Oimage(_1526543, tc_prod(_1526545, _1526547), hAPP(hAPP(c_COMBS(_1526543, _1526547, tc_prod(_1526545, _1526547)), hAPP(hAPP(c_COMBB(_1526545, tc_fun(_1526547, tc_prod(_1526545, _1526547)), _1526543), c_Product__Type_OPair(_1526545, _1526547)), _1526549)), _1526551)), _1526553) = hAPP(hAPP(c_Product__Type_OSigma(_1526545, _1526547), hAPP(c_Set_Oimage(_1526543, _1526545, _1526549), _1526553)), hAPP(hAPP(c_COMBB(tc_fun(_1526543, tc_HOL_Obool), tc_fun(_1526547, tc_HOL_Obool), _1526545), c_Set_Oimage(_1526543, _1526547, _1526551)), hAPP(hAPP(c_COMBC(_1526545, tc_fun(_1526543, tc_HOL_Obool), tc_fun(_1526543, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526543, tc_HOL_Obool), tc_fun(tc_fun(_1526543, tc_HOL_Obool), tc_fun(_1526543, tc_HOL_Obool)), _1526545), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1526543, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1526545, tc_HOL_Obool), tc_fun(_1526543, tc_HOL_Obool), _1526545), c_Set_Ovimage(_1526543, _1526545, _1526549)), hAPP(hAPP(c_COMBC(_1526545, tc_fun(_1526545, tc_HOL_Obool), tc_fun(_1526545, tc_HOL_Obool)), c_Set_Oinsert(_1526545)), c_Orderings_Obot__class_Obot(tc_fun(_1526545, tc_HOL_Obool)))))), _1526553))))], (48553 ^ _780478) ^ [_1760121, _1760123, _1760125, _1760127] : [-(hAPP(hAPP(c_List_Otake(_1760121), _1760123), c_List_Oreplicate(_1760121, _1760125, _1760127)) = c_List_Oreplicate(_1760121, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1760123), _1760125), _1760127))], (28838 ^ _780478) ^ [_1314551, _1314553, _1314555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1314551)), 28841 ^ _780478 : [(28842 ^ _780478) ^ [_1314685] : [28844 ^ _780478 : [(28850 ^ _780478) ^ [] : [-(_1314685 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28846 ^ [_1314551, _1314553, _1314555, _1314685]), 28843 ^ [_1314551, _1314553, _1314555, _1314685]))], (28848 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28846 ^ [_1314551, _1314553, _1314555, _1314685]), _1314553)))], (28845 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28843 ^ [_1314551, _1314553, _1314555, _1314685]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1314551))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1314685), _1314555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1314685), _1314551)), _1314555)))]]], (9802 ^ _780478) ^ [_949873, _949875, _949877, _949879, _949881] : [class_Rings_Ocomm__semiring__1(_949873), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949873), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949873), _949875), _949877)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949873), _949879), _949881)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949873), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949873), _949875), _949879)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949873), _949877), _949881)))], (22911 ^ _780478) ^ [_1206939] : [class_Rings_Oring__1(_1206939), -(hBOOL(hAPP(hAPP(c_member(_1206939), c_Groups_Ozero__class_Ozero(_1206939)), c_Int_Oring__1__class_OInts(_1206939))))], (43526 ^ _780478) ^ [_1649550, _1649552, _1649554] : [-(hAPP(c_List_Oset(_1649550), hAPP(hAPP(c_List_Oappend(_1649550), _1649552), _1649554)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1649550, tc_HOL_Obool)), hAPP(c_List_Oset(_1649550), _1649552)), hAPP(c_List_Oset(_1649550), _1649554)))], (39682 ^ _780478) ^ [_1553141, _1553143, _1553145, _1553147, _1553149] : [c_Finite__Set_Ofun__left__comm(_1553141, _1553143, _1553145), -(hAPP(c_Fun_Ocomp(_1553143, _1553143, _1553143, hAPP(_1553145, _1553147)), hAPP(_1553145, _1553149)) = hAPP(c_Fun_Ocomp(_1553143, _1553143, _1553143, hAPP(_1553145, _1553149)), hAPP(_1553145, _1553147)))], (28648 ^ _780478) ^ [_1310969, _1310971, _1310973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310969)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1310971), _1310973)), 28655 ^ _780478 : [(28656 ^ _780478) ^ [_1311159] : [28658 ^ _780478 : [(28664 ^ _780478) ^ [] : [-(_1311159 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28660 ^ [_1310969, _1310971, _1310973, _1311159]), 28657 ^ [_1310969, _1310971, _1310973, _1311159]))], (28662 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28660 ^ [_1310969, _1310971, _1310973, _1311159]), _1310973)))], (28659 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28657 ^ [_1310969, _1310971, _1310973, _1311159]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1310969))))]], -(_1311159 = _1310971), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1311159), _1310969) = _1310971]]], (30967 ^ _780478) ^ [_1355958, _1355960] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1355958, tc_HOL_Obool)), _1355960)), 30973 ^ _780478 : [(30976 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1355958), 30972 ^ [_1355958, _1355960]))], (30974 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1355958, tc_HOL_Obool)), 30972 ^ [_1355958, _1355960]), _1355960)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1355958), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1355958, tc_HOL_Obool), _1355960))))], (42593 ^ _780478) ^ [_1629242, _1629244] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1629242), _1629244) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1629242, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1629244), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50088 ^ _780478) ^ [_1793049, _1793051, _1793053] : [hAPP(_1793053, hAPP(c_Hilbert__Choice_Oinv__into(_1793049, _1793051, c_Orderings_Otop__class_Otop(tc_fun(_1793049, tc_HOL_Obool)), _1793053), 50089 ^ [_1793049, _1793051, _1793053])) = 50089 ^ [_1793049, _1793051, _1793053], -(hAPP(c_Set_Oimage(_1793049, _1793051, _1793053), c_Orderings_Otop__class_Otop(tc_fun(_1793049, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1793051, tc_HOL_Obool)))], (3678 ^ _780478) ^ [_835552, _835554, _835556, _835558] : [-(c_List_Obutlast(_835558, _835554) = c_List_Obutlast(_835556, _835552)), _835558 = _835556, _835554 = _835552], (43863 ^ _780478) ^ [_1657630, _1657632, _1657634] : [-(hAPP(hAPP(c_List_Odrop(_1657630), _1657632), c_List_Obutlast(_1657630, _1657634)) = c_List_Obutlast(_1657630, hAPP(hAPP(c_List_Odrop(_1657630), _1657632), _1657634)))], (38329 ^ _780478) ^ [_1516696, _1516698] : [hBOOL(hAPP(hAPP(c_member(_1516696), 38330 ^ [_1516696, _1516698]), c_Wellfounded_Oacc(_1516696, _1516698))), -(c_Wellfounded_Owf(_1516696, _1516698))], (9050 ^ _780478) ^ [_936177, _936179, _936181, _936183] : [class_Orderings_Opreorder(_936177), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936177), _936179), _936181)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936177), _936181), _936183)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936177), _936179), _936183)))], (15205 ^ _780478) ^ [_1054174, _1054176, _1054178] : [class_Lattices_Olattice(_1054174), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054174), _1054176)), -(c_Big__Operators_Olattice__class_OSup__fin(_1054174, hAPP(hAPP(c_Set_Oinsert(_1054174), _1054178), _1054176)) = hAPP(hAPP(c_Finite__Set_Ofold(_1054174, _1054174, c_Lattices_Osemilattice__sup__class_Osup(_1054174)), _1054178), _1054176))], (11137 ^ _780478) ^ [_975128, _975130, _975132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_975128, tc_HOL_Obool)), _975132), _975130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_975128, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_975128, tc_HOL_Obool)), _975130)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_975128, tc_HOL_Obool)), _975132))))], (13962 ^ _780478) ^ [_1030081, _1030083, _1030085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030081), _1030083)), _1030085)), 13965 ^ _780478 : [(13968 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030083), _1030085)))], (13966 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030081), _1030085)))]]], (37425 ^ _780478) ^ [_1492999, _1493001] : [-(c_FunDef_Orp__inv__image(_1492999, _1493001) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool), tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool), tc_fun(tc_fun(_1493001, _1492999), tc_prod(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool), tc_fun(tc_fun(_1493001, _1492999), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool), tc_fun(tc_fun(_1493001, _1492999), tc_prod(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1493001, _1492999), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)), tc_fun(tc_fun(_1493001, _1492999), tc_prod(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool), tc_fun(tc_fun(_1493001, _1492999), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool), tc_fun(tc_fun(_1493001, _1492999), tc_prod(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool))))), tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1493001, _1492999), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)), tc_fun(tc_fun(_1493001, _1492999), tc_prod(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool))), tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1493001, _1492999), tc_fun(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1493001, _1492999), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)), tc_fun(tc_fun(_1493001, _1492999), tc_prod(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)))), tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool)), c_COMBS(tc_fun(_1493001, _1492999), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1493001, _1492999), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)), tc_fun(tc_fun(_1493001, _1492999), tc_fun(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)))), tc_fun(tc_prod(_1492999, _1492999), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool))), tc_fun(_1493001, _1492999)), c_Product__Type_OPair(tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool), tc_fun(tc_prod(_1493001, _1493001), tc_HOL_Obool)))), c_Relation_Oinv__image(_1492999, _1493001))))), c_Relation_Oinv__image(_1492999, _1493001))))], (19706 ^ _780478) ^ [_1148259, _1148261, _1148263, _1148265] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1148259, _1148261, _1148263), _1148265), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1148261)], (21642 ^ _780478) ^ [_1182373, _1182375, _1182377] : [class_Rings_Olinordered__idom(_1182373), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182373), c_Groups_Ozero__class_Ozero(_1182373)), _1182375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182373), c_Groups_Ozero__class_Ozero(_1182373)), _1182377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182373), _1182377), c_Groups_Oone__class_Oone(_1182373))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182373), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182373), _1182377), _1182375)), _1182375)))], (22843 ^ _780478) ^ [_1205673, _1205675, _1205677] : [class_Rings_Olinordered__semidom(_1205673), 22846 ^ _780478 : [(22853 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205675), _1205677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205673), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205673), _1205675)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205673), _1205677))))], (22847 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205673), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205673), _1205675)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205673), _1205677))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205675), _1205677)))]]], (47205 ^ _780478) ^ [_1730262, _1730264, _1730266] : [c_List_OtakeWhile(_1730262, _1730264, _1730266) = _1730266, 47208 ^ _780478 : [(47209 ^ _780478) ^ [_1730349] : [hBOOL(hAPP(hAPP(c_member(_1730262), _1730349), hAPP(c_List_Oset(_1730262), _1730266))), -(hBOOL(hAPP(_1730264, _1730349)))]]], (32120 ^ _780478) ^ [_1387036, _1387038, _1387040, _1387042, _1387044, _1387046] : [c_Com_Ocom_OLocal(_1387036, _1387038, _1387040) = c_Com_Ocom_OCond(_1387042, _1387044, _1387046)], (29596 ^ _780478) ^ [_1329937, _1329939] : [-(_1329937 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1329939), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1329937), _1329939))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329937, _1329939)))], (9450 ^ _780478) ^ [_942461, _942463, _942465, _942467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942461, tc_HOL_Obool)), _942463), _942465)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942461, tc_HOL_Obool)), _942465), _942467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942461, tc_HOL_Obool)), _942463), _942467)))], (19592 ^ _780478) ^ [_1146467] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146467), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52447 ^ _780478) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P_H, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q_H, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool)))))], (48945 ^ _780478) ^ [_1768119, _1768121, _1768123, _1768125] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1768119, _1768121)), c_Nitpick_Opair__box_OPairBox(_1768119, _1768121, _1768123, _1768125)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36888 ^ _780478) ^ [_1482210, _1482212, _1482214, _1482216, _1482218] : [hAPP(c_Product__Type_Osnd(_1482210, _1482212), hAPP(hAPP(c_Product__Type_OPair(_1482210, _1482212), _1482214), _1482216)) = _1482218, -(_1482216 = _1482218)], (51175 ^ _780478) ^ [_1817528, _1817530, _1817532, _1817534] : [class_Divides_Osemiring__div(_1817528), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817528), _1817530), _1817532)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817528), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817528), _1817532), _1817530)), _1817534) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817528), _1817532), _1817534)), _1817530))], (25425 ^ _780478) ^ [_1252665, _1252667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252667)), 25432 ^ _780478 : [(25439 ^ _780478) ^ [] : [_1252665 = _1252667, -(hAPP(c_Int_Onat, _1252665) = hAPP(c_Int_Onat, _1252667))], (25433 ^ _780478) ^ [] : [hAPP(c_Int_Onat, _1252665) = hAPP(c_Int_Onat, _1252667), -(_1252665 = _1252667)]]], (43636 ^ _780478) ^ [_1651497, _1651499, _1651501, _1651503] : [-(hAPP(hAPP(c_List_Onth(_1651497), hAPP(hAPP(c_List_Oappend(_1651497), _1651499), _1651501)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651497)), _1651499)), _1651503)) = hAPP(hAPP(c_List_Onth(_1651497), _1651501), _1651503))], (14881 ^ _780478) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (7032 ^ _780478) ^ [_897928, _897930, _897932] : [class_Orderings_Olinorder(_897928), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897928), _897930), _897932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_897928), _897932), _897930)))], (18516 ^ _780478) ^ [_1127444, _1127446, _1127448, _1127450, _1127452] : [_1127444 = c_Orderings_Obot__class_Obot(tc_fun(_1127446, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127448, tc_HOL_Obool)), _1127450), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127446, tc_fun(_1127448, tc_HOL_Obool)), _1127444), _1127452)) = _1127450)], (45442 ^ _780478) ^ [_1692492, _1692494, _1692496, _1692498, _1692500, _1692502] : [c_List_Olist__all2(_1692492, _1692494, _1692496, _1692498, _1692500), -(c_List_Olist__all2(_1692492, _1692494, _1692496, hAPP(hAPP(c_List_Odrop(_1692492), _1692502), _1692498), hAPP(hAPP(c_List_Odrop(_1692494), _1692502), _1692500)))], (32288 ^ _780478) ^ [_1390471, _1390473, _1390475, _1390477] : [class_Int_Onumber__ring(_1390471), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390471), hAPP(c_Int_Onumber__class_Onumber__of(_1390471), _1390473)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390471), hAPP(c_Int_Onumber__class_Onumber__of(_1390471), _1390475)), _1390477)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390471), hAPP(c_Int_Onumber__class_Onumber__of(_1390471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390473), _1390475))), _1390477))], (10401 ^ _780478) ^ [_961914, _961916, _961918, _961920, _961922] : [class_Orderings_Olinorder(_961914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961914), _961916), _961918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961914), _961920), _961922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961914), hAPP(hAPP(c_Orderings_Oord__class_Omax(_961914), _961916), _961920)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_961914), _961918), _961922))))], (14076 ^ _780478) ^ [_1032003, _1032005, _1032007] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032003), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1032005), _1032007)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032003), _1032005)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032003), _1032007)))], (18108 ^ _780478) ^ [_1117889, _1117891, _1117893, _1117895, _1117897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1117889, tc_HOL_Obool)), _1117891), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117893, tc_fun(_1117889, tc_HOL_Obool)), _1117895), _1117897))), 18111 ^ _780478 : [(18112 ^ _780478) ^ [_1118022] : [hBOOL(hAPP(hAPP(c_member(_1117893), _1118022), _1117895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1117889, tc_HOL_Obool)), _1117891), hAPP(_1117897, _1118022))))]]], (34801 ^ _780478) ^ [] : [-(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)))))], (34773 ^ _780478) ^ [_1436035] : [-(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)))), _1436035) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1436035)))], (38588 ^ _780478) ^ [_1523325, _1523327, _1523329, _1523331] : [hBOOL(hAPP(c_Predicate_ORangeP(_1523325, _1523327, _1523329), _1523331)), -(hBOOL(hAPP(hAPP(_1523329, 38591 ^ [_1523325, _1523327, _1523329, _1523331]), _1523331)))], (13940 ^ _780478) ^ [_1029668, _1029670, _1029672, _1029674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029668), _1029670)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029672), _1029674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029668), _1029672)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029670), _1029674))))], (15816 ^ _780478) ^ [_1066685, _1066687, _1066689] : [class_Lattices_Olattice(_1066685), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066685), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066685), _1066687), _1066689)), _1066687)))], (38016 ^ _780478) ^ [_1509281, _1509283, _1509285, _1509287] : [hBOOL(hAPP(hAPP(c_member(_1509281), _1509283), c_Wellfounded_Oacc(_1509281, _1509285))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1509281, _1509281)), hAPP(hAPP(c_Product__Type_OPair(_1509281, _1509281), _1509287), _1509283)), _1509285)), -(hBOOL(hAPP(hAPP(c_member(_1509281), _1509287), c_Wellfounded_Oacc(_1509281, _1509285))))], (23213 ^ _780478) ^ [_1212530, _1212532] : [_1212530 = _1212532, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212530) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212532))], (52123 ^ _780478) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (35591 ^ _780478) ^ [_1450622, _1450624] : [-(_1450622 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450624, _1450622), c_Divides_Odivmod__int(_1450624, _1450622))))], (33056 ^ _780478) ^ [_1405198] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405198) = _1405198)], (44618 ^ _780478) ^ [_1673261, _1673263, _1673265, _1673267] : [-(hAPP(hAPP(c_List_Oappend(_1673261), _1673263), hAPP(hAPP(c_List_Olist_OCons(_1673261), _1673265), c_List_Olist_ONil(_1673261))) = _1673267), -(_1673267 = c_List_Olist_ONil(_1673261)), c_List_Obutlast(_1673261, _1673267) = _1673263, c_List_Olast(_1673261, _1673267) = _1673265], (29993 ^ _780478) ^ [_1336949, _1336951] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1336949), _1336951))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336949, _1336951) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1336949), _1336951), _1336951))], (14299 ^ _780478) ^ [_1035868, _1035870] : [14300 ^ _780478 : [(14303 ^ _780478) ^ [] : [_1035868 = _1035870], (14301 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035868), _1035870))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035868), _1035870)))], (48647 ^ _780478) ^ [_1761868, _1761870, _1761872, _1761874] : [hBOOL(hAPP(_1761868, _1761870)), -(hAPP(c_List_Ofilter(_1761872, _1761868), c_List_Oreplicate(_1761872, _1761874, _1761870)) = c_List_Oreplicate(_1761872, _1761874, _1761870))], (35249 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (48955 ^ _780478) ^ [_1768315, _1768317, _1768319, _1768321, _1768323, _1768325] : [-(c_Nitpick_Opair__box_OPairBox(_1768315, _1768317, _1768319, _1768321) = c_Nitpick_Opair__box_OPairBox(_1768315, _1768317, _1768323, _1768325)), _1768319 = _1768323, _1768321 = _1768325], (38632 ^ _780478) ^ [_1524234, _1524236, _1524238] : [hAPP(c_Relation_ODomain(_1524234, _1524236), _1524238) = c_Orderings_Obot__class_Obot(tc_fun(_1524234, tc_HOL_Obool)), -(_1524238 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524234, _1524236), tc_HOL_Obool)))], (36798 ^ _780478) ^ [_1480400, _1480402, _1480404, _1480406] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480400, _1480402), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1480404), _1480406))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1480400), _1480402) = _1480404)], (43235 ^ _780478) ^ [_1642622, _1642624, _1642626] : [hBOOL(hAPP(hAPP(c_member(_1642622), _1642624), hAPP(c_List_Oset(_1642622), _1642626))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642622)), c_List_Oremove1(_1642622, _1642624, _1642626)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642622)), _1642626)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (18678 ^ _780478) ^ [_1131289, _1131291, _1131293, _1131295, _1131297] : [class_Complete__Lattice_Ocomplete__lattice(_1131289), hBOOL(hAPP(hAPP(c_member(_1131291), _1131293), _1131295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131289), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1131291, _1131289), _1131295), _1131297)), hAPP(_1131297, _1131293))))], (24885 ^ _780478) ^ [_1242660, _1242662, _1242664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242660)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242660), _1242662)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242660), _1242664)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1242662), _1242664))], (11959 ^ _780478) ^ [_990594, _990596, _990598] : [class_Orderings_Olinorder(_990594), hBOOL(hAPP(c_Finite__Set_Ofinite(_990594), _990596)), -(_990596 = c_Orderings_Obot__class_Obot(tc_fun(_990594, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_990594, c_Orderings_Oord__class_Omax(_990594), hAPP(hAPP(c_Set_Oinsert(_990594), _990598), _990596)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_990594), _990598), c_Big__Operators_Olattice_OSup__fin(_990594, c_Orderings_Oord__class_Omax(_990594), _990596)))], (43937 ^ _780478) ^ [_1659390, _1659392, _1659394, _1659396] : [-(hAPP(hAPP(c_List_Oappend(_1659390), _1659392), _1659394) = _1659396), _1659392 = hAPP(hAPP(c_List_Otake(_1659390), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659390)), _1659392)), _1659396), _1659394 = hAPP(hAPP(c_List_Odrop(_1659390), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659390)), _1659392)), _1659396)], (37883 ^ _780478) ^ [_1504723] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1504723) = 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, _1504723)), 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))))))))], (27872 ^ _780478) ^ [_1296030, _1296032, _1296034] : [class_Orderings_Oorder(_1296030), 27875 ^ _780478 : [(27882 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296030), _1296032), _1296034))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1296030, _1296032, _1296034) = c_Orderings_Obot__class_Obot(tc_fun(_1296030, tc_HOL_Obool)))], (27876 ^ _780478) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1296030, _1296032, _1296034) = c_Orderings_Obot__class_Obot(tc_fun(_1296030, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296030), _1296032), _1296034))]]], (45264 ^ _780478) ^ [_1687774, _1687776] : [-(hBOOL(hAPP(c_List_Olistsp(_1687774, _1687776), c_List_Olist_ONil(_1687774))))], (43015 ^ _780478) ^ [_1638493, _1638495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1638493), _1638495)), -(c_List_Oupto(_1638495, _1638493) = c_List_Olist_ONil(tc_Int_Oint))], (50604 ^ _780478) ^ [_1804145, _1804147, _1804149] : [-(c_Fun_Obij__betw(_1804145, _1804147, _1804149, c_Orderings_Otop__class_Otop(tc_fun(_1804145, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804147, tc_HOL_Obool)))), c_Fun_Oinj__on(_1804145, _1804147, _1804149, c_Orderings_Otop__class_Otop(tc_fun(_1804145, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1804145, _1804147, _1804149), c_Orderings_Otop__class_Otop(tc_fun(_1804145, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1804147, tc_HOL_Obool))], (31720 ^ _780478) ^ [_1379419, _1379421, _1379423, _1379425] : [-(hAPP(c_Relation_OImage(_1379419, _1379421, _1379423), _1379425) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379419, tc_fun(_1379421, tc_HOL_Obool)), _1379425), hAPP(hAPP(c_COMBB(tc_fun(_1379419, tc_HOL_Obool), tc_fun(_1379421, tc_HOL_Obool), _1379419), c_Relation_OImage(_1379419, _1379421, _1379423)), hAPP(hAPP(c_COMBC(_1379419, tc_fun(_1379419, tc_HOL_Obool), tc_fun(_1379419, tc_HOL_Obool)), c_Set_Oinsert(_1379419)), c_Orderings_Obot__class_Obot(tc_fun(_1379419, tc_HOL_Obool))))))], (42428 ^ _780478) ^ [_1623678, _1623680] : [-(c_List_Olists(_1623678, _1623680) = hAPP(c_Set_OCollect(tc_List_Olist(_1623678)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623678), tc_fun(_1623678, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1623678, tc_HOL_Obool), tc_fun(tc_fun(_1623678, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1623678)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1623678, tc_HOL_Obool))), c_List_Oset(_1623678))), _1623680)))], (35671 ^ _780478) ^ [_1455218, _1455220, _1455222, _1455224, _1455226, _1455228] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455218, tc_fun(_1455220, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1455218, tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_fun(_1455220, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455220, tc_fun(tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_fun(_1455220, tc_HOL_Obool)), _1455218), c_COMBC(_1455220, tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455220, tc_prod(_1455218, _1455220)), tc_fun(_1455220, tc_fun(tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_HOL_Obool)), _1455218), hAPP(c_COMBB(tc_prod(_1455218, _1455220), tc_fun(tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_HOL_Obool), _1455220), c_member(tc_prod(_1455218, _1455220)))), c_Product__Type_OPair(_1455218, _1455220)))), _1455222)), hAPP(hAPP(c_COMBC(_1455218, tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_fun(_1455220, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455220, tc_fun(tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_fun(_1455220, tc_HOL_Obool)), _1455218), c_COMBC(_1455220, tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455220, tc_prod(_1455218, _1455220)), tc_fun(_1455220, tc_fun(tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_HOL_Obool)), _1455218), hAPP(c_COMBB(tc_prod(_1455218, _1455220), tc_fun(tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool), tc_HOL_Obool), _1455220), c_member(tc_prod(_1455218, _1455220)))), c_Product__Type_OPair(_1455218, _1455220)))), _1455224)), _1455226), _1455228)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1455218, _1455220)), hAPP(hAPP(c_Product__Type_OPair(_1455218, _1455220), _1455226), _1455228)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1455218, _1455220), tc_HOL_Obool)), _1455222), _1455224))))], (6768 ^ _780478) ^ [_892531, _892533, _892535, _892537, _892539, _892541] : [-(_892531 = _892533), -(hAPP(c_Fun_Ofun__upd(_892535, _892537, _892539, _892533, _892541), _892531) = hAPP(_892539, _892531))], (38511 ^ _780478) ^ [_1520988, _1520990, _1520992] : [-(hAPP(c_Relation_ORange(_1520988, _1520990), hAPP(c_Set_OCollect(tc_prod(_1520988, _1520990)), hAPP(c_Product__Type_Oprod_Oprod__case(_1520988, _1520990, tc_HOL_Obool), _1520992))) = hAPP(c_Set_OCollect(_1520990), hAPP(hAPP(c_COMBB(tc_fun(_1520988, tc_HOL_Obool), tc_HOL_Obool, _1520990), c_HOL_OEx(_1520988)), hAPP(c_COMBC(_1520988, _1520990, tc_HOL_Obool), _1520992))))], (29584 ^ _780478) ^ [_1329785, _1329787] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329785, _1329787) = 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), _1329785), _1329787) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5410 ^ _780478) ^ [_863250, _863252] : [_863252 = _863250, -(c_Groups_Oone__class_Oone(_863252) = c_Groups_Oone__class_Oone(_863250))], (26822 ^ _780478) ^ [_1277405, _1277407, _1277409, _1277411] : [class_Fields_Olinordered__field(_1277405), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277405), _1277407), c_Groups_Ozero__class_Ozero(_1277405))), 26829 ^ _780478 : [(26836 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277405), _1277411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277405), _1277409), _1277407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277405), _1277409), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277405), _1277411), _1277407))))], (26830 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277405), _1277409), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277405), _1277411), _1277407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1277405), _1277411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277405), _1277409), _1277407))))]]], (39791 ^ _780478) ^ [_1555389, _1555391, _1555393, _1555395, _1555397, _1555399, _1555401, _1555403, _1555405, _1555407] : [-(c_Product__Type_Omap__pair(_1555389, _1555391, _1555393, _1555395, hAPP(c_Fun_Ocomp(_1555397, _1555391, _1555389, _1555399), _1555401), hAPP(c_Fun_Ocomp(_1555403, _1555395, _1555393, _1555405), _1555407)) = hAPP(c_Fun_Ocomp(tc_prod(_1555397, _1555403), tc_prod(_1555391, _1555395), tc_prod(_1555389, _1555393), c_Product__Type_Omap__pair(_1555397, _1555391, _1555403, _1555395, _1555399, _1555405)), c_Product__Type_Omap__pair(_1555389, _1555397, _1555393, _1555403, _1555401, _1555407)))], (37955 ^ _780478) ^ [_1507563, _1507565, _1507567, _1507569, _1507571, _1507573] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507563, _1507565, _1507567), _1507569), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507565, _1507567), tc_HOL_Obool)), _1507571), _1507573)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1507563, _1507567), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507563, _1507565, _1507567), _1507569), _1507571)), hAPP(hAPP(c_Relation_Orel__comp(_1507563, _1507565, _1507567), _1507569), _1507573)))], (42967 ^ _780478) ^ [_1637717, _1637719] : [-(_1637717 = c_List_Olist_ONil(_1637719)), hBOOL(hAPP(c_List_Odistinct(_1637719), _1637717)), -(hBOOL(hAPP(c_List_Odistinct(_1637719), c_List_Obutlast(_1637719, _1637717))))], (2686 ^ _780478) ^ [_820080, _820082, _820084, _820086, _820088, _820090] : [-(c_Predicate_ORangeP(_820090, _820086, _820082) = c_Predicate_ORangeP(_820088, _820084, _820080)), _820090 = _820088, _820086 = _820084, _820082 = _820080], (39019 ^ _780478) ^ [_1536840, _1536842] : [-(c_Fun_Oinj__on(_1536840, _1536840, c_Fun_Oid(_1536840), _1536842))], (22111 ^ _780478) ^ [_1191483, _1191485, _1191487, _1191489] : [class_Rings_Olinordered__semidom(_1191483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1191485), _1191487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191483), c_Groups_Ozero__class_Ozero(_1191483)), _1191489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191483), _1191489), c_Groups_Oone__class_Oone(_1191483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191483), hAPP(hAPP(c_Power_Opower__class_Opower(_1191483), _1191489), _1191487)), hAPP(hAPP(c_Power_Opower__class_Opower(_1191483), _1191489), _1191485))))], (48561 ^ _780478) ^ [_1760213, _1760215, _1760217, _1760219, _1760221, _1760223] : [-(hAPP(hAPP(c_List_Ozip(_1760213, _1760215), c_List_Oreplicate(_1760213, _1760217, _1760219)), c_List_Oreplicate(_1760215, _1760221, _1760223)) = c_List_Oreplicate(tc_prod(_1760213, _1760215), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1760217), _1760221), hAPP(hAPP(c_Product__Type_OPair(_1760213, _1760215), _1760219), _1760223)))], (6584 ^ _780478) ^ [_888199, _888201, _888203, _888205, _888207, _888209, _888211, _888213] : [c_Finite__Set_Ofolding__image__simple(_888199, _888201, _888203, _888205, _888207, _888209), hBOOL(hAPP(c_Finite__Set_Ofinite(_888201), _888211)), -(hAPP(_888209, hAPP(hAPP(c_Set_Oinsert(_888201), _888213), _888211)) = hAPP(hAPP(_888203, hAPP(_888207, _888213)), hAPP(_888209, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888201, tc_HOL_Obool)), _888211), hAPP(hAPP(c_Set_Oinsert(_888201), _888213), c_Orderings_Obot__class_Obot(tc_fun(_888201, tc_HOL_Obool)))))))], (27571 ^ _780478) ^ [_1290244, _1290246, _1290248] : [class_Rings_Oring__1(_1290244), -(hAPP(c_Int_Oring__1__class_Oof__int(_1290244), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1290246), _1290248)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1290244), hAPP(c_Int_Oring__1__class_Oof__int(_1290244), _1290246)), _1290248))], (36692 ^ _780478) ^ [_1478034, _1478036] : [_1478034 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1478034, _1478036) = 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)))], (23101 ^ _780478) ^ [_1210420, _1210422, _1210424, _1210426, _1210428] : [class_Groups_Oordered__ab__semigroup__add(_1210420), class_Rings_Osemiring__1(_1210420), 23111 ^ _780478 : [(23114 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210420), hAPP(_1210426, 23110 ^ [_1210420, _1210422, _1210424, _1210426, _1210428])), _1210428))], (23112 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1210422), 23110 ^ [_1210420, _1210422, _1210424, _1210426, _1210428]), _1210424)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210420), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1210422, _1210420), _1210426), _1210424)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210420), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210420), hAPP(c_Finite__Set_Ocard(_1210422), _1210424))), _1210428))))], (22769 ^ _780478) ^ [] : [-(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))], (51969 ^ _780478) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (48846 ^ _780478) ^ [_1765934] : [-(c_Lazy__Sequence_Oyieldn(_1765934) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1765934), _1765934, c_Lazy__Sequence_Oyield(_1765934)))], (43109 ^ _780478) ^ [_1640113, _1640115, _1640117, _1640119] : [hAPP(hAPP(c_List_Olist__update(_1640113, _1640115), _1640117), _1640119) = c_List_Olist_ONil(_1640113), -(_1640115 = c_List_Olist_ONil(_1640113))], (48659 ^ _780478) ^ [_1762031, _1762033] : [-(c_List_Oconcat(_1762031, c_List_Oreplicate(tc_List_Olist(_1762031), _1762033, c_List_Olist_ONil(_1762031))) = c_List_Olist_ONil(_1762031))], (37658 ^ _780478) ^ [_1499240, _1499242, _1499244, _1499246] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1499240), _1499242)), 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)), _1499244), _1499240)), 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)), _1499246), _1499242)), 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)), _1499244), _1499246)), _1499242)), c_FunDef_Omax__strict)))], (34595 ^ _780478) ^ [_1432766] : [-(c_Int_Opred(c_Int_OBit0(_1432766)) = c_Int_OBit1(c_Int_Opred(_1432766)))], (8166 ^ _780478) ^ [_920129, _920131, _920133, _920135] : [class_Groups_Ocancel__semigroup__add(_920129), 8169 ^ _780478 : [(8176 ^ _780478) ^ [] : [_920131 = _920135, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920129), _920131), _920133) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920129), _920135), _920133))], (8170 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920129), _920131), _920133) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920129), _920135), _920133), -(_920131 = _920135)]]], (51221 ^ _780478) ^ [_1818455, _1818457, _1818459, _1818461] : [class_Rings_Ocomm__semiring__1(_1818455), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818455), _1818457), _1818459)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818455), _1818457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1818455), _1818461), _1818459))))], (23142 ^ _780478) ^ [_1211289, _1211291] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1211289), _1211291))))], (17432 ^ _780478) ^ [_1103435, _1103437, _1103439, _1103441, _1103443, _1103445, _1103447] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103435, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103437, tc_fun(_1103435, tc_HOL_Obool)), _1103439), _1103441)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103443, tc_fun(_1103435, tc_HOL_Obool)), _1103445), _1103447)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103437, tc_fun(_1103435, tc_HOL_Obool)), _1103439), hAPP(hAPP(c_COMBB(tc_fun(_1103443, tc_fun(_1103435, tc_HOL_Obool)), tc_fun(_1103435, tc_HOL_Obool), _1103437), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103443, tc_fun(_1103435, tc_HOL_Obool)), _1103445)), hAPP(hAPP(c_COMBC(_1103437, tc_fun(_1103443, tc_fun(_1103435, tc_HOL_Obool)), tc_fun(_1103443, tc_fun(_1103435, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1103435, tc_HOL_Obool), tc_fun(_1103435, tc_HOL_Obool)), tc_fun(tc_fun(_1103443, tc_fun(_1103435, tc_HOL_Obool)), tc_fun(_1103443, tc_fun(_1103435, tc_HOL_Obool))), _1103437), c_COMBB(tc_fun(_1103435, tc_HOL_Obool), tc_fun(_1103435, tc_HOL_Obool), _1103443)), hAPP(hAPP(c_COMBB(tc_fun(_1103435, tc_HOL_Obool), tc_fun(tc_fun(_1103435, tc_HOL_Obool), tc_fun(_1103435, tc_HOL_Obool)), _1103437), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103435, tc_HOL_Obool))), _1103441))), _1103447))))], (11743 ^ _780478) ^ [_986374] : [class_Orderings_Oord(_986374), -(c_Orderings_Oord__class_Omin(_986374) = c_Orderings_Oord_Omin(_986374, c_Orderings_Oord__class_Oless__eq(_986374)))], (42858 ^ _780478) ^ [_1635243, _1635245] : [42860 ^ _780478 : [(42864 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42862 ^ [_1635243, _1635245]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635243)), _1635245))))], (42866 ^ _780478) ^ [] : [42859 ^ [_1635243, _1635245] = 42862 ^ [_1635243, _1635245]], (42868 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1635243), _1635245), 42859 ^ [_1635243, _1635245]) = hAPP(hAPP(c_List_Onth(_1635243), _1635245), 42862 ^ [_1635243, _1635245]))], (42861 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42859 ^ [_1635243, _1635245]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635243)), _1635245))))]], -(hBOOL(hAPP(c_List_Odistinct(_1635243), _1635245)))], (45424 ^ _780478) ^ [_1691917, _1691919, _1691921, _1691923, _1691925, _1691927, _1691929] : [c_List_Olist__all2(_1691923, _1691919, hAPP(hAPP(c_COMBB(_1691917, tc_fun(_1691919, tc_HOL_Obool), _1691923), _1691921), _1691925), _1691927, _1691929), -(c_List_Olist__all2(_1691917, _1691919, _1691921, hAPP(hAPP(c_List_Omap(_1691923, _1691917), _1691925), _1691927), _1691929))], (48563 ^ _780478) ^ [_1760306, _1760308, _1760310, _1760312] : [48570 ^ _780478 : [(48573 ^ _780478) ^ [] : [_1760308 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48571 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1760312, _1760310)))]], 48564 ^ _780478 : [(48565 ^ _780478) ^ [_1760378] : [hBOOL(hAPP(hAPP(c_member(_1760306), _1760378), hAPP(c_List_Oset(_1760306), c_List_Oreplicate(_1760306, _1760308, _1760310)))), hBOOL(hAPP(_1760312, _1760378))]]], (28212 ^ _780478) ^ [_1302699] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1302699)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1302699)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1302699), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (28118 ^ _780478) ^ [_1300672, _1300674, _1300676, _1300678] : [class_Groups_Ocomm__monoid__add(_1300672), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1300674), _1300676)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300672), _1300678), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1300674, _1300676)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1300672), hAPP(_1300678, _1300674)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1300672), _1300678), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1300674), _1300676))))], (42662 ^ _780478) ^ [_1630746, _1630748, _1630750, _1630752, _1630754] : [-(hAPP(hAPP(c_List_Olist__update(_1630746, hAPP(hAPP(c_List_Olist__update(_1630746, _1630748), _1630750), _1630752)), _1630750), _1630754) = hAPP(hAPP(c_List_Olist__update(_1630746, _1630748), _1630750), _1630754))], (24571 ^ _780478) ^ [_1236933, _1236935, _1236937, _1236939, _1236941] : [class_Orderings_Olinorder(_1236933), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1236933, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1236933, _1236935, _1236937)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1236933, _1236939, _1236941)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1236933, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1236933), _1236935), _1236939), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1236933), _1236937), _1236941)))], (6011 ^ _780478) ^ [_876147, _876149] : [6012 ^ _780478 : [(6013 ^ _780478) ^ [_876200] : [hBOOL(hAPP(hAPP(c_member(_876147), _876200), _876149))]], _876149 = c_Orderings_Obot__class_Obot(tc_fun(_876147, tc_HOL_Obool))], (170 ^ _780478) ^ [_783205, _783207] : [-(class_Rings_Odivision__ring(_783205)), _783207 = _783205, class_Rings_Odivision__ring(_783207)], (46764 ^ _780478) ^ [_1720960, _1720962, _1720964] : [class_Orderings_Olinorder(_1720960), 46767 ^ _780478 : [(46780 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1720960, hAPP(hAPP(c_List_Olist_OCons(_1720960), _1720962), _1720964))), 46784 ^ _780478 : [(46787 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1720960), _1720962), 46783 ^ [_1720960, _1720962, _1720964]))], (46785 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1720960), 46783 ^ [_1720960, _1720962, _1720964]), hAPP(c_List_Oset(_1720960), _1720964))))]], c_List_Olinorder__class_Osorted(_1720960, _1720964)], (46768 ^ _780478) ^ [] : [c_List_Olinorder__class_Osorted(_1720960, hAPP(hAPP(c_List_Olist_OCons(_1720960), _1720962), _1720964)), 46771 ^ _780478 : [(46772 ^ _780478) ^ [_1721128] : [hBOOL(hAPP(hAPP(c_member(_1720960), _1721128), hAPP(c_List_Oset(_1720960), _1720964))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1720960), _1720962), _1721128)))], (46778 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1720960, _1720964))]]]]], (41027 ^ _780478) ^ [_1585450, _1585452, _1585454, _1585456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585450, _1585452), tc_HOL_Obool)), _1585454), _1585456)), c_Relation_Osingle__valued(_1585450, _1585452, _1585456), -(c_Relation_Osingle__valued(_1585450, _1585452, _1585454))], (34155 ^ _780478) ^ [_1424926, _1424928] : [class_Groups_Omonoid__mult(_1424926), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424926), _1424928), 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(_1424926), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1424926), _1424928), _1424928)), _1424928))], (44837 ^ _780478) ^ [_1678897, _1678899, _1678901, _1678903, _1678905, _1678907] : [-(hAPP(hAPP(c_List_Omap(_1678897, _1678899), _1678901), hAPP(hAPP(c_List_Omap(_1678903, _1678897), _1678905), _1678907)) = hAPP(hAPP(c_List_Omap(_1678903, _1678899), hAPP(c_Fun_Ocomp(_1678897, _1678899, _1678903, _1678901), _1678905)), _1678907))], (9364 ^ _780478) ^ [_940806, _940808, _940810, _940812] : [class_Groups_Oordered__cancel__ab__semigroup__add(_940806), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940806), _940808), _940810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_940806), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940806), _940808), _940812)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_940806), _940810), _940812))))], (4492 ^ _780478) ^ [_848641, _848643] : [_848643 = _848641, -(c_List_Olist_OCons(_848643) = c_List_Olist_OCons(_848641))], (7702 ^ _780478) ^ [_910574, _910576, _910578] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910574, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910574, tc_HOL_Obool)), _910576), _910578)), _910576)))], (45159 ^ _780478) ^ [_1685703, _1685705] : [_1685703 = _1685705, -(hAPP(c_Code__Numeral_Onat__of, _1685703) = hAPP(c_Code__Numeral_Onat__of, _1685705))], (21736 ^ _780478) ^ [_1184101, _1184103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1184101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1184101), hAPP(c_Nat_OSuc, _1184103))), _1184101)))], (40504 ^ _780478) ^ [_1572549, _1572551, _1572553] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572549, _1572549)), hAPP(hAPP(c_Product__Type_OPair(_1572549, _1572549), _1572551), _1572551)), c_Transitive__Closure_Ortrancl(_1572549, _1572553))))], (50393 ^ _780478) ^ [_1800095, _1800097, _1800099, _1800101, _1800103] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1800095, _1800097, tc_HOL_Obool, _1800099), _1800101), _1800103)), -(hBOOL(hAPP(_1800099, hAPP(hAPP(c_Product__Type_OPair(_1800095, _1800097), _1800101), _1800103))))], (13896 ^ _780478) ^ [_1028924, _1028926] : [_1028924 = _1028926, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028924), _1028926)))], (36431 ^ _780478) ^ [_1473634, _1473636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1473634)), 36434 ^ _780478 : [(36441 ^ _780478) ^ [] : [-(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), _1473636), _1473634)))), -(c_Divides_OnegDivAlg(_1473636, _1473634) = hAPP(c_Divides_Oadjust(_1473634), c_Divides_OnegDivAlg(_1473636, 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)))), _1473634))))], (36435 ^ _780478) ^ [] : [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), _1473636), _1473634))), -(c_Divides_OnegDivAlg(_1473636, _1473634) = 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), _1473636), _1473634)))]]], (24223 ^ _780478) ^ [_1231324] : [-(_1231324 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1231324), _1231324) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (28198 ^ _780478) ^ [_1302434, _1302436, _1302438, _1302440] : [class_Orderings_Olinorder(_1302434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302434), _1302436), _1302438)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302434), _1302438), _1302440)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302434, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1302434, _1302436, _1302438)), c_SetInterval_Oord__class_OatLeastAtMost(_1302434, _1302438, _1302440)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1302434, _1302436, _1302440))], (28256 ^ _780478) ^ [_1303566] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1303566))))], (52237 ^ _780478) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (31039 ^ _780478) ^ [_1357726, _1357728] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1357726), _1357728) = 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), _1357726)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1357728)))))], (43837 ^ _780478) ^ [_1657120, _1657122, _1657124, _1657126, _1657128] : [hAPP(hAPP(c_List_Odrop(_1657120), _1657122), _1657124) = hAPP(hAPP(c_List_Olist_OCons(_1657120), _1657126), _1657128), -(hAPP(hAPP(c_List_Onth(_1657120), _1657124), _1657122) = _1657126)], (830 ^ _780478) ^ [_792903, _792905, _792907, _792909] : [-(c_Predicate_Otransp(_792907, _792903)), c_Predicate_Otransp(_792909, _792905), _792909 = _792907, _792905 = _792903], (20540 ^ _780478) ^ [_1163519, _1163521, _1163523, _1163525] : [class_Rings_Olinordered__ring__strict(_1163519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163519), _1163521), _1163523)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163519), _1163525), c_Groups_Ozero__class_Ozero(_1163519))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163519), _1163525), _1163523)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163519), _1163525), _1163521))))], (36355 ^ _780478) ^ [_1472140, _1472142, _1472144, _1472146] : [-(c_HOL_OThe(tc_prod(_1472140, _1472142), hAPP(c_Product__Type_Oprod_Oprod__case(_1472140, _1472142, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1472140, tc_fun(_1472142, tc_HOL_Obool), tc_fun(_1472142, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1472142, tc_HOL_Obool), tc_fun(_1472142, tc_HOL_Obool)), _1472140), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1472142)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1472140), c_fconj), hAPP(c_fequal, _1472144)))), hAPP(c_fequal, _1472146)))) = hAPP(hAPP(c_Product__Type_OPair(_1472140, _1472142), _1472144), _1472146))], (50004 ^ _780478) ^ [_1791264, _1791266, _1791268, _1791270, _1791272] : [c_Fun_Oinj__on(_1791264, _1791266, _1791268, c_Orderings_Otop__class_Otop(tc_fun(_1791264, tc_HOL_Obool))), hAPP(_1791268, _1791270) = _1791272, -(hAPP(c_Hilbert__Choice_Oinv__into(_1791264, _1791266, c_Orderings_Otop__class_Otop(tc_fun(_1791264, tc_HOL_Obool)), _1791268), _1791272) = _1791270)], (28600 ^ _780478) ^ [_1310035, _1310037, _1310039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310035)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1310037), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1310039)), 28607 ^ _780478 : [(28608 ^ _780478) ^ [_1310243] : [28610 ^ _780478 : [(28616 ^ _780478) ^ [] : [-(_1310243 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28612 ^ [_1310035, _1310037, _1310039, _1310243]), 28609 ^ [_1310035, _1310037, _1310039, _1310243]))], (28614 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28612 ^ [_1310035, _1310037, _1310039, _1310243]), _1310039)))], (28611 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28609 ^ [_1310035, _1310037, _1310039, _1310243]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1310035))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1310037), _1310243)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1310037), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1310243), _1310035))))]]], (13314 ^ _780478) ^ [_1017347, _1017349, _1017351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017347, tc_HOL_Obool)), _1017349), _1017351)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017347, tc_HOL_Obool)), _1017349), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1017347, tc_HOL_Obool)), _1017351), _1017349)) = _1017351)], (19128 ^ _780478) ^ [_1139668, _1139670] : [class_Power_Opower(_1139668), class_Rings_Osemiring__0(_1139668), 19135 ^ _780478 : [(19142 ^ _780478) ^ [] : [-(_1139670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1139668), c_Groups_Ozero__class_Ozero(_1139668)), _1139670) = c_Groups_Ozero__class_Ozero(_1139668))], (19136 ^ _780478) ^ [] : [_1139670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1139668), c_Groups_Ozero__class_Ozero(_1139668)), _1139670) = c_Groups_Oone__class_Oone(_1139668))]]], (6500 ^ _780478) ^ [_886505, _886507, _886509, _886511] : [hBOOL(hAPP(hAPP(c_member(_886505), _886507), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886505, tc_HOL_Obool)), _886509), _886511))), 6503 ^ _780478 : [(6506 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_886505), _886507), _886511))], (6504 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886505), _886507), _886509)))]]], (34865 ^ _780478) ^ [_1437670, _1437672, _1437674] : [class_Rings_Olinordered__semidom(_1437670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437670), hAPP(hAPP(c_Power_Opower__class_Opower(_1437670), _1437672), 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(_1437670), _1437674), 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(_1437670), c_Groups_Ozero__class_Ozero(_1437670)), _1437674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437670), _1437672), _1437674)))], (21077 ^ _780478) ^ [_1172401] : [-(hAPP(c_Finite__Set_Ocard(_1172401), c_Orderings_Obot__class_Obot(tc_fun(_1172401, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2036 ^ _780478) ^ [_810039, _810041, _810043, _810045, _810047, _810049] : [-(c_Finite__Set_Ofold1Set(_810049, _810045, _810041) = c_Finite__Set_Ofold1Set(_810047, _810043, _810039)), _810049 = _810047, _810045 = _810043, _810041 = _810039], (40875 ^ _780478) ^ [_1580981, _1580983] : [-(hAPP(c_Relation_OField(_1580981), hAPP(c_Relation_Oconverse(_1580981, _1580981), _1580983)) = hAPP(c_Relation_OField(_1580981), _1580983))], (22329 ^ _780478) ^ [_1195777, _1195779, _1195781] : [-(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), _1195777)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1195779))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195781))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195781), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195777), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195777), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1195781), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1195779)))))], (26578 ^ _780478) ^ [_1272843, _1272845, _1272847, _1272849, _1272851] : [class_Fields_Olinordered__field(_1272843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272843), c_Groups_Ozero__class_Ozero(_1272843)), _1272845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272843), _1272845), _1272847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272843), c_Groups_Ozero__class_Ozero(_1272843)), _1272849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272843), _1272849), _1272851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272843), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272843), _1272845), _1272851)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272843), _1272847), _1272849))))], (10805 ^ _780478) ^ [_968923, _968925, _968927, _968929] : [class_Orderings_Olinorder(_968923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968923), _968925), _968927)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_968923), _968925), hAPP(hAPP(c_Orderings_Oord__class_Omax(_968923), _968929), _968927))))], (34941 ^ _780478) ^ [_1438949, _1438951] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1438949), hAPP(c_Int_Onumber__class_Onumber__of(_1438949), _1438951)), 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(_1438949), hAPP(c_Int_Onumber__class_Onumber__of(_1438949), _1438951)), hAPP(c_Int_Onumber__class_Onumber__of(_1438949), _1438951))), class_Groups_Omonoid__mult(_1438949), class_Int_Onumber(_1438949)], (22741 ^ _780478) ^ [_1203852, _1203854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203852)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203854))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1203852), _1203854)))], (37275 ^ _780478) ^ [_1489731, _1489733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489731), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1489733), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1489731), _1489733) = 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), _1489731), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489733)))))], (22959 ^ _780478) ^ [_1207799] : [class_Rings_Oring__1(_1207799), -(hBOOL(hAPP(hAPP(c_member(_1207799), c_Groups_Oone__class_Oone(_1207799)), c_Int_Oring__1__class_OInts(_1207799))))], (22614 ^ _780478) ^ [_1201600, _1201602] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201600), _1201602) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201602), _1201600))], (43411 ^ _780478) ^ [_1646828, _1646830, _1646832, _1646834] : [-(hAPP(hAPP(c_List_Oappend(_1646828), hAPP(hAPP(c_List_Olist_OCons(_1646828), _1646830), _1646832)), _1646834) = hAPP(hAPP(c_List_Olist_OCons(_1646828), _1646830), hAPP(hAPP(c_List_Oappend(_1646828), _1646832), _1646834)))], (8619 ^ _780478) ^ [_929723, _929725, _929727, _929729, _929731, _929733, _929735] : [c_Big__Operators_Ocomm__monoid__big(_929723, _929725, _929727, _929729, _929731), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_929725), _929733))), -(hAPP(hAPP(_929731, _929735), _929733) = _929729)], (44251 ^ _780478) ^ [_1666249, _1666251] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666249), _1666251) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44254 ^ _780478 : [(44257 ^ _780478) ^ [_1666363] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1666363), hAPP(c_List_Oset(tc_Nat_Onat), _1666251))), -(_1666363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44255 ^ _780478) ^ [] : [-(_1666249 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (34775 ^ _780478) ^ [_1436067] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1436067), 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, _1436067)))], (14597 ^ _780478) ^ [_1041445, _1041447, _1041449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041445), _1041447)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041449), _1041447)), _1041445) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041449), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041447), _1041445)))], (33202 ^ _780478) ^ [_1407776, _1407778] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407776))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407776), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407778)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36401 ^ _780478) ^ [_1473178, _1473180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1473178), 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)), _1473180)), -(c_Divides_OnegDivAlg(_1473178, _1473180) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1473178), _1473180)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1473178, _1473180)))], (16627 ^ _780478) ^ [_1084296, _1084298, _1084300, _1084302, _1084304] : [class_Groups_Ocomm__monoid__add(_1084296), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084298), _1084300)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084298), _1084302)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1084296), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084298, _1084296), _1084304), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1084298, tc_HOL_Obool)), _1084300), _1084302))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084298, _1084296), _1084304), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1084298, tc_HOL_Obool)), _1084300), _1084302))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1084296), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084298, _1084296), _1084304), _1084300)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084298, _1084296), _1084304), _1084302)))], (9868 ^ _780478) ^ [_951548, _951550, _951552, _951554] : [class_Rings_Ocomm__semiring__1(_951548), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951548), _951550), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951548), _951552), _951554)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951548), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951548), _951550), _951552)), _951554))], (46286 ^ _780478) ^ [_1712199, _1712201] : [46287 ^ _780478 : [(46290 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712201), _1712199))], (46288 ^ _780478) ^ [] : [_1712201 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1712199, _1712201) = c_List_Olist_ONil(tc_Nat_Onat))], (37736 ^ _780478) ^ [_1500778, _1500780] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1500778, _1500778)), _1500780)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1500778), hAPP(c_Relation_OField(_1500778), _1500780))))], (770 ^ _780478) ^ [_792055, _792057, _792059, _792061, _792063, _792065] : [-(c_Equiv__Relations_Oequiv(_792063, _792059, _792055)), c_Equiv__Relations_Oequiv(_792065, _792061, _792057), _792065 = _792063, _792061 = _792059, _792057 = _792055], (52259 ^ 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hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943933, _943931), _943935), _943937)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943939, _943931), _943941), _943943)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943933, _943931), hAPP(hAPP(c_COMBC(_943933, tc_fun(_943939, tc_HOL_Obool), _943931), hAPP(hAPP(c_COMBB(tc_fun(_943939, _943931), tc_fun(tc_fun(_943939, tc_HOL_Obool), _943931), _943933), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_943939, _943931)), hAPP(hAPP(c_COMBC(_943933, tc_fun(_943939, _943931), tc_fun(_943939, _943931)), hAPP(hAPP(c_COMBB(tc_fun(_943931, _943931), tc_fun(tc_fun(_943939, _943931), tc_fun(_943939, _943931)), _943933), c_COMBB(_943931, _943931, _943939)), hAPP(hAPP(c_COMBB(_943931, tc_fun(_943931, _943931), _943933), c_Groups_Otimes__class_Otimes(_943931)), _943935))), _943941))), _943943)), _943937))], (28302 ^ _780478) ^ [_1304322, _1304324] : [class_Orderings_Oorder(_1304322), 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hAPP(hAPP(c_COMBC(_1534836, tc_fun(_1534838, tc_HOL_Obool), tc_fun(_1534838, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1534838, tc_HOL_Obool), tc_fun(_1534838, tc_HOL_Obool)), _1534836), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1534838)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1534836), c_fconj), hAPP(hAPP(c_COMBC(_1534836, tc_fun(_1534836, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534836)), _1534844)))), hAPP(hAPP(c_COMBC(_1534838, tc_fun(_1534838, tc_HOL_Obool), tc_HOL_Obool), c_member(_1534838)), _1534846))))))))], (28918 ^ _780478) ^ [_1316168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1316168)), 28922 ^ _780478 : [(28925 ^ _780478) ^ [] : [-(_1316168 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 28921 ^ [_1316168]))], (28923 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 28921 ^ [_1316168])))]]], (3470 ^ _780478) ^ [_832270, _832272, _832274, _832276] : [-(c_Random_Oselect__weight(_832276, _832272) = c_Random_Oselect__weight(_832274, _832270)), _832276 = _832274, _832272 = _832270], (41708 ^ _780478) ^ [_1602596, _1602598] : [-(c_List_Olenlex(_1602596, _1602598) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1602596), tc_List_Olist(_1602596))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1602596), tc_List_Olist(_1602596), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1602596), tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602596), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool)), tc_List_Olist(_1602596)), c_COMBS(tc_List_Olist(_1602596), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602596), 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hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602596), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool)), tc_List_Olist(_1602596)), c_COMBS(tc_List_Olist(_1602596), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602596), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1602596)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1602596)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1602596), tc_fun(tc_List_Olist(_1602596), tc_Nat_Onat), tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1602596), tc_Nat_Onat), tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool)), tc_List_Olist(_1602596)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1602596))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1602596)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1602596))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1602596)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1602596), tc_fun(tc_prod(tc_List_Olist(_1602596), tc_List_Olist(_1602596)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602596), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1602596), tc_List_Olist(_1602596)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1602596), tc_List_Olist(_1602596)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1602596), tc_HOL_Obool)), tc_List_Olist(_1602596)), c_COMBC(tc_List_Olist(_1602596), tc_fun(tc_prod(tc_List_Olist(_1602596), tc_List_Olist(_1602596)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1602596), tc_prod(tc_List_Olist(_1602596), tc_List_Olist(_1602596))), tc_fun(tc_List_Olist(_1602596), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1602596), tc_List_Olist(_1602596)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1602596)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1602596), tc_List_Olist(_1602596)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1602596), tc_List_Olist(_1602596)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1602596)), c_member(tc_prod(tc_List_Olist(_1602596), tc_List_Olist(_1602596))))), c_Product__Type_OPair(tc_List_Olist(_1602596), tc_List_Olist(_1602596))))), c_List_Olex(_1602596, _1602598)))))))], (48485 ^ _780478) ^ [_1758141, _1758143, _1758145, _1758147, _1758149] : [hBOOL(hAPP(hAPP(_1758145, _1758149), _1758147)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1758141, _1758143, _1758145), _1758147), _1758149)))], (45924 ^ _780478) ^ [_1702473, _1702475] : [45926 ^ _780478 : [(45929 ^ _780478) ^ [] : [45925 ^ [_1702473, _1702475] = c_List_Olist_ONil(_1702473)], (45927 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1702473)), 45925 ^ [_1702473, _1702475]), hAPP(c_List_Oset(tc_List_Olist(_1702473)), _1702475))))]], -(c_List_Olist_ONil(_1702473) = c_List_Oconcat(_1702473, _1702475))], (28356 ^ _780478) ^ [_1305253, _1305255, _1305257] : [class_Orderings_Oorder(_1305253), 28359 ^ _780478 : [(28366 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305253), _1305257), _1305255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305253, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1305253), _1305255)), hAPP(c_SetInterval_Oord__class_OatLeast(_1305253), _1305257))))], (28360 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1305253, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1305253), _1305255)), hAPP(c_SetInterval_Oord__class_OatLeast(_1305253), _1305257))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305253), _1305257), _1305255)))]]], (37589 ^ _780478) ^ [_1497752, _1497754, _1497756, _1497758, _1497760, _1497762, _1497764] : [-(hAPP(c_Product__Type_Oapfst(_1497752, _1497754, _1497756, _1497758), hAPP(c_Product__Type_Oapsnd(_1497760, _1497756, _1497752, _1497762), _1497764)) = hAPP(hAPP(c_Product__Type_OPair(_1497754, _1497756), hAPP(_1497758, hAPP(c_Product__Type_Ofst(_1497752, _1497760), _1497764))), hAPP(_1497762, hAPP(c_Product__Type_Osnd(_1497752, _1497760), _1497764))))], (51945 ^ _780478) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (15908 ^ _780478) ^ [_1068268, _1068270, _1068272] : [class_Lattices_Osemilattice__inf(_1068268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068268), _1068270), _1068272)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068268), _1068272), _1068270) = _1068270)], (45845 ^ _780478) ^ [_1700907, _1700909] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700907)), c_List_Oremdups(_1700907, c_List_Oconcat(_1700907, _1700909))) = hAPP(c_Finite__Set_Ocard(_1700907), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1700907), tc_fun(_1700907, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1700907)), _1700909)), c_List_Oset(_1700907))))], (28074 ^ _780478) ^ [_1299772, _1299774, _1299776, _1299778] : [class_Orderings_Olinorder(_1299772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299772), _1299774), _1299776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299772), _1299776), _1299778)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1299772, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1299772, _1299774, _1299776)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1299772, _1299776, _1299778)) = c_SetInterval_Oord__class_OatLeastAtMost(_1299772, _1299774, _1299778))], (47385 ^ _780478) ^ [_1733969, _1733971, _1733973] : [hBOOL(hAPP(c_List_Odistinct(_1733969), _1733971)), -(hBOOL(hAPP(c_List_Odistinct(_1733969), c_List_OdropWhile(_1733969, _1733973, _1733971))))], (24711 ^ _780478) ^ [_1239630, _1239632, _1239634, _1239636] : [class_Orderings_Olinorder(_1239630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1239630), _1239632), _1239634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1239630), _1239634), _1239636)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1239630, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1239630, _1239632, _1239634)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1239630, _1239634), _1239636)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1239630, _1239632, _1239636))], (15759 ^ _780478) ^ [_1065401, _1065403, _1065405, _1065407] : [class_Lattices_Osemilattice__inf(_1065401), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065401), _1065403), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065401), _1065405), _1065407)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065401), _1065405), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065401), _1065403), _1065407)))], (49738 ^ _780478) ^ [_1786468, _1786470] : [c_Relation_Osym(_1786468, _1786470), -(hAPP(c_Relation_Oconverse(_1786468, _1786468), _1786470) = _1786470)], (51881 ^ _780478) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (16296 ^ _780478) ^ [_1076701, _1076703, _1076705] : [class_Lattices_Oboolean__algebra(_1076701), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1076701), _1076703), _1076705) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076701), _1076703), hAPP(c_Groups_Ouminus__class_Ouminus(_1076701), _1076705)))], (33316 ^ _780478) ^ [_1409755] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1409755) = c_Int_OPls)], (10713 ^ _780478) ^ [_967366, _967368, _967370, _967372] : [class_Orderings_Olinorder(_967366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967366), _967368), _967370)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967366), hAPP(hAPP(c_Orderings_Oord__class_Omin(_967366), _967372), _967368)), _967370)))], (46240 ^ _780478) ^ [_1711484, _1711486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711484), _1711486)), -(c_List_Oupt(_1711484, hAPP(c_Nat_OSuc, _1711486)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1711484, _1711486)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1711486), c_List_Olist_ONil(tc_Nat_Onat))))], (41945 ^ _780478) ^ [_1610711, _1610713, _1610715] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610711), tc_List_Olist(_1610711))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610711), tc_List_Olist(_1610711)), _1610713), _1610713)), c_List_Olistrel(_1610711, c_Transitive__Closure_Ortrancl(_1610711, _1610715)))))], (15735 ^ _780478) ^ [_1064865, _1064867, _1064869] : [class_Lattices_Olattice(_1064865), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064865), _1064867), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064865), _1064867), _1064869)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064865), _1064867), _1064869))], (41269 ^ _780478) ^ [_1591154, _1591156, _1591158, _1591160, _1591162, _1591164] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591154, _1591154)), hAPP(hAPP(c_Product__Type_OPair(_1591154, _1591154), _1591156), _1591158)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591154, _1591154), tc_HOL_Obool), _1591160), _1591162))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591154, _1591154)), hAPP(hAPP(c_Product__Type_OPair(_1591154, _1591154), _1591158), _1591164)), _1591162)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591154, _1591154)), hAPP(hAPP(c_Product__Type_OPair(_1591154, _1591154), _1591156), _1591164)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1591154, _1591154), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1591160)), _1591162))))], (46121 ^ _780478) ^ [_1707600, _1707602, _1707604, _1707606] : [-(c_List_Otranspose(_1707600, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707602), tc_List_Olist(_1707600)), hAPP(c_List_Omap(_1707602, _1707600), _1707604)), _1707606)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1707602), tc_List_Olist(_1707600)), hAPP(c_List_Omap(_1707602, _1707600), _1707604)), c_List_Otranspose(_1707602, _1707606)))], (38523 ^ _780478) ^ [_1521326, _1521328, _1521330] : [-(hAPP(c_Relation_ORange(_1521326, _1521328), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1521326, _1521328), tc_HOL_Obool), _1521330)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1521326, _1521328), tc_HOL_Obool), tc_fun(_1521328, tc_HOL_Obool)), _1521330), c_Relation_ORange(_1521326, _1521328)))], (14014 ^ _780478) ^ [_1031054, _1031056, _1031058] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031054), _1031056)), _1031058) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031054), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031056), _1031058)))], (12826 ^ _780478) ^ [_1007781, _1007783, _1007785] : [class_Lattices_Osemilattice__sup(_1007781), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007781), _1007783), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007781), _1007783), _1007785))))], (7932 ^ _780478) ^ [_915194, _915196, _915198, _915200] : [-(_915194 = c_Orderings_Obot__class_Obot(tc_fun(_915196, tc_HOL_Obool))), 7935 ^ _780478 : [(7936 ^ _780478) ^ [] : [-(hAPP(c_Set_Oimage(_915198, _915196, 7943 ^ [_915194, _915196, _915198, _915200]), _915200) = _915194), 7937 ^ _780478 : [(7938 ^ _780478) ^ [_915335] : [c_Fun_Oinj__on(_915196, _915198, _915335, _915194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915198, tc_HOL_Obool)), hAPP(c_Set_Oimage(_915196, _915198, _915335), _915194)), _915200))]]], (7947 ^ _780478) ^ [] : [7948 ^ _780478 : [(7949 ^ _780478) ^ [_915527] : [hAPP(c_Set_Oimage(_915198, _915196, _915527), _915200) = _915194]], 7951 ^ _780478 : [(7954 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915198, tc_HOL_Obool)), hAPP(c_Set_Oimage(_915196, _915198, 7950 ^ [_915194, _915196, _915198, _915200]), _915194)), _915200)))], (7952 ^ _780478) ^ [] : [-(c_Fun_Oinj__on(_915196, _915198, 7950 ^ [_915194, _915196, _915198, _915200], _915194))]]]]], (43171 ^ _780478) ^ [_1641239, _1641241] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641239), tc_List_Olist(_1641239))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641239), tc_List_Olist(_1641239)), c_List_Olist_ONil(_1641239)), c_List_Olist_ONil(_1641239))), c_List_Olistrel(_1641239, _1641241))))], (22357 ^ _780478) ^ [_1196230] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1196230)) = 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), _1196230))))], (15439 ^ _780478) ^ [_1058617, _1058619, _1058621, _1058623] : [class_Groups_Omonoid__mult(_1058617), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1058617), _1058619), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1058621), _1058623)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058617), hAPP(hAPP(c_Power_Opower__class_Opower(_1058617), _1058619), _1058621)), hAPP(hAPP(c_Power_Opower__class_Opower(_1058617), _1058619), _1058623)))], (49104 ^ _780478) ^ [_1771612, _1771614, _1771616] : [49106 ^ _780478 : [(49109 ^ _780478) ^ [] : [hBOOL(hAPP(_1771612, 49105 ^ [_1771612, _1771614, _1771616]))], (49107 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 49105 ^ [_1771612, _1771614, _1771616]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1771614, _1771616))))]], -(c_List_Oall__interval__int(_1771612, _1771614, _1771616))], (50309 ^ _780478) ^ [_1798219, _1798221, _1798223] : [c_Fun_Obij__betw(_1798219, _1798221, _1798223, c_Orderings_Otop__class_Otop(tc_fun(_1798219, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1798221, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1798221, _1798219, c_Hilbert__Choice_Oinv__into(_1798219, _1798221, c_Orderings_Otop__class_Otop(tc_fun(_1798219, tc_HOL_Obool)), _1798223), c_Orderings_Otop__class_Otop(tc_fun(_1798221, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1798219, tc_HOL_Obool))))], (48891 ^ _780478) ^ [_1766893, _1766895] : [hBOOL(hAPP(hAPP(c_List_Omember(_1766893), c_List_Olist_ONil(_1766893)), _1766895))], (1474 ^ _780478) ^ [_801767, _801769] : [-(class_Finite__Set_Ofinite(_801767)), _801769 = _801767, class_Finite__Set_Ofinite(_801769)], (44119 ^ _780478) ^ [_1663472, _1663474] : [hBOOL(hAPP(c_List_Odistinct(_1663472), _1663474)), -(hBOOL(hAPP(c_List_Odistinct(_1663472), hAPP(c_List_Otl(_1663472), _1663474))))], (16641 ^ _780478) ^ [_1084657, _1084659, _1084661, _1084663, _1084665] : [c_Fun_Oinj__on(_1084657, _1084659, _1084661, c_Orderings_Otop__class_Otop(tc_fun(_1084657, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084659, tc_HOL_Obool)), _1084663), hAPP(c_Set_Oimage(_1084657, _1084659, _1084661), _1084665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084657, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1084657, _1084659, _1084661), _1084663)), _1084665)))], (30673 ^ _780478) ^ [_1350011, _1350013, _1350015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1350011, tc_HOL_Obool), tc_HOL_Obool)), _1350013), _1350015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350011, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350011, tc_HOL_Obool), _1350013)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350011, tc_HOL_Obool), _1350015))))], (30314 ^ _780478) ^ [_1342881, _1342883, _1342885] : [class_Rings_Olinordered__idom(_1342881), -(hAPP(c_Groups_Oabs__class_Oabs(_1342881), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342881), _1342883), _1342885)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1342881), hAPP(c_Groups_Oabs__class_Oabs(_1342881), _1342883)), hAPP(c_Groups_Oabs__class_Oabs(_1342881), _1342885)))], (29975 ^ _780478) ^ [_1336686, _1336688] : [29976 ^ _780478 : [(29977 ^ _780478) ^ [_1336735] : [_1336686 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1336688), _1336735)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336686, _1336688) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2070 ^ _780478) ^ [_810558, _810560, _810562, _810564, _810566, _810568] : [-(c_SetInterval_Oord_OatMost(_810568, _810564, _810560) = c_SetInterval_Oord_OatMost(_810566, _810562, _810558)), _810568 = _810566, _810564 = _810562, _810560 = _810558], (18357 ^ _780478) ^ [_1123868, _1123870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123868), _1123870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123868)), _1123870)))], (24811 ^ _780478) ^ [_1241440, _1241442] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241440)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241442)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1241440), _1241442)))], (42558 ^ _780478) ^ [_1628586, _1628588] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1628586, _1628588) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1628586, _1628588)))], (25529 ^ _780478) ^ [_1254482, _1254484, _1254486] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1254482), _1254484), _1254486) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1254482), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1254482, tc_Int_Oint), _1254484), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254486))), class_Groups_Ocomm__monoid__add(_1254482), class_Groups_Ocomm__monoid__mult(_1254482)], (19678 ^ _780478) ^ [_1147769, _1147771, _1147773, _1147775] : [class_Rings_Olinordered__semidom(_1147769), hAPP(hAPP(c_Power_Opower__class_Opower(_1147769), _1147771), _1147773) = hAPP(hAPP(c_Power_Opower__class_Opower(_1147769), _1147775), _1147773), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147769), c_Groups_Ozero__class_Ozero(_1147769)), _1147771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147769), c_Groups_Ozero__class_Ozero(_1147769)), _1147775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147773)), -(_1147771 = _1147775)], (46092 ^ _780478) ^ [_1706997, _1706999, _1707001] : [46094 ^ _780478 : [(46097 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1706999, 46093 ^ [_1706997, _1706999, _1707001])))], (46095 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1706997), 46093 ^ [_1706997, _1706999, _1707001]), hAPP(c_List_Oset(_1706997), _1707001))))]], -(hAPP(c_List_Ofilter(_1706997, _1706999), _1707001) = c_List_Olist_ONil(_1706997))], (44540 ^ _780478) ^ [_1672121, _1672123, _1672125] : [_1672121 = c_List_Olist_ONil(_1672123), -(c_List_Olast(_1672123, hAPP(hAPP(c_List_Olist_OCons(_1672123), _1672125), _1672121)) = _1672125)], (18528 ^ _780478) ^ [_1127685, _1127687, _1127689, _1127691, _1127693] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127685, tc_fun(_1127687, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1127685), _1127689), _1127691)), _1127693) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127687, tc_HOL_Obool)), hAPP(_1127693, _1127689)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127685, tc_fun(_1127687, tc_HOL_Obool)), _1127691), _1127693)))], (50082 ^ _780478) ^ [_1792899, _1792901, _1792903] : [hAPP(c_Set_Oimage(_1792899, _1792901, _1792903), c_Orderings_Otop__class_Otop(tc_fun(_1792899, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792901, tc_HOL_Obool)), 50085 ^ _780478 : [(50086 ^ _780478) ^ [_1793010] : [-(hAPP(_1792903, hAPP(c_Hilbert__Choice_Oinv__into(_1792899, _1792901, c_Orderings_Otop__class_Otop(tc_fun(_1792899, tc_HOL_Obool)), _1792903), _1793010)) = _1793010)]]], (18071 ^ _780478) ^ [_1116804, _1116806, _1116808] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1116804, tc_HOL_Obool)), _1116806), _1116808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1116804, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116804, tc_HOL_Obool), _1116808)), _1116806)))], (15577 ^ _780478) ^ [_1061704, _1061706, _1061708, _1061710] : [hBOOL(hAPP(_1061704, _1061706)), hBOOL(hAPP(_1061708, _1061706)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1061710, tc_HOL_Obool)), _1061704), _1061708), _1061706)))], (27926 ^ _780478) ^ [_1296915, _1296917, _1296919] : [class_Orderings_Oorder(_1296915), _1296917 = _1296919, -(c_SetInterval_Oord__class_OatLeastAtMost(_1296915, _1296917, _1296919) = hAPP(hAPP(c_Set_Oinsert(_1296915), _1296917), c_Orderings_Obot__class_Obot(tc_fun(_1296915, tc_HOL_Obool))))], (25019 ^ _780478) ^ [_1245215, _1245217, _1245219, _1245221] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1245215, _1245217)), c_Sum__Type_OPlus(_1245215, _1245217, _1245219, _1245221)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245215), _1245219)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245217), _1245221))], (48231 ^ _780478) ^ [_1752682, _1752684, _1752686] : [c_FunDef_Ois__measure(_1752682, _1752684), -(c_FunDef_Ois__measure(tc_prod(_1752686, _1752682), hAPP(hAPP(c_COMBB(_1752682, tc_Nat_Onat, tc_prod(_1752686, _1752682)), _1752684), c_Product__Type_Osnd(_1752686, _1752682))))], (16356 ^ _780478) ^ [_1077933, _1077935, _1077937, _1077939] : [hBOOL(hAPP(hAPP(c_member(_1077933), _1077935), _1077937)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077933, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1077933), _1077935), _1077939)), _1077937) = hAPP(hAPP(c_Set_Oinsert(_1077933), _1077935), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077933, tc_HOL_Obool)), _1077939), _1077937)))], (52253 ^ _780478) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (43051 ^ _780478) ^ [_1639073, _1639075] : [-(c_List_Olistrelp(_1639073, _1639075, c_List_Olist_ONil(_1639073), c_List_Olist_ONil(_1639073)))], (50221 ^ _780478) ^ [_1796600] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1796600), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1796600 = hAPP(c_Code__Numeral_Onat__of, 50224 ^ [_1796600]))], (33356 ^ _780478) ^ [_1410304, _1410306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1410304)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1410306)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410304)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1410306), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1410304))))], (12484 ^ _780478) ^ [_1000798, _1000800] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1000798, tc_HOL_Obool)), _1000800)))], (30847 ^ _780478) ^ [_1353401] : [class_Complete__Lattice_Ocomplete__lattice(_1353401), -(c_Complete__Lattice_OSup__class_OSup(_1353401, c_Orderings_Otop__class_Otop(tc_fun(_1353401, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1353401))], (1544 ^ _780478) ^ [_802642, _802644] : [-(class_Groups_Oordered__ab__semigroup__add(_802642)), _802644 = _802642, class_Groups_Oordered__ab__semigroup__add(_802644)], (51991 ^ _780478) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (50897 ^ _780478) ^ [_1812134, _1812136, _1812138] : [c_List_Oall__interval__nat(_1812134, _1812136, _1812138), 50900 ^ _780478 : [(50901 ^ _780478) ^ [_1812214] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1812214), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1812136), _1812138))), -(hBOOL(hAPP(_1812134, _1812214)))]]], (434 ^ _780478) ^ [_787027, _787029, _787031, _787033, _787035, _787037] : [-(c_Nitpick_Oless__frac(_787035, _787031, _787027)), c_Nitpick_Oless__frac(_787037, _787033, _787029), _787037 = _787035, _787033 = _787031, _787029 = _787027], (47554 ^ _780478) ^ [_1737608, _1737610, _1737612] : [-(hBOOL(hAPP(hAPP(c_member(_1737608), _1737610), hAPP(c_List_Oset(_1737608), _1737612)))), -(c_List_Oinsert(_1737608, _1737610, _1737612) = hAPP(hAPP(c_List_Olist_OCons(_1737608), _1737610), _1737612))], (46943 ^ _780478) ^ [_1724690, _1724692] : [_1724692 = c_List_Olist_ONil(_1724690), -(hAPP(c_List_Orev(_1724690), _1724692) = c_List_Olist_ONil(_1724690))], (3176 ^ _780478) ^ [_827673, _827675, _827677, _827679] : [-(c_Big__Operators_Olinorder__class_OMin(_827679, _827675) = c_Big__Operators_Olinorder__class_OMin(_827677, _827673)), _827679 = _827677, _827675 = _827673], (10293 ^ _780478) ^ [_959969, _959971, _959973] : [class_Orderings_Olinorder(_959969), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_959969), _959971), hAPP(hAPP(c_Orderings_Oord__class_Omin(_959969), _959971), _959973)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_959969), _959971), _959973))], (16699 ^ _780478) ^ [_1086116, _1086118, _1086120] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1086116), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086116, tc_HOL_Obool)), _1086118), _1086120))), -(hAPP(c_Finite__Set_Ocard(_1086116), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1086116, tc_HOL_Obool)), _1086118), _1086120)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1086116), _1086118)), hAPP(c_Finite__Set_Ocard(_1086116), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086116, tc_HOL_Obool)), _1086118), _1086120))))], (18440 ^ _780478) ^ [_1125627, _1125629, _1125631, _1125633] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125627, tc_fun(_1125629, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1125627, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1125629, tc_HOL_Obool), tc_fun(_1125629, tc_HOL_Obool), _1125627), hAPP(c_COMBC(_1125629, tc_fun(_1125629, tc_HOL_Obool), tc_HOL_Obool), c_member(_1125629))), _1125631)), _1125633)), -(hBOOL(hAPP(hAPP(c_member(_1125629), _1125633), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125627, tc_fun(_1125629, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1125627, tc_HOL_Obool))), _1125631))))], (48204 ^ _780478) ^ [_1752150, _1752152] : [-(c_FunDef_Ois__measure(_1752150, _1752152))], (44348 ^ _780478) ^ [_1668298, _1668300, _1668302] : [class_Orderings_Olinorder(_1668298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1668298), _1668300)), -(c_List_Olinorder__class_Osorted__list__of__set(_1668298, hAPP(hAPP(c_Set_Oinsert(_1668298), _1668302), _1668300)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1668298, _1668298, c_COMBI(_1668298)), _1668302), c_List_Olinorder__class_Osorted__list__of__set(_1668298, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1668298, tc_HOL_Obool)), _1668300), hAPP(hAPP(c_Set_Oinsert(_1668298), _1668302), c_Orderings_Obot__class_Obot(tc_fun(_1668298, tc_HOL_Obool)))))))], (14805 ^ _780478) ^ [_1045812, _1045814, _1045816, _1045818, _1045820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045812), _1045814)), 14808 ^ _780478 : [(14815 ^ _780478) ^ [] : [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), _1045814), _1045812)), _1045816)), _1045818)), _1045820)), -(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), _1045814), _1045816)), _1045818)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045812), _1045816)), _1045820))))], (14809 ^ _780478) ^ [] : [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), _1045814), _1045816)), _1045818)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045812), _1045816)), _1045820))), -(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), _1045814), _1045812)), _1045816)), _1045818)), _1045820)))]]], (21041 ^ _780478) ^ [_1171863, _1171865] : [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), _1171863), _1171865))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171863))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171865)))], (18472 ^ _780478) ^ [_1126470, _1126472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126470), _1126472)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126472)), _1126470) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1126472), _1126470)))], (40189 ^ _780478) ^ [_1564733, _1564735, _1564737, _1564739, _1564741] : [c_Finite__Set_Ofolding__idem(_1564733, _1564735, _1564737, _1564739), -(hAPP(c_Fun_Ocomp(_1564735, _1564735, _1564735, hAPP(_1564737, _1564741)), hAPP(_1564737, _1564741)) = hAPP(_1564737, _1564741))], (45315 ^ _780478) ^ [_1688885, _1688887, _1688889, _1688891] : [hBOOL(hAPP(c_List_Olistsp(_1688885, _1688887), hAPP(hAPP(c_List_Olist_OCons(_1688885), _1688889), _1688891))), 45318 ^ _780478 : [(45321 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1688885, _1688887), _1688891)))], (45319 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1688887, _1688889)))]]], (34367 ^ _780478) ^ [_1428797] : [c_Int_OPls = c_Int_OBit0(_1428797), -(c_Int_OPls = _1428797)], (12844 ^ _780478) ^ [_1008102, _1008104, _1008106] : [class_Lattices_Osemilattice__sup(_1008102), 12847 ^ _780478 : [(12854 ^ _780478) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1008102), _1008104), _1008106) = _1008106, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008102), _1008104), _1008106)))], (12848 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008102), _1008104), _1008106)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1008102), _1008104), _1008106) = _1008106)]]], (15789 ^ _780478) ^ [_1066110, _1066112] : [-(hAPP(c_Set_Ovimage(_1066110, _1066110, c_COMBI(_1066110)), _1066112) = _1066112)], (49676 ^ _780478) ^ [_1785297, _1785299] : [c_Relation_Osym(_1785297, _1785299), 49679 ^ _780478 : [(49680 ^ _780478) ^ [_1785403, _1785405] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785297, _1785297)), hAPP(hAPP(c_Product__Type_OPair(_1785297, _1785297), _1785405), _1785403)), _1785299)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785297, _1785297)), hAPP(hAPP(c_Product__Type_OPair(_1785297, _1785297), _1785403), _1785405)), _1785299)))]]], (45051 ^ _780478) ^ [_1683420, _1683422, _1683424] : [-(hAPP(hAPP(c_List_Ozip(_1683420, _1683422), hAPP(hAPP(c_List_Omap(tc_prod(_1683420, _1683422), _1683420), c_Product__Type_Ofst(_1683420, _1683422)), _1683424)), hAPP(hAPP(c_List_Omap(tc_prod(_1683420, _1683422), _1683422), c_Product__Type_Osnd(_1683420, _1683422)), _1683424)) = _1683424)], (13054 ^ _780478) ^ [_1011776, _1011778, _1011780, _1011782] : [hBOOL(hAPP(hAPP(c_member(_1011776), _1011778), _1011780)), -(hBOOL(hAPP(hAPP(c_member(_1011776), _1011778), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011776, tc_HOL_Obool)), _1011782), _1011780))))], (10341 ^ _780478) ^ [_960889, _960891, _960893] : [class_Orderings_Olinorder(_960889), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_960889), _960891), _960893) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_960889), _960893), _960891))], (37427 ^ _780478) ^ [_1493512] : [-(c_Wellfounded_Ofinite__psubset(_1493512) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1493512, tc_HOL_Obool), tc_fun(_1493512, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1493512, tc_HOL_Obool), tc_fun(_1493512, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1493512, tc_HOL_Obool), tc_fun(tc_fun(_1493512, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1493512, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1493512, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1493512, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1493512, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1493512, tc_HOL_Obool)), c_COMBS(tc_fun(_1493512, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1493512, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1493512, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1493512, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1493512, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1493512, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1493512)))))], (43506 ^ _780478) ^ [_1648979, _1648981, _1648983, _1648985] : [-(hAPP(hAPP(c_List_Oappend(_1648979), hAPP(hAPP(c_List_Oappend(_1648979), _1648981), _1648983)), _1648985) = hAPP(hAPP(c_List_Oappend(_1648979), _1648981), hAPP(hAPP(c_List_Oappend(_1648979), _1648983), _1648985)))], (21570 ^ _780478) ^ [_1181089, _1181091, _1181093, _1181095] : [class_Rings_Olinordered__semiring__strict(_1181089), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181089), _1181091), _1181093)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181089), _1181091), _1181095))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181089), c_Groups_Ozero__class_Ozero(_1181089)), _1181091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181089), _1181093), _1181095)))], (8040 ^ _780478) ^ [_917644, _917646, _917648, _917650, _917652] : [class_Groups_Oordered__ab__group__add(_917644), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_917644), _917646), _917648) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_917644), _917650), _917652), 8047 ^ _780478 : [(8054 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917644), _917650), _917652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917644), _917646), _917648)))], (8048 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917644), _917646), _917648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917644), _917650), _917652)))]]], (52067 ^ _780478) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (49387 ^ _780478) ^ [_1778810, _1778812, _1778814, _1778816] : [class_Complete__Lattice_Ocomplete__lattice(_1778810), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1778812, _1778810), _1778814), _1778816) = c_Complete__Lattice_OSup__class_OSup(_1778810, hAPP(c_Set_OCollect(_1778810), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778812, _1778810), tc_HOL_Obool), tc_HOL_Obool, _1778810), c_HOL_OEx(tc_fun(_1778812, _1778810))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778812, _1778810), tc_HOL_Obool), tc_fun(tc_fun(_1778812, _1778810), tc_HOL_Obool), _1778810), hAPP(c_COMBS(tc_fun(_1778812, _1778810), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1778812, _1778810)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1778812, _1778810), tc_fun(tc_fun(_1778812, _1778810), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1778812, _1778810))), _1778814)))), hAPP(hAPP(c_COMBC(_1778810, tc_fun(tc_fun(_1778812, _1778810), _1778810), tc_fun(tc_fun(_1778812, _1778810), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1778810, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1778812, _1778810), _1778810), tc_fun(tc_fun(_1778812, _1778810), tc_HOL_Obool)), _1778810), c_COMBB(_1778810, tc_HOL_Obool, tc_fun(_1778812, _1778810))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1778812, _1778810), _1778812, _1778810), c_COMBI(tc_fun(_1778812, _1778810))), _1778816)))))))], (51925 ^ _780478) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (34275 ^ _780478) ^ [_1426943, _1426945] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426943)))), _1426945) = 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)))), _1426943)), _1426945))], (31895 ^ _780478) ^ [_1382787, _1382789, _1382791, _1382793, _1382795] : [c_Com_Ocom_OWhile(_1382787, _1382789) = c_Com_Ocom_OCond(_1382791, _1382793, _1382795)], (40243 ^ _780478) ^ [_1566017, _1566019, _1566021] : [-(hBOOL(hAPP(hAPP(c_member(_1566017), _1566019), c_Wellfounded_Oacc(_1566017, _1566021)))), 40247 ^ _780478 : [(40250 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1566017), 40246 ^ [_1566017, _1566019, _1566021]), c_Wellfounded_Oacc(_1566017, _1566021)))], (40248 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566017, _1566017)), hAPP(hAPP(c_Product__Type_OPair(_1566017, _1566017), 40246 ^ [_1566017, _1566019, _1566021]), _1566019)), _1566021)))]]], (19410 ^ _780478) ^ [_1143832] : [class_Groups_Ogroup__add(_1143832), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1143832), c_Groups_Ozero__class_Ozero(_1143832)) = c_Groups_Ozero__class_Ozero(_1143832))], (4666 ^ _780478) ^ [_851506, _851508, _851510, _851512] : [-(c_List_Oupto(_851512, _851508) = c_List_Oupto(_851510, _851506)), _851512 = _851510, _851508 = _851506], (38336 ^ _780478) ^ [_1516829, _1516831, _1516833] : [c_Wellfounded_Owf(_1516829, _1516831), -(hBOOL(hAPP(hAPP(c_member(_1516829), _1516833), c_Wellfounded_Oacc(_1516829, _1516831))))], (25515 ^ _780478) ^ [_1254145] : [-(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)), _1254145)) = _1254145)], (11577 ^ _780478) ^ [_983344, _983346, _983348, _983350, _983352] : [class_Groups_Ocomm__monoid__mult(_983344), hBOOL(hAPP(c_Finite__Set_Ofinite(_983346), _983348)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_983346, _983344), _983350), hAPP(hAPP(c_Set_Oinsert(_983346), _983352), _983348)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983344), hAPP(_983350, _983352)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_983346, _983344), _983350), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983346, tc_HOL_Obool)), _983348), hAPP(hAPP(c_Set_Oinsert(_983346), _983352), c_Orderings_Obot__class_Obot(tc_fun(_983346, tc_HOL_Obool)))))))], (49696 ^ _780478) ^ [_1785825, _1785827, _1785829] : [c_Relation_Osym(_1785825, _1785827), c_Relation_Osym(_1785825, _1785829), -(c_Relation_Osym(_1785825, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1785825, _1785825), tc_HOL_Obool)), _1785827), _1785829)))], (16272 ^ _780478) ^ [_1076145, _1076147, _1076149, _1076151] : [class_Lattices_Olattice(_1076145), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076145), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076145), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076145), _1076147), _1076149)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076145), _1076147), _1076151))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076145), _1076147), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076145), _1076149), _1076151)))))], (5881 ^ _780478) ^ [_873842, _873844, _873846] : [hBOOL(hAPP(hAPP(c_member(_873842), _873844), hAPP(hAPP(c_Set_Oinsert(_873842), _873846), c_Orderings_Obot__class_Obot(tc_fun(_873842, tc_HOL_Obool))))), -(_873844 = _873846)], (30153 ^ _780478) ^ [_1339967, _1339969] : [class_Rings_Olinordered__idom(_1339967), 30156 ^ _780478 : [(30163 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339967), c_Groups_Ozero__class_Ozero(_1339967)), _1339969)), -(c_Groups_Osgn__class_Osgn(_1339967, _1339969) = c_Groups_Oone__class_Oone(_1339967))], (30157 ^ _780478) ^ [] : [c_Groups_Osgn__class_Osgn(_1339967, _1339969) = c_Groups_Oone__class_Oone(_1339967), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339967), c_Groups_Ozero__class_Ozero(_1339967)), _1339969)))]]], (32230 ^ _780478) ^ [_1389248, _1389250, _1389252] : [class_Int_Onumber(_1389248), class_Orderings_Oord(_1389248), 32237 ^ _780478 : [(32244 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389248), hAPP(c_Int_Onumber__class_Onumber__of(_1389248), _1389250)), hAPP(c_Int_Onumber__class_Onumber__of(_1389248), _1389252)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1389248), hAPP(c_Int_Onumber__class_Onumber__of(_1389248), _1389250)), hAPP(c_Int_Onumber__class_Onumber__of(_1389248), _1389252)) = hAPP(c_Int_Onumber__class_Onumber__of(_1389248), _1389252))], (32238 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1389248), hAPP(c_Int_Onumber__class_Onumber__of(_1389248), _1389250)), hAPP(c_Int_Onumber__class_Onumber__of(_1389248), _1389252))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1389248), hAPP(c_Int_Onumber__class_Onumber__of(_1389248), _1389250)), hAPP(c_Int_Onumber__class_Onumber__of(_1389248), _1389252)) = hAPP(c_Int_Onumber__class_Onumber__of(_1389248), _1389250))]]], (18288 ^ _780478) ^ [_1122590, _1122592] : [18289 ^ _780478 : [(18290 ^ _780478) ^ [_1122643] : [_1122592 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122590), _1122643))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122590), _1122592)))], (41782 ^ _780478) ^ [_1605710, _1605712, _1605714, _1605716] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1605710), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1605712), _1605714)))), -(hAPP(c_Random_Opick(_1605712, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1605712)), _1605714), _1605716)), _1605710) = hAPP(c_Random_Opick(_1605712, _1605716), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1605710), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1605712), _1605714))))], (2868 ^ _780478) ^ [_822931, _822933] : [_822933 = _822931, -(c_Nat_Ofunpow(_822933) = c_Nat_Ofunpow(_822931))], (19640 ^ _780478) ^ [_1147141, _1147143, _1147145] : [19641 ^ _780478 : [(19644 ^ _780478) ^ [] : [_1147143 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19642 ^ _780478) ^ [] : [_1147141 = _1147145]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147141), _1147143) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147145), _1147143))], (23971 ^ _780478) ^ [_1226167] : [-(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)), _1226167))))], (4166 ^ _780478) ^ [_843526, _843528, _843530, _843532, _843534, _843536] : [-(c_List_Osplice(_843536, _843532, _843528) = c_List_Osplice(_843534, _843530, _843526)), _843536 = _843534, _843532 = _843530, _843528 = _843526], (51551 ^ _780478) ^ [_1824115, _1824117, _1824119] : [class_Rings_Ocomm__ring__1(_1824115), 51554 ^ _780478 : [(51561 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824115), _1824117), _1824119)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824115), _1824117), hAPP(c_Groups_Ouminus__class_Ouminus(_1824115), _1824119))))], (51555 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824115), _1824117), hAPP(c_Groups_Ouminus__class_Ouminus(_1824115), _1824119))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824115), _1824117), _1824119)))]]], (11925 ^ _780478) ^ [_990048, _990050] : [class_Orderings_Olinorder(_990048), hBOOL(hAPP(c_Finite__Set_Ofinite(_990048), _990050)), -(c_Big__Operators_Olattice_OInf__fin(_990048, c_Orderings_Oord__class_Omin(_990048), _990050) = hAPP(c_Finite__Set_Ofold1(_990048, c_Orderings_Oord__class_Omin(_990048)), _990050))], (51265 ^ _780478) ^ [_1819249, _1819251, _1819253, _1819255] : [class_Rings_Ocomm__semiring__1(_1819249), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819249), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1819249), _1819251), _1819253)), _1819255)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1819249), _1819253), _1819255)))], (12582 ^ _780478) ^ [_1002718, _1002720, _1002722, _1002724] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002718, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002718, tc_HOL_Obool)), _1002720), _1002722)), _1002724) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002718, tc_HOL_Obool)), _1002720), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002718, tc_HOL_Obool)), _1002722), _1002724)))], (34461 ^ _780478) ^ [_1430399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1430399)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430399), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (43508 ^ _780478) ^ [_1649040, _1649042, _1649044] : [class_Groups_Omonoid__add(_1649040), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1649040), hAPP(hAPP(c_List_Oappend(_1649040), _1649042), _1649044)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1649040), hAPP(c_List_Omonoid__add__class_Olistsum(_1649040), _1649042)), hAPP(c_List_Omonoid__add__class_Olistsum(_1649040), _1649044)))], (25946 ^ _780478) ^ [_1261478] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1261478)), -(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, _1261478))))], (52195 ^ _780478) ^ [_1832093, _1832095] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1832093, _1832095)))], (41882 ^ _780478) ^ [_1608722, _1608724, _1608726, _1608728] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608722), tc_List_Olist(_1608722))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608722), tc_List_Olist(_1608722)), _1608724), _1608726)), c_List_Olistrel1(_1608722, _1608728))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608722)), _1608724) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608722)), _1608726))], (27459 ^ _780478) ^ [_1288344] : [class_Rings_Oring__1(_1288344), -(hAPP(c_Int_Oring__1__class_Oof__int(_1288344), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1288344))], (18243 ^ _780478) ^ [_1121644, _1121646, _1121648, _1121650, _1121652] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1121644, _1121646, _1121648), _1121650), hAPP(c_Nat_OSuc, _1121652)) = hAPP(hAPP(_1121648, _1121650), hAPP(hAPP(c_Power_Opower_Opower(_1121644, _1121646, _1121648), _1121650), _1121652)))], (41389 ^ _780478) ^ [_1594235, _1594237, _1594239, _1594241, _1594243] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594235, _1594235)), hAPP(hAPP(c_Product__Type_OPair(_1594235, _1594235), _1594237), _1594239)), c_Transitive__Closure_Ortrancl(_1594235, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1594235, _1594235), tc_HOL_Obool)), _1594241), _1594243)))), 41395 ^ _780478 : [(41401 ^ _780478) ^ [] : [41397 ^ [_1594235, _1594237, _1594239, _1594241, _1594243] = 41394 ^ [_1594235, _1594237, _1594239, _1594241, _1594243]], (41399 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594235, _1594235)), hAPP(hAPP(c_Product__Type_OPair(_1594235, _1594235), 41397 ^ [_1594235, _1594237, _1594239, _1594241, _1594243]), 41394 ^ [_1594235, _1594237, _1594239, _1594241, _1594243])), _1594243)))], (41396 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594235, _1594235)), hAPP(hAPP(c_Product__Type_OPair(_1594235, _1594235), 41394 ^ [_1594235, _1594237, _1594239, _1594241, _1594243]), _1594239)), c_Transitive__Closure_Ortrancl(_1594235, _1594241))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594235, _1594235)), hAPP(hAPP(c_Product__Type_OPair(_1594235, _1594235), _1594237), _1594239)), c_Transitive__Closure_Ortrancl(_1594235, _1594241))))], (26346 ^ _780478) ^ [_1268846, _1268848, _1268850] : [class_Fields_Olinordered__field(_1268846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268846), c_Groups_Ozero__class_Ozero(_1268846)), _1268848)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268846), _1268850), c_Groups_Ozero__class_Ozero(_1268846))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1268846), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268846), _1268848), _1268850)), c_Groups_Ozero__class_Ozero(_1268846))))], (43291 ^ _780478) ^ [_1643978, _1643980, _1643982] : [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), _1643978), _1643980))), -(hBOOL(hAPP(hAPP(_1643982, _1643978), _1643980))), 43298 ^ _780478 : [(43301 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 43296 ^ [_1643978, _1643980, _1643982]), 43297 ^ [_1643978, _1643980, _1643982])), -(hBOOL(hAPP(hAPP(_1643982, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 43296 ^ [_1643978, _1643980, _1643982]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 43297 ^ [_1643978, _1643980, _1643982])))], (43307 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1643982, 43296 ^ [_1643978, _1643980, _1643982]), 43297 ^ [_1643978, _1643980, _1643982]))], (43299 ^ _780478) ^ [] : [-(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), 43296 ^ [_1643978, _1643980, _1643982]), 43297 ^ [_1643978, _1643980, _1643982]))))]]], (30689 ^ _780478) ^ [_1350381] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350381, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1350381, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1350381, tc_HOL_Obool)))], (26440 ^ _780478) ^ [_1270598, _1270600, _1270602, _1270604] : [class_Fields_Ofield__inverse__zero(_1270598), -(_1270600 = c_Groups_Ozero__class_Ozero(_1270598)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270598), _1270600), _1270602)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270598), _1270600), _1270604)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270598), _1270602), _1270604))], (35285 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (36421 ^ _780478) ^ [_1473562, _1473564] : [-(c_Divides_OnegDivAlg(_1473562, _1473564) = hAPP(c_Divides_Oadjust(_1473564), c_Divides_OnegDivAlg(_1473562, 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)))), _1473564)))), -(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), _1473562), _1473564)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1473564), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6544 ^ _780478) ^ [_887412, _887414, _887416, _887418] : [hBOOL(hAPP(hAPP(c_member(_887412), _887414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887412, tc_HOL_Obool)), _887416), _887418))), 6547 ^ _780478 : [(6550 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_887412), _887414), _887418))], (6548 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_887412), _887414), _887416)))]]], (43045 ^ _780478) ^ [_1638964, _1638966, _1638968, _1638970] : [-(c_List_Oremove1(_1638964, _1638966, c_List_Oremove1(_1638964, _1638968, _1638970)) = c_List_Oremove1(_1638964, _1638968, c_List_Oremove1(_1638964, _1638966, _1638970)))], (34189 ^ _780478) ^ [_1425443, _1425445] : [class_Int_Onumber__ring(_1425443), class_Rings_Olinordered__idom(_1425443), 34196 ^ _780478 : [(34203 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425445), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425443), hAPP(c_Int_Onumber__class_Onumber__of(_1425443), _1425445)), c_Groups_Oone__class_Oone(_1425443))))], (34197 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1425443), hAPP(c_Int_Onumber__class_Onumber__of(_1425443), _1425445)), c_Groups_Oone__class_Oone(_1425443))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425445), c_Int_OBit1(c_Int_OPls))))]]], (36204 ^ _780478) ^ [_1468761, _1468763, _1468765, _1468767, _1468769, _1468771] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468761, tc_fun(_1468763, tc_HOL_Obool))), _1468765), _1468767), _1468769), _1468771)), 36207 ^ _780478 : [(36210 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1468767, _1468769), _1468771)))], (36208 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1468765, _1468769), _1468771)))]]], (16420 ^ _780478) ^ [_1079962, _1079964, _1079966] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079962, tc_HOL_Obool)), _1079964), _1079966) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079962, tc_HOL_Obool)), _1079964), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079962, tc_HOL_Obool)), _1079966)))], (31476 ^ _780478) ^ [_1370450, _1370452, _1370454] : [class_Groups_Olinordered__ab__semigroup__add(_1370450), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370450), _1370452)), -(_1370452 = c_Orderings_Obot__class_Obot(tc_fun(_1370450, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1370450), _1370454), c_Big__Operators_Olinorder__class_OMin(_1370450, _1370452)) = c_Big__Operators_Olinorder__class_OMin(_1370450, hAPP(c_Set_OCollect(_1370450), hAPP(hAPP(c_COMBB(tc_fun(_1370450, tc_HOL_Obool), tc_HOL_Obool, _1370450), c_HOL_OEx(_1370450)), hAPP(hAPP(c_COMBC(_1370450, tc_fun(_1370450, tc_HOL_Obool), tc_fun(_1370450, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370450, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1370450, tc_HOL_Obool), tc_fun(_1370450, tc_HOL_Obool)), _1370450), c_COMBS(_1370450, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370450, tc_HOL_Obool), tc_fun(_1370450, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1370450), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1370450), c_fconj)), hAPP(hAPP(c_COMBC(_1370450, tc_fun(_1370450, _1370450), tc_fun(_1370450, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370450, tc_HOL_Obool), tc_fun(tc_fun(_1370450, _1370450), tc_fun(_1370450, tc_HOL_Obool)), _1370450), c_COMBB(_1370450, tc_HOL_Obool, _1370450)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1370450), _1370454))))), hAPP(hAPP(c_COMBC(_1370450, tc_fun(_1370450, tc_HOL_Obool), tc_HOL_Obool), c_member(_1370450)), _1370452))))))], (19604 ^ _780478) ^ [_1146609, _1146611] : [19605 ^ _780478 : [(19608 ^ _780478) ^ [] : [_1146611 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19606 ^ _780478) ^ [] : [_1146609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146609), _1146611) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49339 ^ _780478) ^ [_1777281, _1777283, _1777285] : [-(c_List_Olist__ex(_1777281, _1777285, _1777283)), 49340 ^ _780478 : [(49341 ^ _780478) ^ [_1777338] : [hBOOL(hAPP(hAPP(c_member(_1777281), _1777338), hAPP(c_List_Oset(_1777281), _1777283))), hBOOL(hAPP(_1777285, _1777338))]]], (6462 ^ _780478) ^ [_885707, _885709, _885711] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_885707), _885709)), hBOOL(hAPP(_885711, c_Orderings_Obot__class_Obot(tc_fun(_885707, tc_HOL_Obool)))), 6473 ^ _780478 : [(6476 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_885707), 6471 ^ [_885707, _885709, _885711]), 6472 ^ [_885707, _885709, _885711]))], (6478 ^ _780478) ^ [] : [-(hBOOL(hAPP(_885711, 6472 ^ [_885707, _885709, _885711])))], (6480 ^ _780478) ^ [] : [hBOOL(hAPP(_885711, hAPP(hAPP(c_Set_Oinsert(_885707), 6471 ^ [_885707, _885709, _885711]), 6472 ^ [_885707, _885709, _885711])))], (6474 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_885707), 6472 ^ [_885707, _885709, _885711])))]], -(hBOOL(hAPP(_885711, _885709)))], (33436 ^ _780478) ^ [_1411525] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411525), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411525), c_Int_OPls)))], (22185 ^ _780478) ^ [_1192841, _1192843, _1192845, _1192847] : [class_Groups_Ocomm__monoid__add(_1192841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192843), _1192845)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192843, _1192841), _1192847), _1192845) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1192841, _1192843, c_Groups_Oplus__class_Oplus(_1192841)), _1192847), c_Groups_Ozero__class_Ozero(_1192841)), _1192845))], (35894 ^ _780478) ^ [_1461953, _1461955, _1461957, _1461959, _1461961] : [c_Equiv__Relations_Oequiv(_1461953, _1461955, _1461957), hBOOL(hAPP(hAPP(c_member(tc_prod(_1461953, _1461953)), hAPP(hAPP(c_Product__Type_OPair(_1461953, _1461953), _1461959), _1461961)), _1461957)), -(hAPP(c_Relation_OImage(_1461953, _1461953, _1461957), hAPP(hAPP(c_Set_Oinsert(_1461953), _1461959), c_Orderings_Obot__class_Obot(tc_fun(_1461953, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1461953, _1461953, _1461957), hAPP(hAPP(c_Set_Oinsert(_1461953), _1461961), c_Orderings_Obot__class_Obot(tc_fun(_1461953, tc_HOL_Obool)))))], (31148 ^ _780478) ^ [_1360190, _1360192, _1360194] : [hBOOL(hAPP(hAPP(c_member(_1360190), _1360192), hAPP(c_Set_OCollect(_1360190), _1360194))), -(hBOOL(hAPP(_1360194, _1360192)))], (17552 ^ _780478) ^ [_1106604, _1106606, _1106608, _1106610, _1106612] : [-(_1106604 = c_Orderings_Obot__class_Obot(tc_fun(_1106606, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106608, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106606, tc_fun(_1106608, tc_HOL_Obool)), _1106604), _1106610)), _1106612) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106606, tc_fun(_1106608, tc_HOL_Obool)), _1106604), hAPP(hAPP(c_COMBC(_1106606, tc_fun(_1106608, tc_HOL_Obool), tc_fun(_1106608, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1106608, tc_HOL_Obool), tc_fun(tc_fun(_1106608, tc_HOL_Obool), tc_fun(_1106608, tc_HOL_Obool)), _1106606), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106608, tc_HOL_Obool))), _1106610)), _1106612)))], (12740 ^ _780478) ^ [_1005934, _1005936, _1005938] : [class_Lattices_Osemilattice__sup(_1005934), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005934), _1005936), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005934), _1005936), _1005938)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005934), _1005936), _1005938))], (51869 ^ _780478) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (48905 ^ _780478) ^ [_1767177, _1767179, _1767181, _1767183, _1767185, _1767187] : [-(c_Nitpick_Opair__box_Opair__box__size(_1767177, _1767179, _1767181, _1767183, c_Nitpick_Opair__box_OPairBox(_1767177, _1767179, _1767185, _1767187)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1767181, _1767185)), hAPP(_1767183, _1767187))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45895 ^ _780478) ^ [_1701855, _1701857] : [c_List_Oconcat(_1701855, _1701857) = c_List_Olist_ONil(_1701855), 45898 ^ _780478 : [(45899 ^ _780478) ^ [_1701946] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1701855)), _1701946), hAPP(c_List_Oset(tc_List_Olist(_1701855)), _1701857))), -(_1701946 = c_List_Olist_ONil(_1701855))]]], (43722 ^ _780478) ^ [_1653773, _1653775, _1653777, _1653779] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653773), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653775)), _1653777)))), -(hAPP(hAPP(c_List_Onth(_1653775), hAPP(hAPP(c_List_Oappend(_1653775), _1653777), _1653779)), _1653773) = hAPP(hAPP(c_List_Onth(_1653775), _1653779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1653773), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653775)), _1653777))))], (35726 ^ _780478) ^ [_1457580, _1457582, _1457584, _1457586, _1457588, _1457590] : [hBOOL(hAPP(hAPP(c_member(_1457580), _1457582), _1457584)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1457580, _1457586)), hAPP(hAPP(c_Product__Type_OPair(_1457580, _1457586), _1457582), _1457588)), _1457590)), -(hBOOL(hAPP(hAPP(c_member(_1457586), _1457588), hAPP(c_Relation_OImage(_1457580, _1457586, _1457590), _1457584))))], (36772 ^ _780478) ^ [_1479970, _1479972, _1479974, _1479976] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479970, _1479972), _1479974)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479970, _1479972), _1479976)), -(_1479974 = _1479976)], (35968 ^ _780478) ^ [_1463448, _1463450, _1463452, _1463454] : [-(hAPP(c_Relation_OImage(_1463448, _1463450, _1463452), hAPP(hAPP(c_Set_Oinsert(_1463448), _1463454), c_Orderings_Obot__class_Obot(tc_fun(_1463448, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1463450), hAPP(hAPP(c_COMBC(_1463450, tc_fun(tc_prod(_1463448, _1463450), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1463448, _1463450), tc_fun(tc_fun(tc_prod(_1463448, _1463450), tc_HOL_Obool), tc_HOL_Obool), _1463450), c_member(tc_prod(_1463448, _1463450))), hAPP(c_Product__Type_OPair(_1463448, _1463450), _1463454))), _1463452)))], (52007 ^ _780478) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (39945 ^ _780478) ^ [_1558900, _1558902, _1558904, _1558906, _1558908, _1558910] : [c_Finite__Set_Ofolding(_1558900, _1558902, _1558904, _1558906), -(hAPP(c_Fun_Ocomp(_1558902, _1558902, _1558902, hAPP(_1558904, _1558908)), hAPP(_1558904, _1558910)) = hAPP(c_Fun_Ocomp(_1558902, _1558902, _1558902, hAPP(_1558904, _1558910)), hAPP(_1558904, _1558908)))], (7792 ^ _780478) ^ [_912405, _912407, _912409, _912411] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912405, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912405), _912407), _912409)), _912411))), hBOOL(hAPP(hAPP(c_member(_912405), _912407), _912411)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912405, tc_HOL_Obool)), _912409), _912411))], (33730 ^ _780478) ^ [_1416957] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416957))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416957)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (46497 ^ _780478) ^ [_1716241, _1716243] : [class_Orderings_Olinorder(_1716241), c_List_Olinorder__class_Osorted(_1716241, _1716243), -(c_List_Olinorder__class_Osorted(_1716241, hAPP(c_List_Otl(_1716241), _1716243)))], (8714 ^ _780478) ^ [_931186, _931188, _931190] : [class_Orderings_Opreorder(_931186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931186), _931188), _931190)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931186), _931190), _931188))], (44107 ^ _780478) ^ [_1663256, _1663258, _1663260] : [-(_1663256 = c_List_Olist_ONil(_1663258)), -(hAPP(c_List_Ohd(_1663258), hAPP(c_List_Orotate(_1663258, _1663260), _1663256)) = hAPP(hAPP(c_List_Onth(_1663258), _1663256), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1663260, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663258)), _1663256))))], (40063 ^ _780478) ^ [_1561584, _1561586, _1561588, _1561590, _1561592, _1561594] : [c_Finite__Set_Ofolding(_1561584, _1561586, _1561588, _1561590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561584), _1561592)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561584), _1561594)), -(hAPP(c_Fun_Ocomp(_1561586, _1561586, _1561586, hAPP(_1561590, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1561584, tc_HOL_Obool)), _1561592), _1561594))), hAPP(_1561590, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1561584, tc_HOL_Obool)), _1561592), _1561594))) = hAPP(c_Fun_Ocomp(_1561586, _1561586, _1561586, hAPP(_1561590, _1561592)), hAPP(_1561590, _1561594)))], (43891 ^ _780478) ^ [_1658372, _1658374] : [hAPP(c_List_Orotate1(_1658372), _1658374) = c_List_Olist_ONil(_1658372), -(_1658374 = c_List_Olist_ONil(_1658372))], (47362 ^ _780478) ^ [_1733554, _1733556, _1733558] : [47364 ^ _780478 : [(47367 ^ _780478) ^ [] : [hBOOL(hAPP(_1733556, 47363 ^ [_1733554, _1733556, _1733558]))], (47365 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733554), 47363 ^ [_1733554, _1733556, _1733558]), hAPP(c_List_Oset(_1733554), _1733558))))]], -(c_List_OdropWhile(_1733554, _1733556, _1733558) = c_List_Olist_ONil(_1733554))], (3336 ^ _780478) ^ [_830175, _830177, _830179, _830181, _830183, _830185, _830187, _830189] : [-(c_Enum_Oproduct(_830189, _830185, _830181, _830177) = c_Enum_Oproduct(_830187, _830183, _830179, _830175)), _830189 = _830187, _830185 = _830183, _830181 = _830179, _830177 = _830175], (27096 ^ _780478) ^ [_1282626, _1282628] : [-(c_Int_Onat__aux(_1282626, _1282628) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1282626)), _1282628))], (40913 ^ _780478) ^ [_1581934, _1581936, _1581938, _1581940, _1581942] : [-(hAPP(c_Relation_Oconverse(_1581934, _1581936), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581938, tc_fun(tc_prod(_1581934, _1581936), tc_HOL_Obool)), _1581940), _1581942)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581938, tc_fun(tc_prod(_1581936, _1581934), tc_HOL_Obool)), _1581940), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1581934, _1581936), tc_HOL_Obool), tc_fun(tc_prod(_1581936, _1581934), tc_HOL_Obool), _1581938), c_Relation_Oconverse(_1581934, _1581936)), _1581942)))], (40800 ^ _780478) ^ [_1579316, _1579318, _1579320] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1579316), _1579318))), -(c_Random_Ominus__shift(_1579320, _1579316, _1579318) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1579316), _1579318))], (37129 ^ _780478) ^ [_1486711, _1486713, _1486715, _1486717] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486711, _1486711)), hAPP(hAPP(c_Product__Type_OPair(_1486711, _1486711), _1486713), _1486715)), hAPP(c_Wellfounded_Omeasure(_1486711), _1486717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1486717, _1486713)), hAPP(_1486717, _1486715))))], (46080 ^ _780478) ^ [_1706711, _1706713, _1706715, _1706717] : [-(hAPP(c_List_Ofilter(_1706711, _1706713), hAPP(hAPP(c_List_Oappend(_1706711), _1706715), _1706717)) = hAPP(hAPP(c_List_Oappend(_1706711), hAPP(c_List_Ofilter(_1706711, _1706713), _1706715)), hAPP(c_List_Ofilter(_1706711, _1706713), _1706717)))], (31714 ^ _780478) ^ [_1379248, _1379250, _1379252, _1379254] : [hBOOL(hAPP(hAPP(c_member(_1379248), _1379250), _1379252)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1379248, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379248, _1379248, _1379254), hAPP(hAPP(c_Set_Oinsert(_1379248), _1379250), c_Orderings_Obot__class_Obot(tc_fun(_1379248, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1379248), _1379252), _1379254))))], (49248 ^ _780478) ^ [_1775412, _1775414] : [-(c_Relation_Otrans(_1775412, c_Transitive__Closure_Otrancl(_1775412, _1775414)))], (44324 ^ _780478) ^ [_1667712, _1667714, _1667716] : [class_Orderings_Olinorder(_1667712), -(c_Big__Operators_Olattice_OSup__fin(_1667712, c_Orderings_Oord__class_Omax(_1667712), hAPP(c_List_Oset(_1667712), hAPP(hAPP(c_List_Olist_OCons(_1667712), _1667714), _1667716))) = hAPP(c_List_Ofoldl(_1667712, _1667712, c_Orderings_Oord__class_Omax(_1667712), _1667714), _1667716))], (42597 ^ _780478) ^ [_1629338] : [c_List_Onat__list(_1629338), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1629338)))], (13402 ^ _780478) ^ [_1019192] : [-(c_Fun_Oinj__on(_1019192, tc_fun(_1019192, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1019192, tc_fun(_1019192, tc_HOL_Obool), tc_fun(_1019192, tc_HOL_Obool)), c_Set_Oinsert(_1019192)), c_Orderings_Obot__class_Obot(tc_fun(_1019192, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1019192, tc_HOL_Obool))))], (7433 ^ _780478) ^ [_905136, _905138, _905140, _905142, _905144] : [class_Groups_Oab__group__add(_905136), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_905138, _905136), hAPP(hAPP(c_COMBS(_905138, _905136, _905136), hAPP(hAPP(c_COMBB(_905136, tc_fun(_905136, _905136), _905138), c_Groups_Ominus__class_Ominus(_905136)), _905140)), _905142)), _905144) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_905136), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_905138, _905136), _905140), _905144)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_905138, _905136), _905142), _905144)))], (49430 ^ _780478) ^ [_1780665, _1780667] : [c_Predicate_Otransp(_1780665, _1780667), -(c_Relation_Otrans(_1780665, hAPP(c_Set_OCollect(tc_prod(_1780665, _1780665)), hAPP(c_Product__Type_Oprod_Oprod__case(_1780665, _1780665, tc_HOL_Obool), _1780667))))], (4 ^ _780478) ^ [_780528, _780530] : [_780530 = _780528, -(_780528 = _780530)], (13554 ^ _780478) ^ [_1022272, _1022274] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1022272), c_Orderings_Otop__class_Otop(tc_fun(_1022272, tc_HOL_Obool)))), c_Fun_Oinj__on(_1022272, _1022272, _1022274, c_Orderings_Otop__class_Otop(tc_fun(_1022272, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1022272, _1022272, _1022274), c_Orderings_Otop__class_Otop(tc_fun(_1022272, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1022272, tc_HOL_Obool)))], (19782 ^ _780478) ^ [_1149685, _1149687, _1149689] : [class_Groups_Oordered__comm__monoid__add(_1149685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149685), _1149687), c_Groups_Ozero__class_Ozero(_1149685))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149685), _1149689), c_Groups_Ozero__class_Ozero(_1149685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149685), _1149687), _1149689)), c_Groups_Ozero__class_Ozero(_1149685))))], (40602 ^ _780478) ^ [_1574962, _1574964, _1574966, _1574968, _1574970] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574962, _1574962)), hAPP(hAPP(c_Product__Type_OPair(_1574962, _1574962), _1574964), _1574966)), c_Transitive__Closure_Ortrancl(_1574962, _1574968))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574962, _1574962)), hAPP(hAPP(c_Product__Type_OPair(_1574962, _1574962), _1574966), _1574970)), c_Transitive__Closure_Otrancl(_1574962, _1574968))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574962, _1574962)), hAPP(hAPP(c_Product__Type_OPair(_1574962, _1574962), _1574964), _1574970)), c_Transitive__Closure_Otrancl(_1574962, _1574968))))], (34963 ^ _780478) ^ [_1439252, _1439254] : [class_Rings_Oring__1__no__zero__divisors(_1439252), 34966 ^ _780478 : [(34967 ^ _780478) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1439252), _1439254), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1439252), -(_1439254 = c_Groups_Oone__class_Oone(_1439252)), -(_1439254 = hAPP(c_Groups_Ouminus__class_Ouminus(_1439252), c_Groups_Oone__class_Oone(_1439252)))], (34977 ^ _780478) ^ [] : [34978 ^ _780478 : [(34981 ^ _780478) ^ [] : [_1439254 = hAPP(c_Groups_Ouminus__class_Ouminus(_1439252), c_Groups_Oone__class_Oone(_1439252))], (34979 ^ _780478) ^ [] : [_1439254 = c_Groups_Oone__class_Oone(_1439252)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1439252), _1439254), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1439252))]]], (37305 ^ _780478) ^ [_1490399, _1490401] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1490399), _1490401) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1490399, _1490401)))], (32150 ^ _780478) ^ [_1387614, _1387616, _1387618, _1387620] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387614), hAPP(c_Int_Onumber__class_Onumber__of(_1387614), _1387616)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387614), _1387618), _1387620)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387614), hAPP(c_Int_Onumber__class_Onumber__of(_1387614), _1387616)), _1387618)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387614), hAPP(c_Int_Onumber__class_Onumber__of(_1387614), _1387616)), _1387620))), class_Int_Onumber(_1387614), class_Rings_Osemiring(_1387614)], (46989 ^ _780478) ^ [_1725628, _1725630] : [-(hAPP(c_List_Orev(_1725628), c_List_Oconcat(_1725628, _1725630)) = c_List_Oconcat(_1725628, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1725628), tc_List_Olist(_1725628)), c_List_Orev(_1725628)), hAPP(c_List_Orev(tc_List_Olist(_1725628)), _1725630))))], (17416 ^ _780478) ^ [_1102660, _1102662, _1102664, _1102666, _1102668, _1102670] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102660, tc_fun(_1102662, tc_HOL_Obool)), _1102664), hAPP(hAPP(c_COMBB(_1102666, tc_fun(_1102662, tc_HOL_Obool), _1102660), _1102668), _1102670)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102666, tc_fun(_1102662, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1102660, _1102666, _1102670), _1102664)), _1102668))], (26912 ^ _780478) ^ [_1279132, _1279134, _1279136, _1279138] : [class_Fields_Ofield(_1279132), -(_1279134 = c_Groups_Ozero__class_Ozero(_1279132)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279132), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279132), _1279136), _1279134)), _1279138) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279132), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279132), _1279136), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279132), _1279134), _1279138))), _1279134))], (22793 ^ _780478) ^ [_1204797, _1204799] : [class_Rings_Olinordered__semidom(_1204797), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1204797), c_Groups_Ozero__class_Ozero(_1204797)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1204797), _1204799))))], (29415 ^ _780478) ^ [_1326732, _1326734, _1326736, _1326738] : [class_Divides_Osemiring__div(_1326732), -(c_Divides_Odiv__class_Omod(_1326732, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326732), _1326734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326732), _1326736), _1326738)), _1326738) = c_Divides_Odiv__class_Omod(_1326732, _1326734, _1326738))], (37151 ^ _780478) ^ [_1487200, _1487202, _1487204] : [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), _1487200), _1487202))), -(hBOOL(hAPP(hAPP(_1487204, _1487200), _1487202))), 37158 ^ _780478 : [(37161 ^ _780478) ^ [] : [-(37157 ^ [_1487200, _1487202, _1487204] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1487204, 37157 ^ [_1487200, _1487202, _1487204]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 37156 ^ [_1487200, _1487202, _1487204], 37157 ^ [_1487200, _1487202, _1487204]))))], (37167 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1487204, 37156 ^ [_1487200, _1487202, _1487204]), 37157 ^ [_1487200, _1487202, _1487204]))], (37159 ^ _780478) ^ [] : [-(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), 37156 ^ [_1487200, _1487202, _1487204]), 37157 ^ [_1487200, _1487202, _1487204]))))]]], (4402 ^ _780478) ^ [_847244, _847246, _847248, _847250] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_847250, _847246) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_847248, _847244)), _847250 = _847248, _847246 = _847244], (20158 ^ _780478) ^ [_1156493, _1156495, _1156497] : [class_Rings_Oordered__ring(_1156493), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156493), c_Groups_Ozero__class_Ozero(_1156493)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156493), _1156495), _1156497)))), 20163 ^ _780478 : [(20170 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156493), _1156495), c_Groups_Ozero__class_Ozero(_1156493))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156493), _1156497), c_Groups_Ozero__class_Ozero(_1156493)))], (20164 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156493), c_Groups_Ozero__class_Ozero(_1156493)), _1156495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156493), c_Groups_Ozero__class_Ozero(_1156493)), _1156497))]]], (15455 ^ _780478) ^ [_1058971] : [class_Power_Opower(_1058971), -(c_Power_Opower__class_Opower(_1058971) = c_Power_Opower_Opower(_1058971, c_Groups_Oone__class_Oone(_1058971), c_Groups_Otimes__class_Otimes(_1058971)))], (36375 ^ _780478) ^ [_1472729] : [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), _1472729))), 36378 ^ _780478 : [(36385 ^ _780478) ^ [] : [-(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), _1472729))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472729)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472729)), 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), _1472729)))))], (36379 ^ _780478) ^ [] : [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), _1472729)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472729)) = 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), _1472729))))]]], (49058 ^ _780478) ^ [_1770834] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1770834)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770834)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38931 ^ _780478) ^ [_1533102, _1533104, _1533106, _1533108] : [_1533102 = c_Orderings_Obot__class_Obot(tc_fun(_1533104, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1533106, _1533104), _1533106, c_Product__Type_Ofst(_1533106, _1533104)), hAPP(hAPP(c_Product__Type_OSigma(_1533106, _1533104), _1533108), hAPP(c_COMBK(tc_fun(_1533104, tc_HOL_Obool), _1533106), _1533102))) = c_Orderings_Obot__class_Obot(tc_fun(_1533106, tc_HOL_Obool)))], (34145 ^ _780478) ^ [_1424807] : [class_Int_Onumber__ring(_1424807), -(c_Int_Oiszero(_1424807, hAPP(c_Int_Onumber__class_Onumber__of(_1424807), c_Int_OPls)))], (38192 ^ _780478) ^ [_1514234, _1514236, _1514238, _1514240] : [c_Wellfounded_Owf(_1514234, _1514236), -(c_Wellfounded_Owf(_1514238, hAPP(hAPP(c_Relation_Oinv__image(_1514234, _1514238), _1514236), _1514240)))], (46376 ^ _780478) ^ [_1713843, _1713845] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1713843, _1713845) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1713843), hAPP(c_Nat_OSuc, _1713845))))], (15747 ^ _780478) ^ [_1065115, _1065117, _1065119, _1065121] : [class_Lattices_Osemilattice__inf(_1065115), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065115), _1065117), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065115), _1065119), _1065121)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065115), _1065119), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065115), _1065117), _1065121)))], (46276 ^ _780478) ^ [_1712097, _1712099] : [c_List_Oupt(_1712097, _1712099) = c_List_Olist_ONil(tc_Nat_Onat), -(_1712099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712099), _1712097)))], (29255 ^ _780478) ^ [_1323580, _1323582, _1323584, _1323586] : [class_Divides_Osemiring__div(_1323580), -(c_Divides_Odiv__class_Omod(_1323580, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323580), _1323582), c_Divides_Odiv__class_Omod(_1323580, _1323584, _1323586)), _1323586) = c_Divides_Odiv__class_Omod(_1323580, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1323580), _1323582), _1323584), _1323586))], (37628 ^ _780478) ^ [_1498619, _1498621, _1498623, _1498625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1498619), _1498621)), -(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), _1498619), _1498623)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1498621), _1498625))), c_FunDef_Opair__less)))], (40869 ^ _780478) ^ [_1580860, _1580862, _1580864] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580862, _1580860)), _1580864)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580860, _1580862)), hAPP(c_Relation_Oconverse(_1580862, _1580860), _1580864))))], (6526 ^ _780478) ^ [_887021, _887023, _887025, _887027, _887029, _887031, _887033] : [c_Finite__Set_Ofolding__image__simple__idem(_887021, _887023, _887025, _887027, _887029, _887031), -(hAPP(hAPP(_887025, _887033), _887033) = _887033)], (34919 ^ _780478) ^ [_1438574, _1438576, _1438578] : [class_Rings_Olinordered__idom(_1438574), 34922 ^ _780478 : [(34931 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438574), hAPP(hAPP(c_Power_Opower__class_Opower(_1438574), _1438576), 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(_1438574), _1438578), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1438574)), _1438576 = c_Groups_Ozero__class_Ozero(_1438574), _1438578 = c_Groups_Ozero__class_Ozero(_1438574)], (34923 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438574), hAPP(hAPP(c_Power_Opower__class_Opower(_1438574), _1438576), 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(_1438574), _1438578), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1438574), 34926 ^ _780478 : [(34929 ^ _780478) ^ [] : [-(_1438578 = c_Groups_Ozero__class_Ozero(_1438574))], (34927 ^ _780478) ^ [] : [-(_1438576 = c_Groups_Ozero__class_Ozero(_1438574))]]]]], (35764 ^ _780478) ^ [_1458213, _1458215, _1458217] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1458213, _1458213), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1458215), _1458217))), -(_1458213 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1458217 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50471 ^ _780478) ^ [_1801662, _1801664, _1801666, _1801668] : [c_Fun_Oinj__on(_1801662, _1801664, _1801666, _1801668), -(c_Fun_Obij__betw(_1801662, _1801664, _1801666, _1801668, hAPP(c_Set_Oimage(_1801662, _1801664, _1801666), _1801668)))], (27433 ^ _780478) ^ [_1287995, _1287997] : [c_Nat__Transfer_Ois__nat(_1287995), c_Nat__Transfer_Ois__nat(_1287997), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1287995), _1287997)))], (50614 ^ _780478) ^ [_1804354, _1804356, _1804358] : [c_Fun_Oinj__on(_1804354, _1804356, _1804358, c_Orderings_Otop__class_Otop(tc_fun(_1804354, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1804354, _1804356, _1804358), c_Orderings_Otop__class_Otop(tc_fun(_1804354, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1804356, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1804354, _1804356, _1804358, c_Orderings_Otop__class_Otop(tc_fun(_1804354, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804356, tc_HOL_Obool))))], (19222 ^ _780478) ^ [_1141093, _1141095] : [class_Rings_Ocomm__semiring__1(_1141093), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141093), c_Groups_Ozero__class_Ozero(_1141093)), _1141095) = c_Groups_Ozero__class_Ozero(_1141093))], (46316 ^ _780478) ^ [_1712724, _1712726, _1712728] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1712724), c_List_Oupt(_1712726, _1712728)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1712726), _1712724), _1712728))], (6804 ^ _780478) ^ [_893047, _893049, _893051, _893053, _893055, _893057] : [-(_893047 = _893049), -(hAPP(c_Fun_Ofun__upd(_893051, _893053, _893055, _893049, _893057), _893047) = hAPP(_893055, _893047))], (29345 ^ _780478) ^ [_1325303, _1325305, _1325307, _1325309] : [class_Divides_Osemiring__div(_1325303), -(c_Divides_Odiv__class_Omod(_1325303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325303), c_Divides_Odiv__class_Omod(_1325303, _1325305, _1325307)), _1325309), _1325307) = c_Divides_Odiv__class_Omod(_1325303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325303), _1325305), _1325309), _1325307))], (38342 ^ _780478) ^ [_1516928, _1516930] : [hAPP(hAPP(c_Relation_Orel__comp(_1516928, _1516928, _1516928), _1516930), _1516930) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1516928, _1516928), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1516928, _1516930))], (35267 ^ _780478) ^ [_1445491] : [c_Int_OMin = c_Int_OBit1(_1445491), -(c_Int_OMin = _1445491)], (17412 ^ _780478) ^ [_1102499, _1102501, _1102503, _1102505, _1102507, _1102509] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102499, tc_fun(_1102501, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1102503, _1102499, _1102505), _1102507)), _1102509) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102503, tc_fun(_1102501, tc_HOL_Obool)), _1102507), hAPP(hAPP(c_COMBB(_1102499, tc_fun(_1102501, tc_HOL_Obool), _1102503), _1102509), _1102505)))], (37877 ^ _780478) ^ [_1504526] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1504526) = 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), _1504526), 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))))))], (40392 ^ _780478) ^ [_1569674, _1569676, _1569678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569674, _1569674), tc_HOL_Obool)), _1569676), _1569678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569674, _1569674), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1569674, _1569674, _1569674), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1569674, _1569674), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1569674, _1569676)), _1569678)), _1569676)), _1569678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569674, _1569674), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1569674, _1569676)), _1569678)))], (17372 ^ _780478) ^ [_1101416, _1101418, _1101420] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101416, tc_fun(_1101418, tc_HOL_Obool)), _1101420), hAPP(c_COMBK(tc_fun(_1101418, tc_HOL_Obool), _1101416), c_Orderings_Obot__class_Obot(tc_fun(_1101418, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1101418, tc_HOL_Obool)))], (47113 ^ _780478) ^ [_1728407, _1728409, _1728411, _1728413] : [class_Orderings_Olinorder(_1728407), c_List_Olinorder__class_Osorted(_1728407, hAPP(c_List_Orev(_1728407), _1728409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1728411), _1728413)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1728413), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1728407)), _1728409))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1728407), hAPP(hAPP(c_List_Onth(_1728407), _1728409), _1728413)), hAPP(hAPP(c_List_Onth(_1728407), _1728409), _1728411))))], (15932 ^ _780478) ^ [_1068678, _1068680, _1068682, _1068684] : [class_Lattices_Osemilattice__inf(_1068678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068678), _1068680), _1068682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068678), _1068680), _1068684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068678), _1068680), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068678), _1068682), _1068684))))], (20058 ^ _780478) ^ [_1154571, _1154573, _1154575, _1154577] : [class_Rings_Oordered__semiring(_1154571), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154571), _1154573), _1154575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154571), c_Groups_Ozero__class_Ozero(_1154571)), _1154577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154571), _1154577), _1154573)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154571), _1154577), _1154575))))], (29077 ^ _780478) ^ [_1319897, _1319899, _1319901] : [class_Fields_Olinordered__field__inverse__zero(_1319897), 29083 ^ _780478 : [(29088 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319897), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319897), 29082 ^ [_1319897, _1319899, _1319901]), _1319899)), _1319901))], (29086 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319897), 29082 ^ [_1319897, _1319899, _1319901]), c_Groups_Oone__class_Oone(_1319897))))], (29084 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1319897), c_Groups_Ozero__class_Ozero(_1319897)), 29082 ^ [_1319897, _1319899, _1319901])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319897), _1319899), _1319901)))], (44165 ^ _780478) ^ [_1664368, _1664370, _1664372] : [-(_1664368 = c_List_Olist_ONil(_1664370)), -(hAPP(c_List_Otl(_1664370), hAPP(hAPP(c_List_Oappend(_1664370), _1664368), _1664372)) = hAPP(hAPP(c_List_Oappend(_1664370), hAPP(c_List_Otl(_1664370), _1664368)), _1664372))], (13640 ^ _780478) ^ [_1024014, _1024016, _1024018] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1024014), _1024016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1024014), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1024014, tc_HOL_Obool)), _1024016), hAPP(hAPP(c_Set_Oinsert(_1024014), _1024018), c_Orderings_Obot__class_Obot(tc_fun(_1024014, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1024014), _1024016))))], (20969 ^ _780478) ^ [_1170776, _1170778] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170776), hAPP(c_Nat_OSuc, _1170778)))), 20970 ^ _780478 : [(20973 ^ _780478) ^ [_1170864] : [_1170776 = hAPP(c_Nat_OSuc, _1170864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170864), _1170778))], (20971 ^ _780478) ^ [] : [_1170776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (18019 ^ _780478) ^ [_1115904, _1115906] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115904), _1115906))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115906)), _1115904)))], (52143 ^ _780478) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (52187 ^ _780478) ^ [_1831994] : [class_Enum_Oenum(_1831994), -(class_Enum_Oenum(tc_Option_Ooption(_1831994)))], (44179 ^ _780478) ^ [_1664638, _1664640, _1664642] : [-(hAPP(c_List_Otl(_1664638), hAPP(hAPP(c_List_Oappend(_1664638), _1664640), _1664642)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1664638), _1664638, hAPP(c_List_Otl(_1664638), _1664642), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1664638), tc_List_Olist(_1664638)), _1664638), hAPP(hAPP(c_COMBC(tc_List_Olist(_1664638), tc_List_Olist(_1664638), tc_List_Olist(_1664638)), c_List_Oappend(_1664638)), _1664642))), _1664640))], (37417 ^ _780478) ^ [_1492811, _1492813, _1492815, _1492817, _1492819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1492811, _1492813)), hAPP(_1492811, _1492815))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492817, _1492817)), hAPP(hAPP(c_Product__Type_OPair(_1492817, _1492817), _1492813), _1492815)), c_Wellfounded_Omlex__prod(_1492817, _1492811, _1492819))))], (48409 ^ _780478) ^ [_1756289, _1756291, _1756293, _1756295, _1756297] : [-(hAPP(c_New__DSequence_Oneg__bind(_1756289, _1756291, _1756293, _1756295), _1756297) = c_Lazy__Sequence_Ohb__bind(_1756289, _1756291, hAPP(_1756293, _1756297), hAPP(hAPP(c_COMBC(_1756289, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1756291))), _1756295), _1756297)))], (38494 ^ _780478) ^ [_1520664, _1520666] : [-(c_List_Olex(_1520664, _1520666) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1520664), tc_List_Olist(_1520664)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1520664, _1520666)))], (14535 ^ _780478) ^ [_1040294, _1040296, _1040298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040294), _1040296)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040294), _1040298)), 14542 ^ _780478 : [(14549 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040296), _1040298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040296), _1040294)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040298), _1040294))))], (14543 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040296), _1040294)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040298), _1040294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040296), _1040298)))]]], (13100 ^ _780478) ^ [_1012641, _1012643, _1012645] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012641), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012641, tc_HOL_Obool)), _1012643), _1012645)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012641), _1012643)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012641), _1012645))], (41421 ^ _780478) ^ [_1595353, _1595355, _1595357, _1595359, _1595361] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595353, _1595353)), hAPP(hAPP(c_Product__Type_OPair(_1595353, _1595353), _1595355), _1595357)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595353, _1595353), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1595359)), _1595361))), 41425 ^ _780478 : [(41428 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595353, _1595353)), hAPP(hAPP(c_Product__Type_OPair(_1595353, _1595353), 41424 ^ [_1595353, _1595355, _1595357, _1595359, _1595361]), _1595357)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595353, _1595353), tc_HOL_Obool), _1595359), _1595361))))], (41426 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595353, _1595353)), hAPP(hAPP(c_Product__Type_OPair(_1595353, _1595353), _1595355), 41424 ^ [_1595353, _1595355, _1595357, _1595359, _1595361])), _1595361)))]]], (9788 ^ _780478) ^ [_949738, _949740, _949742] : [class_Rings_Olinordered__idom(_949738), -(_949740 = _949742), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949738), _949740), _949742))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_949738), _949742), _949740)))], (24151 ^ _780478) ^ [_1230159, _1230161] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230159), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230161)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230159)), _1230161))], (6282 ^ _780478) ^ [_881487, _881489, _881491, _881493, _881495, _881497] : [c_Hoare__Mirabelle_Ohoare__derivs(_881487, _881489, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_881487)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_881487), _881491), _881493), _881495)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_881487), tc_HOL_Obool)))), 6289 ^ _780478 : [(6292 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_881491, 6287 ^ [_881487, _881489, _881491, _881493, _881495, _881497]), 6288 ^ [_881487, _881489, _881491, _881493, _881495, _881497]))], (6290 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_881497, 6287 ^ [_881487, _881489, _881491, _881493, _881495, _881497]), 6288 ^ [_881487, _881489, _881491, _881493, _881495, _881497])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_881487, _881489, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_881487)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_881487), _881497), _881493), _881495)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_881487), tc_HOL_Obool)))))], (49580 ^ _780478) ^ [_1783182] : [-(c_Relation_Oantisym(_1783182, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1783182, _1783182), tc_HOL_Obool))))], (24114 ^ _780478) ^ [_1229308, _1229310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1229308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229310)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1229310), _1229308)), _1229310) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1229310), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1229308), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (3816 ^ _780478) ^ [_837697, _837699, _837701, _837703, _837705, _837707] : [-(c_List_OdropWhile(_837707, _837703, _837699) = c_List_OdropWhile(_837705, _837701, _837697)), _837707 = _837705, _837703 = _837701, _837699 = _837697], (7357 ^ _780478) ^ [_903513, _903515, _903517, _903519] : [7359 ^ _780478 : [(7363 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_903513), 7361 ^ [_903513, _903515, _903517, _903519]), _903519)))], (7365 ^ _780478) ^ [] : [-(hAPP(_903517, 7358 ^ [_903513, _903515, _903517, _903519]) = hAPP(_903517, 7361 ^ [_903513, _903515, _903517, _903519]))], (7367 ^ _780478) ^ [] : [7358 ^ [_903513, _903515, _903517, _903519] = 7361 ^ [_903513, _903515, _903517, _903519]], (7360 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_903513), 7358 ^ [_903513, _903515, _903517, _903519]), _903519)))]], -(c_Fun_Oinj__on(_903513, _903515, _903517, _903519))], (7455 ^ _780478) ^ [_905634, _905636, _905638] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_905634), _905636)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905634, tc_HOL_Obool)), _905636), hAPP(c_Set_Oimage(_905634, _905634, _905638), _905636))), -(c_Fun_Oinj__on(_905634, _905634, _905638, _905636))], (3304 ^ _780478) ^ [_829707, _829709] : [_829709 = _829707, -(c_Lazy__Sequence_Ohb__not__seq(_829709) = c_Lazy__Sequence_Ohb__not__seq(_829707))], (26996 ^ _780478) ^ [_1280662, _1280664, _1280666] : [class_Fields_Olinordered__field(_1280662), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280662), _1280664), _1280666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280662), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280662), _1280664), _1280666)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280662), c_Groups_Oone__class_Oone(_1280662)), c_Groups_Oone__class_Oone(_1280662)))), _1280666)))], (44979 ^ _780478) ^ [_1682096, _1682098, _1682100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682096), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682098)), _1682100))), -(hAPP(c_Random_Opick(_1682098, hAPP(hAPP(c_List_Omap(_1682098, tc_prod(tc_Code__Numeral_Ocode__numeral, _1682098)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1682098), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1682100)), hAPP(c_Code__Numeral_Oof__nat, _1682096)) = hAPP(hAPP(c_List_Onth(_1682098), _1682100), _1682096))], (23313 ^ _780478) ^ [_1214144, _1214146, _1214148] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214144), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214146), _1214148)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214146), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214144), _1214148)))], (47754 ^ _780478) ^ [_1742414, _1742416, _1742418, _1742420] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1742414, _1742416, _1742418, _1742420) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1742414, _1742416), _1742418), _1742420)))], (16252 ^ _780478) ^ [_1075582, _1075584, _1075586, _1075588] : [-(hAPP(c_Set_Ovimage(_1075582, _1075584, _1075586), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1075584, tc_HOL_Obool)), _1075588)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1075582, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1075582, _1075584, _1075586), _1075588)))], (14659 ^ _780478) ^ [_1042600, _1042602, _1042604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042600), _1042602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042600), _1042604)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042602), _1042604))))], (31328 ^ _780478) ^ [_1364714, _1364716, _1364718, _1364720] : [_1364714 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1364716, _1364718), 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)), _1364720))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1364716), _1364714)))], (3888 ^ _780478) ^ [_838785, _838787, _838789, _838791, _838793, _838795, _838797, _838799, _838801, _838803, _838805, _838807, _838809, _838811] : [-(c_New__Random__Sequence_Oneg__decr__bind(_838811, _838807, _838803, _838799, _838795, _838791, _838787) = c_New__Random__Sequence_Oneg__decr__bind(_838809, _838805, _838801, _838797, _838793, _838789, _838785)), _838811 = _838809, _838807 = _838805, _838803 = _838801, _838799 = _838797, _838795 = _838793, _838791 = _838789, _838787 = _838785], (18672 ^ _780478) ^ [_1131140, _1131142, _1131144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1131140), _1131142)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1131142), _1131140))), _1131144) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1131142)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1131140), _1131144)))], (51853 ^ _780478) ^ [_1828789, _1828791] : [class_Groups_Ominus(_1828789), -(class_Groups_Ominus(tc_fun(_1828791, _1828789)))], (4472 ^ _780478) ^ [_848335, _848337, _848339, _848341, _848343, _848345] : [-(c_Lazy__Sequence_Oanamorph(_848345, _848341, _848337) = c_Lazy__Sequence_Oanamorph(_848343, _848339, _848335)), _848345 = _848343, _848341 = _848339, _848337 = _848335], (30055 ^ _780478) ^ [_1338084, _1338086, _1338088] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338084), _1338086)), _1338088) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338084), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1338086), _1338088))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338084), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338086, _1338088))), _1338088)))], (43955 ^ _780478) ^ [_1659819, _1659821, _1659823, _1659825] : [-(_1659819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1659821), _1659819), hAPP(hAPP(c_List_Olist_OCons(_1659821), _1659823), _1659825)) = hAPP(hAPP(c_List_Odrop(_1659821), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1659819), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1659825))], (33492 ^ _780478) ^ [_1412457] : [-(c_Int_Osucc(_1412457) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1412457), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (13380 ^ _780478) ^ [_1018783] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018783, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1018783, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1018783, tc_HOL_Obool)))], (43961 ^ _780478) ^ [_1659891, _1659893, _1659895, _1659897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1659891), _1659893)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659895)), _1659897))), -(hAPP(hAPP(c_List_Onth(_1659895), hAPP(hAPP(c_List_Odrop(_1659895), _1659891), _1659897)), _1659893) = hAPP(hAPP(c_List_Onth(_1659895), _1659897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1659891), _1659893)))], (46955 ^ _780478) ^ [_1724893, _1724895] : [_1724895 = c_List_Olist_ONil(_1724893), -(c_List_Olist_ONil(_1724893) = hAPP(c_List_Orev(_1724893), _1724895))], (22887 ^ _780478) ^ [_1206497] : [class_Rings_Osemiring__1(_1206497), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206497), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1206497))], (37497 ^ _780478) ^ [_1495642, _1495644] : [c_Equiv__Relations_Oequivp(_1495642, hAPP(hAPP(c_COMBC(_1495642, tc_fun(tc_prod(_1495642, _1495642), tc_HOL_Obool), tc_fun(_1495642, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495642, tc_fun(tc_fun(tc_prod(_1495642, _1495642), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1495642, _1495642), tc_HOL_Obool), tc_fun(_1495642, tc_HOL_Obool)), _1495642), c_COMBC(_1495642, tc_fun(tc_prod(_1495642, _1495642), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1495642, tc_prod(_1495642, _1495642)), tc_fun(_1495642, tc_fun(tc_fun(tc_prod(_1495642, _1495642), tc_HOL_Obool), tc_HOL_Obool)), _1495642), hAPP(c_COMBB(tc_prod(_1495642, _1495642), tc_fun(tc_fun(tc_prod(_1495642, _1495642), tc_HOL_Obool), tc_HOL_Obool), _1495642), c_member(tc_prod(_1495642, _1495642)))), c_Product__Type_OPair(_1495642, _1495642)))), _1495644)), -(c_Equiv__Relations_Oequiv(_1495642, c_Orderings_Otop__class_Otop(tc_fun(_1495642, tc_HOL_Obool)), _1495644))], (52105 ^ _780478) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (16046 ^ _780478) ^ [_1070926, _1070928] : [class_Lattices_Obounded__lattice__top(_1070926), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070926), _1070928), c_Orderings_Otop__class_Otop(_1070926)) = _1070928)], (52273 ^ _780478) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52141 ^ _780478) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (12882 ^ _780478) ^ [_1008738, _1008740, _1008742, _1008744] : [class_Lattices_Osemilattice__sup(_1008738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008738), _1008740), _1008742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008738), _1008740), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1008738), _1008742), _1008744))))], (12037 ^ _780478) ^ [_991948, _991950, _991952] : [class_Orderings_Olinorder(_991948), hBOOL(hAPP(c_Finite__Set_Ofinite(_991948), _991950)), -(c_Big__Operators_Olattice_OInf__fin(_991948, c_Orderings_Oord__class_Omin(_991948), hAPP(hAPP(c_Set_Oinsert(_991948), _991952), _991950)) = hAPP(hAPP(c_Finite__Set_Ofold(_991948, _991948, c_Orderings_Oord__class_Omin(_991948)), _991952), _991950))], (40127 ^ _780478) ^ [_1563505, _1563507, _1563509, _1563511, _1563513] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1563505, _1563507, _1563509), _1563511), _1563513)), 40130 ^ _780478 : [(40133 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1563509, _1563513)))], (40131 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1563507, _1563511), _1563513)))]]], (37949 ^ _780478) ^ [_1507321, _1507323, _1507325, _1507327, _1507329, _1507331, _1507333] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507321, _1507323, _1507325), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1507327, tc_fun(tc_prod(_1507321, _1507323), tc_HOL_Obool)), _1507329), _1507331)), _1507333) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1507327, tc_fun(tc_prod(_1507321, _1507325), tc_HOL_Obool)), _1507329), hAPP(hAPP(c_COMBC(_1507327, tc_fun(tc_prod(_1507323, _1507325), tc_HOL_Obool), tc_fun(tc_prod(_1507321, _1507325), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1507321, _1507323), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1507323, _1507325), tc_HOL_Obool), tc_fun(tc_prod(_1507321, _1507325), tc_HOL_Obool)), _1507327), c_Relation_Orel__comp(_1507321, _1507323, _1507325)), _1507331)), _1507333)))], (44871 ^ _780478) ^ [_1679639, _1679641, _1679643, _1679645, _1679647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679639), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679641)), _1679643))), -(hAPP(hAPP(c_List_Onth(_1679645), hAPP(hAPP(c_List_Omap(_1679641, _1679645), _1679647), _1679643)), _1679639) = hAPP(_1679647, hAPP(hAPP(c_List_Onth(_1679641), _1679643), _1679639)))], (51923 ^ _780478) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (44177 ^ _780478) ^ [_1664591, _1664593, _1664595] : [-(hAPP(c_List_Orotate(_1664591, hAPP(c_Nat_OSuc, _1664593)), _1664595) = hAPP(c_List_Orotate1(_1664591), hAPP(c_List_Orotate(_1664591, _1664593), _1664595)))], (46899 ^ _780478) ^ [_1723582, _1723584, _1723586] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1723582), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1723582))), _1723584))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723586), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1723582))), _1723584))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1723582), _1723582), hAPP(hAPP(c_COMBC(tc_List_Olist(_1723582), tc_Nat_Onat, _1723582), c_List_Onth(_1723582)), _1723586)), hAPP(c_List_Ofilter(tc_List_Olist(_1723582), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1723582)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1723586)), c_Nat_Osize__class_Osize(tc_List_Olist(_1723582)))), c_List_Otranspose(_1723582, _1723584))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1723582)), _1723584), _1723586))], (27423 ^ _780478) ^ [_1287860, _1287862] : [c_Nat__Transfer_Ois__nat(_1287860), c_Nat__Transfer_Ois__nat(_1287862), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1287860), _1287862)))], (12860 ^ _780478) ^ [_1008358, _1008360, _1008362, _1008364] : [class_Lattices_Osemilattice__sup(_1008358), 12863 ^ _780478 : [(12872 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008358), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1008358), _1008360), _1008362)), _1008364))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008358), _1008360), _1008364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008358), _1008362), _1008364))], (12864 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008358), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1008358), _1008360), _1008362)), _1008364)), 12867 ^ _780478 : [(12870 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008358), _1008362), _1008364)))], (12868 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008358), _1008360), _1008364)))]]]]], (49756 ^ _780478) ^ [_1786744, _1786746] : [c_Relation_Osym(_1786744, _1786746), -(c_Relation_Osym(_1786744, hAPP(c_Relation_Oconverse(_1786744, _1786744), _1786746)))], (32300 ^ _780478) ^ [_1390775, _1390777, _1390779] : [class_Int_Onumber__ring(_1390775), -(hAPP(c_Int_Onumber__class_Onumber__of(_1390775), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390777), _1390779)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390775), hAPP(c_Int_Onumber__class_Onumber__of(_1390775), _1390777)), hAPP(c_Int_Onumber__class_Onumber__of(_1390775), _1390779)))], (10169 ^ _780478) ^ [_957104, _957106, _957108] : [class_Groups_Olinordered__ab__group__add(_957104), -(hAPP(c_Groups_Ouminus__class_Ouminus(_957104), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957104), _957106), _957108)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_957104), hAPP(c_Groups_Ouminus__class_Ouminus(_957104), _957106)), hAPP(c_Groups_Ouminus__class_Ouminus(_957104), _957108)))], (10987 ^ _780478) ^ [_972105, _972107, _972109] : [class_Groups_Oab__group__add(_972105), -(hAPP(c_Groups_Ouminus__class_Ouminus(_972105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972105), _972107), _972109)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972105), hAPP(c_Groups_Ouminus__class_Ouminus(_972105), _972107)), hAPP(c_Groups_Ouminus__class_Ouminus(_972105), _972109)))], (27802 ^ _780478) ^ [_1294778, _1294780] : [27804 ^ _780478 : [(27807 ^ _780478) ^ [] : [hBOOL(hAPP(_1294780, 27803 ^ [_1294778, _1294780]))], (27805 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27803 ^ [_1294778, _1294780]), _1294778)))]], 27808 ^ _780478 : [(27809 ^ _780478) ^ [_1294929] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1294929), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1294778))), -(hBOOL(hAPP(_1294780, _1294929)))]]], (3146 ^ _780478) ^ [_827226, _827228, _827230, _827232] : [-(c_Finite__Set_Ofold1(_827232, _827228) = c_Finite__Set_Ofold1(_827230, _827226)), _827232 = _827230, _827228 = _827226], (28088 ^ _780478) ^ [_1300037, _1300039, _1300041] : [class_Orderings_Oorder(_1300037), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300037, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1300037), _1300039)), c_SetInterval_Oord__class_OatLeastAtMost(_1300037, _1300039, _1300041)) = c_Orderings_Obot__class_Obot(tc_fun(_1300037, tc_HOL_Obool)))], (6228 ^ _780478) ^ [_880337, _880339, _880341, _880343, _880345, _880347] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_880337, _880339, _880341, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_880337), _880343), _880345), _880347)) = hAPP(hAPP(hAPP(_880341, _880343), _880345), _880347))], (20114 ^ _780478) ^ [_1155647, _1155649, _1155651, _1155653, _1155655] : [class_Rings_Oordered__semiring(_1155647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155647), _1155649), _1155651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155647), _1155653), _1155655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155647), c_Groups_Ozero__class_Ozero(_1155647)), _1155649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155647), c_Groups_Ozero__class_Ozero(_1155647)), _1155653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155647), _1155649), _1155653)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155647), _1155651), _1155655))))], (35245 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (7174 ^ _780478) ^ [_900166, _900168, _900170] : [class_Orderings_Oorder(_900166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900166), _900168), _900170)), 7181 ^ _780478 : [(7188 ^ _780478) ^ [] : [_900170 = _900168, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900166), _900170), _900168)))], (7182 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900166), _900170), _900168)), -(_900170 = _900168)]]], (41541 ^ _780478) ^ [_1598716, _1598718] : [-(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)))), _1598716)) = 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)))), _1598718))), 41543 ^ _780478 : [(41546 ^ _780478) ^ [] : [41547 ^ _780478 : [(41550 ^ _780478) ^ [] : [hBOOL(hAPP(_1598718, 41542 ^ [_1598716, _1598718]))], (41548 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1598716, 41542 ^ [_1598716, _1598718])))]], 41551 ^ _780478 : [(41554 ^ _780478) ^ [] : [hBOOL(hAPP(_1598716, 41542 ^ [_1598716, _1598718]))], (41552 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1598718, 41542 ^ [_1598716, _1598718])))]]], (41544 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 41542 ^ [_1598716, _1598718])))]]], (7738 ^ _780478) ^ [_911208, _911210, _911212, _911214] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911208, _911210, _911212, _911214, c_Orderings_Obot__class_Obot(tc_fun(_911208, tc_HOL_Obool))), _911214)))], (28478 ^ _780478) ^ [_1307512, _1307514, _1307516, _1307518] : [class_Orderings_Olinorder(_1307512), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307512, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1307512), _1307514)), c_SetInterval_Oord__class_OatLeastAtMost(_1307512, _1307516, _1307518)) = c_SetInterval_Oord__class_OatLeastAtMost(_1307512, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1307512), _1307514), _1307516), _1307518))], (26898 ^ _780478) ^ [_1278885, _1278887, _1278889, _1278891, _1278893] : [class_Fields_Ofield(_1278885), -(_1278887 = c_Groups_Ozero__class_Ozero(_1278885)), -(_1278889 = c_Groups_Ozero__class_Ozero(_1278885)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278885), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278885), _1278891), _1278887)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278885), _1278893), _1278889)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278885), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278885), _1278891), _1278889)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278885), _1278893), _1278887))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278885), _1278887), _1278889)))], (48321 ^ _780478) ^ [_1754389, _1754391, _1754393, _1754395] : [-(c_List_Olist__ex1(_1754389, _1754391, hAPP(hAPP(c_List_Olist_OCons(_1754389), _1754393), _1754395))), 48324 ^ _780478 : [(48327 ^ _780478) ^ [] : [c_List_Olist__all(_1754389, hAPP(hAPP(c_COMBS(_1754389, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1754389), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1754389), c_fNot), _1754391))), hAPP(c_fequal, _1754393)), _1754395)], (48325 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1754391, _1754393)))]], 48328 ^ _780478 : [(48331 ^ _780478) ^ [] : [c_List_Olist__ex1(_1754389, _1754391, _1754395)], (48329 ^ _780478) ^ [] : [hBOOL(hAPP(_1754391, _1754393))]]], (28390 ^ _780478) ^ [_1305855, _1305857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1305855)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1305855, _1305857)))], (6690 ^ _780478) ^ [_890769, _890771] : [c_Com_Ocom_OSemi(_890769, _890771) = c_Com_Ocom_OSKIP], (14403 ^ _780478) ^ [_1037630, _1037632] : [14404 ^ _780478 : [(14407 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037632), _1037630))], (14405 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037630), _1037632))]], _1037630 = _1037632], (30963 ^ _780478) ^ [_1355864, _1355866] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1355864, tc_HOL_Obool), _1355866) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1355864, tc_HOL_Obool), tc_fun(_1355864, tc_HOL_Obool)), _1355866), c_COMBI(tc_fun(_1355864, tc_HOL_Obool))))], (7150 ^ _780478) ^ [_899782, _899784, _899786, _899788] : [class_Orderings_Oord(_899782), _899784 = _899786, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899782), _899786), _899788)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899782), _899784), _899788)))], (30867 ^ _780478) ^ [_1354063, _1354065] : [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), _1354063)), _1354065))), _1354063 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1354065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41854 ^ _780478) ^ [_1607799, _1607801, _1607803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1607799, _1607799), tc_HOL_Obool)), _1607801), _1607803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1607799), tc_List_Olist(_1607799)), tc_HOL_Obool)), c_List_Olistrel1(_1607799, _1607801)), c_List_Olistrel1(_1607799, _1607803))))], (2616 ^ _780478) ^ [_819021, _819023, _819025, _819027] : [-(c_Nitpick_Onumber__of__frac(_819027, _819023) = c_Nitpick_Onumber__of__frac(_819025, _819021)), _819027 = _819025, _819023 = _819021], (21085 ^ _780478) ^ [_1172490, _1172492] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1172490), _1172492) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21088 ^ _780478 : [(21091 ^ _780478) ^ [] : [-(_1172492 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21089 ^ _780478) ^ [] : [-(_1172490 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (42947 ^ _780478) ^ [_1637296, _1637298, _1637300, _1637302] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1637296) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1637298), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1637296)), hAPP(hAPP(c_List_Olist_OCons(_1637298), _1637300), _1637302)) = hAPP(hAPP(c_List_Olist_OCons(_1637298), _1637300), hAPP(hAPP(c_List_Otake(_1637298), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1637296)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1637302)))], (26976 ^ _780478) ^ [_1280269, _1280271, _1280273, _1280275] : [class_Fields_Ofield(_1280269), -(_1280271 = c_Groups_Ozero__class_Ozero(_1280269)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1280269), _1280273), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280269), _1280275), _1280271)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280269), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1280269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1280269), _1280271), _1280273)), _1280275)), _1280271))], (49877 ^ _780478) ^ [_1788573, _1788575, _1788577, _1788579, _1788581] : [c_Equiv__Relations_Opart__equivp(_1788573, _1788575), hBOOL(hAPP(hAPP(_1788575, _1788577), _1788579)), hBOOL(hAPP(hAPP(_1788575, _1788579), _1788581)), -(hBOOL(hAPP(hAPP(_1788575, _1788577), _1788581)))], (45095 ^ _780478) ^ [_1684402, _1684404, _1684406] : [-(c_List_Olist_Olist__size(_1684402, _1684404, _1684406) = 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(_1684402, tc_Nat_Onat), _1684404), _1684406))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684402)), _1684406)))], (18874 ^ _780478) ^ [_1134824, _1134826, _1134828] : [class_Lattices_Olattice(_1134824), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134824), _1134826)), -(hBOOL(hAPP(hAPP(c_member(_1134824), _1134828), _1134826))), -(_1134826 = c_Orderings_Obot__class_Obot(tc_fun(_1134824, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1134824, hAPP(hAPP(c_Set_Oinsert(_1134824), _1134828), _1134826)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1134824), _1134828), c_Big__Operators_Olattice__class_OInf__fin(_1134824, _1134826)))], (47071 ^ _780478) ^ [_1727413, _1727415, _1727417, _1727419] : [_1727415 = hAPP(hAPP(c_List_Oappend(_1727413), hAPP(c_List_Orev(_1727413), _1727419)), hAPP(hAPP(c_List_Olist_OCons(_1727413), _1727417), c_List_Olist_ONil(_1727413))), -(hAPP(c_List_Orev(_1727413), _1727415) = hAPP(hAPP(c_List_Olist_OCons(_1727413), _1727417), _1727419))], (22604 ^ _780478) ^ [_1201403, _1201405] : [class_Rings_Oring__1(_1201403), -(hBOOL(hAPP(hAPP(c_member(_1201403), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1201403), _1201405)), c_Int_Oring__1__class_OInts(_1201403))))], (41642 ^ _780478) ^ [_1601176, _1601178, _1601180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1601176), c_Nitpick_Oplus__frac(_1601176, _1601178, c_Nitpick_Ouminus__frac(_1601176, _1601180)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1601176, _1601178, _1601180))], (31924 ^ _780478) ^ [_1383397, _1383399, _1383401] : [31926 ^ _780478 : [(31929 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1383397), _1383401), 31925 ^ [_1383397, _1383399, _1383401]))], (31927 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1383397, tc_HOL_Obool)), 31925 ^ [_1383397, _1383399, _1383401]), _1383399)))]], -(hBOOL(hAPP(hAPP(c_member(_1383397), _1383401), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1383397, tc_HOL_Obool), _1383399))))], (47059 ^ _780478) ^ [_1727085, _1727087] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727085)), hAPP(c_List_Orev(_1727085), _1727087)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727085)), _1727087))], (28112 ^ _780478) ^ [_1300545, _1300547, _1300549] : [class_Orderings_Oorder(_1300545), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300545, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300545, _1300547, _1300549)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1300545), _1300549)) = c_Orderings_Obot__class_Obot(tc_fun(_1300545, tc_HOL_Obool)))], (13430 ^ _780478) ^ [_1019835, _1019837, _1019839, _1019841, _1019843, _1019845, _1019847] : [c_Finite__Set_Ofolding__image__simple(_1019835, _1019837, _1019839, _1019841, _1019843, _1019845), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019837), _1019847)), -(hAPP(_1019845, _1019847) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1019835, _1019837, _1019839), _1019843), _1019841), _1019847))], (52375 ^ _780478) ^ [_1834125, _1834127] : [hBOOL(hAPP(hAPP(c_fconj, _1834125), _1834127)), -(hBOOL(_1834125))], (33290 ^ _780478) ^ [_1409331, _1409333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1409331), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409333)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409331)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409333))], (47302 ^ _780478) ^ [_1732259] : [c_List_Onat__list(_1732259), -(c_List_Oembed__list(c_List_Oreturn__list(_1732259)) = _1732259)], (16665 ^ _780478) ^ [_1085241, _1085243, _1085245, _1085247, _1085249] : [class_Groups_Ocomm__monoid__mult(_1085241), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085243), _1085245)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085243), _1085247)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085241), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1085243, _1085241), _1085249), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1085243, tc_HOL_Obool)), _1085245), _1085247))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1085243, _1085241), _1085249), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1085243, tc_HOL_Obool)), _1085245), _1085247))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1085241), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1085243, _1085241), _1085249), _1085245)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1085243, _1085241), _1085249), _1085247)))], (9776 ^ _780478) ^ [_949420, _949422, _949424, _949426] : [class_Rings_Ocomm__semiring(_949420), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949420), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949420), _949422), _949424)), _949426) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949420), _949422), _949426)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949420), _949424), _949426)))], (36870 ^ _780478) ^ [_1481754, _1481756, _1481758, _1481760, _1481762, _1481764] : [hAPP(c_Product__Type_Oapsnd(_1481754, _1481756, _1481758, _1481760), _1481762) = hAPP(c_Product__Type_Oapsnd(_1481754, _1481756, _1481758, _1481764), _1481762), -(hAPP(_1481760, hAPP(c_Product__Type_Osnd(_1481758, _1481754), _1481762)) = hAPP(_1481764, hAPP(c_Product__Type_Osnd(_1481758, _1481754), _1481762)))], (33068 ^ _780478) ^ [_1405436, _1405438] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405436), _1405438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405436)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405438))))], (39921 ^ _780478) ^ [_1558364, _1558366, _1558368, _1558370, _1558372, _1558374] : [c_Finite__Set_Ofolding(_1558364, _1558366, _1558368, _1558370), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558364), _1558372)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1558364), _1558374)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1558364, tc_HOL_Obool)), _1558372), _1558374) = c_Orderings_Obot__class_Obot(tc_fun(_1558364, tc_HOL_Obool)), -(hAPP(_1558370, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1558364, tc_HOL_Obool)), _1558372), _1558374)) = hAPP(c_Fun_Ocomp(_1558366, _1558366, _1558366, hAPP(_1558370, _1558372)), hAPP(_1558370, _1558374)))], (52009 ^ _780478) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (43231 ^ _780478) ^ [_1642458, _1642460] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1642458), tc_List_Olist(_1642458), c_List_Olistrel(_1642458, _1642460)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1642458)), c_List_Olist_ONil(_1642458)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1642458), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1642458)), c_List_Olist_ONil(_1642458)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1642458), tc_HOL_Obool))))], (11451 ^ _780478) ^ [_981146, _981148, _981150, _981152, _981154] : [class_Groups_Ocomm__monoid__mult(_981146), hBOOL(hAPP(c_Finite__Set_Ofinite(_981148), _981150)), -(hBOOL(hAPP(hAPP(c_member(_981148), _981152), _981150))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_981148, _981146), _981154), hAPP(hAPP(c_Set_Oinsert(_981148), _981152), _981150)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981146), hAPP(_981154, _981152)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_981148, _981146), _981154), _981150)))], (50796 ^ _780478) ^ [_1808083, _1808085, _1808087, _1808089, _1808091, _1808093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1808083, tc_HOL_Obool)), _1808085), _1808087)), 50802 ^ _780478 : [(50805 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1808089, tc_HOL_Obool)), hAPP(_1808091, 50801 ^ [_1808083, _1808085, _1808087, _1808089, _1808091, _1808093])), hAPP(_1808093, 50801 ^ [_1808083, _1808085, _1808087, _1808089, _1808091, _1808093])))], (50803 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808083), 50801 ^ [_1808083, _1808085, _1808087, _1808089, _1808091, _1808093]), _1808087)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1808089, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1808083, tc_fun(_1808089, tc_HOL_Obool)), _1808087), _1808091)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1808083, tc_fun(_1808089, tc_HOL_Obool)), _1808087), _1808093))))], (4216 ^ _780478) ^ [_844287, _844289] : [_844289 = _844287, -(c_List_Odrop(_844289) = c_List_Odrop(_844287))], (42692 ^ _780478) ^ [_1631465, _1631467, _1631469, _1631471] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1631465, tc_HOL_Obool)), hAPP(c_List_Oset(_1631465), hAPP(hAPP(c_List_Olist__update(_1631465, _1631467), _1631469), _1631471))), hAPP(hAPP(c_Set_Oinsert(_1631465), _1631471), hAPP(c_List_Oset(_1631465), _1631467)))))], (33448 ^ _780478) ^ [] : [-(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))))], (40931 ^ _780478) ^ [_1582332, _1582334, _1582336] : [-(hAPP(c_Relation_ORange(_1582332, _1582334), hAPP(c_Relation_Oconverse(_1582334, _1582332), _1582336)) = hAPP(c_Relation_ODomain(_1582334, _1582332), _1582336))], (34373 ^ _780478) ^ [_1428872] : [c_Int_OPls = _1428872, -(c_Int_OPls = c_Int_OBit0(_1428872))], (43514 ^ _780478) ^ [_1649179, _1649181, _1649183] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649179)), hAPP(hAPP(c_List_Oappend(_1649179), _1649181), _1649183)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649179)), _1649181)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649179)), _1649183)))], (16092 ^ _780478) ^ [_1071763, _1071765, _1071767, _1071769, _1071771] : [hBOOL(hAPP(hAPP(c_member(_1071763), hAPP(_1071765, _1071767)), _1071769)), -(hBOOL(hAPP(hAPP(c_member(_1071771), _1071767), hAPP(c_Set_Ovimage(_1071771, _1071763, _1071765), _1071769))))], (39161 ^ _780478) ^ [_1540310, _1540312, _1540314, _1540316, _1540318, _1540320] : [-(c_Product__Type_Omap__pair(_1540310, _1540312, _1540314, _1540316, _1540318, _1540320) = hAPP(c_Product__Type_Oprod_Oprod__case(_1540310, _1540314, tc_prod(_1540312, _1540316)), hAPP(hAPP(c_COMBC(_1540310, tc_fun(_1540314, _1540316), tc_fun(_1540314, tc_prod(_1540312, _1540316))), hAPP(hAPP(c_COMBB(tc_fun(_1540316, tc_prod(_1540312, _1540316)), tc_fun(tc_fun(_1540314, _1540316), tc_fun(_1540314, tc_prod(_1540312, _1540316))), _1540310), c_COMBB(_1540316, tc_prod(_1540312, _1540316), _1540314)), hAPP(hAPP(c_COMBB(_1540312, tc_fun(_1540316, tc_prod(_1540312, _1540316)), _1540310), c_Product__Type_OPair(_1540312, _1540316)), _1540318))), _1540320)))], (49082 ^ _780478) ^ [_1771275, _1771277, _1771279] : [c_List_Olist__ex(tc_Int_Oint, _1771275, c_List_Oupto(_1771277, _1771279)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1771275), _1771277, _1771279)], (45510 ^ _780478) ^ [_1693868, _1693870, _1693872] : [c_List_Olist__all2(_1693872, _1693872, c_fequal, _1693868, _1693870), -(_1693868 = _1693870)], (18369 ^ _780478) ^ [_1124087, _1124089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1124087), _1124089)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1124087), hAPP(c_Nat_OSuc, _1124089))))], (20708 ^ _780478) ^ [_1166426, _1166428] : [class_Groups_Oordered__ab__group__add(_1166426), 20711 ^ _780478 : [(20718 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166426), _1166428), c_Groups_Ozero__class_Ozero(_1166426))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166426), c_Groups_Ozero__class_Ozero(_1166426)), hAPP(c_Groups_Ouminus__class_Ouminus(_1166426), _1166428))))], (20712 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166426), c_Groups_Ozero__class_Ozero(_1166426)), hAPP(c_Groups_Ouminus__class_Ouminus(_1166426), _1166428))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166426), _1166428), c_Groups_Ozero__class_Ozero(_1166426))))]]], (13362 ^ _780478) ^ [_1018437, _1018439, _1018441] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018437, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018437, tc_HOL_Obool)), _1018439), _1018441)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1018437, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018437, tc_HOL_Obool)), _1018439)), _1018441))], (30123 ^ _780478) ^ [_1339470, _1339472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339470)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1339472)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1339470), hAPP(c_Int_Onat, _1339472)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1339470, _1339472)))], (46202 ^ _780478) ^ [_1710412, _1710414, _1710416, _1710418, _1710420, _1710422] : [-(c_List_Ofoldr(_1710412, _1710414, _1710416, hAPP(hAPP(c_List_Oappend(_1710412), _1710418), _1710420), _1710422) = c_List_Ofoldr(_1710412, _1710414, _1710416, _1710418, c_List_Ofoldr(_1710412, _1710414, _1710416, _1710420, _1710422)))], (51907 ^ _780478) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (50351 ^ _780478) ^ [_1799257, _1799259, _1799261, _1799263, _1799265, _1799267, _1799269, _1799271] : [c_Fun_Obij__betw(_1799257, _1799259, _1799261, _1799263, _1799265), c_Fun_Obij__betw(_1799259, _1799267, _1799269, _1799265, _1799271), -(c_Fun_Obij__betw(_1799257, _1799267, hAPP(c_Fun_Ocomp(_1799259, _1799267, _1799257, _1799269), _1799261), _1799263, _1799271))], (37249 ^ _780478) ^ [_1489270, _1489272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489270)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489272)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1489270), _1489272) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1489270, _1489272)))], (52003 ^ _780478) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (44937 ^ _780478) ^ [_1681101, _1681103, _1681105, _1681107] : [class_Groups_Ocomm__monoid__add(_1681101), hBOOL(hAPP(c_List_Odistinct(_1681103), _1681105)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1681101), hAPP(hAPP(c_List_Omap(_1681103, _1681101), _1681107), _1681105)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1681103, _1681101), _1681107), hAPP(c_List_Oset(_1681103), _1681105)))], (36864 ^ _780478) ^ [_1481592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1481592)), 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), _1481592)) = 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), _1481592))))))], (14697 ^ _780478) ^ [_1043404, _1043406, _1043408, _1043410, _1043412] : [class_Groups_Ocomm__monoid__mult(_1043404), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043406), _1043408)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1043404, _1043406, c_Groups_Otimes__class_Otimes(_1043404)), hAPP(hAPP(c_COMBS(_1043406, _1043404, _1043404), hAPP(hAPP(c_COMBB(_1043404, tc_fun(_1043404, _1043404), _1043406), c_Groups_Otimes__class_Otimes(_1043404)), _1043410)), _1043412)), c_Groups_Oone__class_Oone(_1043404)), _1043408) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043404), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1043404, _1043406, c_Groups_Otimes__class_Otimes(_1043404)), _1043410), c_Groups_Oone__class_Oone(_1043404)), _1043408)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1043404, _1043406, c_Groups_Otimes__class_Otimes(_1043404)), _1043412), c_Groups_Oone__class_Oone(_1043404)), _1043408)))], (49135 ^ _780478) ^ [_1772573, _1772575, _1772577, _1772579, _1772581, _1772583, _1772585] : [hBOOL(hAPP(hAPP(_1772573, hAPP(c_Product__Type_Osnd(_1772575, _1772577), _1772579)), hAPP(c_Product__Type_Ofst(_1772575, _1772577), _1772579))), 49142 ^ _780478 : [(49145 ^ _780478) ^ [] : [hBOOL(hAPP(_1772581, hAPP(hAPP(_1772583, 49140 ^ [_1772573, _1772575, _1772577, _1772579, _1772581, _1772583, _1772585]), 49141 ^ [_1772573, _1772575, _1772577, _1772579, _1772581, _1772583, _1772585])))], (49143 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1772573, 49141 ^ [_1772573, _1772575, _1772577, _1772579, _1772581, _1772583, _1772585]), 49140 ^ [_1772573, _1772575, _1772577, _1772579, _1772581, _1772583, _1772585])))]], -(hBOOL(hAPP(_1772581, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1772575, _1772577, _1772585), _1772583), _1772579))))], (29013 ^ _780478) ^ [_1318203, _1318205, _1318207] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1318203, tc_HOL_Obool)), _1318205), hAPP(c_Set_OPow(_1318203), _1318207))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318203, tc_HOL_Obool)), _1318205), _1318207)))], (52031 ^ _780478) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (44913 ^ _780478) ^ [_1680543, _1680545, _1680547, _1680549] : [c_Fun_Oinj__on(_1680543, _1680545, _1680547, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1680543, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1680543), tc_fun(_1680543, tc_HOL_Obool), c_List_Oset(_1680543)), _1680549))), -(c_Fun_Oinj__on(tc_List_Olist(_1680543), tc_List_Olist(_1680545), hAPP(c_List_Omap(_1680543, _1680545), _1680547), _1680549))], (5825 ^ _780478) ^ [_872740] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_872740), c_Orderings_Obot__class_Obot(tc_fun(_872740, tc_HOL_Obool)))))], (36353 ^ _780478) ^ [_1472072, _1472074, _1472076, _1472078] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1472072, _1472074, _1472076), hAPP(hAPP(c_COMBB(tc_fun(_1472074, tc_prod(_1472072, _1472074)), tc_fun(_1472074, _1472076), _1472072), hAPP(c_COMBB(tc_prod(_1472072, _1472074), _1472076, _1472074), _1472078)), c_Product__Type_OPair(_1472072, _1472074))) = _1472078)], (36678 ^ _780478) ^ [_1477821, _1477823] : [-(c_Divides_Opdivmod(_1477821, _1477823) = 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), _1477821)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477823))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477821), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1477823))))], (34001 ^ _780478) ^ [_1422511] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1422511)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422511), c_Int_OPls)))], (8724 ^ _780478) ^ [_931346, _931348, _931350, _931352] : [class_Orderings_Oorder(_931346), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931346), _931348), _931350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931346), _931352), _931348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931346), _931352), _931350)))], (15657 ^ _780478) ^ [_1063263, _1063265] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063263, tc_HOL_Obool)), _1063265), _1063265) = _1063265)], (40261 ^ _780478) ^ [_1566503, _1566505, _1566507, _1566509] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1566503, tc_HOL_Obool), tc_fun(_1566503, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1566503, tc_HOL_Obool), tc_fun(_1566503, tc_HOL_Obool)), _1566505), _1566507)), c_Wellfounded_Omax__ext(_1566503, _1566509))), 40264 ^ _780478 : [(40267 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1566503), _1566507)))], (40269 ^ _780478) ^ [] : [_1566507 = c_Orderings_Obot__class_Obot(tc_fun(_1566503, tc_HOL_Obool))], (40271 ^ _780478) ^ [_1566797] : [hBOOL(hAPP(hAPP(c_member(_1566503), _1566797), _1566505)), 40275 ^ _780478 : [(40278 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566503, _1566503)), hAPP(hAPP(c_Product__Type_OPair(_1566503, _1566503), _1566797), 40274 ^ [_1566503, _1566505, _1566507, _1566509, _1566797])), _1566509)))], (40276 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566503), 40274 ^ [_1566503, _1566505, _1566507, _1566509, _1566797]), _1566507)))]]], (40265 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1566503), _1566505)))]]], (46252 ^ _780478) ^ [_1711656, _1711658, _1711660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711656), _1711658)), -(c_List_Oupt(_1711656, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1711658), _1711660)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1711656, _1711658)), c_List_Oupt(_1711658, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1711658), _1711660))))], (22899 ^ _780478) ^ [_1206709, _1206711, _1206713, _1206715] : [class_Rings_Osemiring__1(_1206709), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206709), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1206711, tc_Nat_Onat), _1206713), _1206715)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1206711, _1206709), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1206709, _1206711), c_Nat_Osemiring__1__class_Oof__nat(_1206709)), _1206713)), _1206715))], (7992 ^ _780478) ^ [_916385, _916387, _916389, _916391, _916393, _916395] : [c_Finite__Set_Ofun__left__comm(_916385, _916387, _916389), hBOOL(hAPP(c_Finite__Set_Ofinite(_916385), _916391)), -(hAPP(hAPP(c_Finite__Set_Ofold(_916385, _916387, _916389), _916393), hAPP(hAPP(c_Set_Oinsert(_916385), _916395), _916391)) = hAPP(hAPP(_916389, _916395), hAPP(hAPP(c_Finite__Set_Ofold(_916385, _916387, _916389), _916393), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916385, tc_HOL_Obool)), _916391), hAPP(hAPP(c_Set_Oinsert(_916385), _916395), c_Orderings_Obot__class_Obot(tc_fun(_916385, tc_HOL_Obool)))))))], (27166 ^ _780478) ^ [_1283717] : [27168 ^ _780478 : [(27171 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27167 ^ [_1283717]))], (27169 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 27167 ^ [_1283717]), _1283717)))]], -(c_Nat__Transfer_Onat__set(_1283717))], (3864 ^ _780478) ^ [_838445, _838447] : [_838447 = _838445, -(c_Enum_Oenum__class_Oenum__all(_838447) = c_Enum_Oenum__class_Oenum__all(_838445))], (40314 ^ _780478) ^ [_1567916, _1567918, _1567920, _1567922, _1567924, _1567926, _1567928, _1567930] : [class_Groups_Ocomm__monoid__add(_1567916), class_Orderings_Oord(_1567918), _1567920 = _1567922, _1567924 = _1567926, 40332 ^ _780478 : [(40337 ^ _780478) ^ [] : [hAPP(_1567928, 40331 ^ [_1567916, _1567918, _1567920, _1567922, _1567924, _1567926, _1567928, _1567930]) = hAPP(_1567930, 40331 ^ [_1567916, _1567918, _1567920, _1567922, _1567924, _1567926, _1567928, _1567930])], (40335 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1567918), 40331 ^ [_1567916, _1567918, _1567920, _1567922, _1567924, _1567926, _1567928, _1567930]), _1567926)))], (40333 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1567918), _1567922), 40331 ^ [_1567916, _1567918, _1567920, _1567922, _1567924, _1567926, _1567928, _1567930])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1567918, _1567916), _1567928), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1567918, _1567920), _1567924)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1567918, _1567916), _1567930), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1567918, _1567922), _1567926)))], (9969 ^ _780478) ^ [_953744, _953746, _953748] : [class_Orderings_Olinorder(_953744), hBOOL(hAPP(c_Finite__Set_Ofinite(_953744), _953746)), hBOOL(hAPP(hAPP(c_member(_953744), _953748), _953746)), 9980 ^ _780478 : [(9987 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953744, tc_HOL_Obool)), _953746), hAPP(hAPP(c_Set_Oinsert(_953744), _953748), c_Orderings_Obot__class_Obot(tc_fun(_953744, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_953744, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_953744, _953746) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_953744), _953748), c_Big__Operators_Olinorder__class_OMax(_953744, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953744, tc_HOL_Obool)), _953746), hAPP(hAPP(c_Set_Oinsert(_953744), _953748), c_Orderings_Obot__class_Obot(tc_fun(_953744, tc_HOL_Obool)))))))], (9981 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953744, tc_HOL_Obool)), _953746), hAPP(hAPP(c_Set_Oinsert(_953744), _953748), c_Orderings_Obot__class_Obot(tc_fun(_953744, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_953744, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_953744, _953746) = _953748)]]], (37227 ^ _780478) ^ [_1488707, _1488709, _1488711, _1488713, _1488715] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1488707, _1488709, _1488711), _1488713), _1488715) = hAPP(hAPP(_1488713, hAPP(c_Product__Type_Ofst(_1488707, _1488709), _1488715)), hAPP(c_Product__Type_Osnd(_1488707, _1488709), _1488715)))], (47429 ^ _780478) ^ [_1734967, _1734969, _1734971, _1734973, _1734975] : [class_Groups_Omonoid__add(_1734967), 47435 ^ _780478 : [(47440 ^ _780478) ^ [] : [hAPP(_1734975, 47434 ^ [_1734967, _1734969, _1734971, _1734973, _1734975]) = c_Groups_Ozero__class_Ozero(_1734967)], (47438 ^ _780478) ^ [] : [hBOOL(hAPP(_1734973, 47434 ^ [_1734967, _1734969, _1734971, _1734973, _1734975]))], (47436 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734969), 47434 ^ [_1734967, _1734969, _1734971, _1734973, _1734975]), hAPP(c_List_Oset(_1734969), _1734971))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1734967), hAPP(hAPP(c_List_Omap(_1734969, _1734967), _1734975), hAPP(c_List_Ofilter(_1734969, _1734973), _1734971))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1734967), hAPP(hAPP(c_List_Omap(_1734969, _1734967), _1734975), _1734971)))], (38837 ^ _780478) ^ [_1530676, _1530678, _1530680, _1530682] : [38838 ^ _780478 : [(38839 ^ _780478) ^ [_1530730] : [hBOOL(hAPP(hAPP(_1530680, _1530682), _1530730))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1530676, _1530678, _1530680), _1530682)))], (47756 ^ _780478) ^ [_1742459, _1742461, _1742463, _1742465] : [47758 ^ _780478 : [(47761 ^ _780478) ^ [] : [hBOOL(hAPP(_1742463, 47757 ^ [_1742459, _1742461, _1742463, _1742465]))], (47759 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742459), 47757 ^ [_1742459, _1742461, _1742463, _1742465]), hAPP(c_List_Oset(_1742459), _1742461))))]], -(c_List_OdropWhile(_1742459, _1742463, hAPP(hAPP(c_List_Oappend(_1742459), _1742461), _1742465)) = c_List_OdropWhile(_1742459, _1742463, _1742465))], (14279 ^ _780478) ^ [_1035593, _1035595] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035593), _1035595))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035593), _1035595)), -(_1035593 = _1035595)], (49399 ^ _780478) ^ [_1779696, _1779698, _1779700, _1779702] : [class_Complete__Lattice_Ocomplete__lattice(_1779696), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1779698, _1779696), _1779700), _1779702) = c_Complete__Lattice_OInf__class_OInf(_1779696, hAPP(c_Set_OCollect(_1779696), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779698, _1779696), tc_HOL_Obool), tc_HOL_Obool, _1779696), c_HOL_OEx(tc_fun(_1779698, _1779696))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779698, _1779696), tc_HOL_Obool), tc_fun(tc_fun(_1779698, _1779696), tc_HOL_Obool), _1779696), hAPP(c_COMBS(tc_fun(_1779698, _1779696), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1779698, _1779696)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1779698, _1779696), tc_fun(tc_fun(_1779698, _1779696), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1779698, _1779696))), _1779700)))), hAPP(hAPP(c_COMBC(_1779696, tc_fun(tc_fun(_1779698, _1779696), _1779696), tc_fun(tc_fun(_1779698, _1779696), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1779696, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1779698, _1779696), _1779696), tc_fun(tc_fun(_1779698, _1779696), tc_HOL_Obool)), _1779696), c_COMBB(_1779696, tc_HOL_Obool, tc_fun(_1779698, _1779696))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1779698, _1779696), _1779698, _1779696), c_COMBI(tc_fun(_1779698, _1779696))), _1779702)))))))], (41648 ^ _780478) ^ [_1601311, _1601313, _1601315] : [c_Nitpick_Oless__eq__frac(_1601311, _1601313, _1601315), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1601311), c_Nitpick_Oplus__frac(_1601311, _1601313, c_Nitpick_Ouminus__frac(_1601311, _1601315)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (38537 ^ _780478) ^ [_1521639, _1521641] : [-(hAPP(c_Relation_ORange(_1521639, _1521641), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1521639, _1521641), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1521641, tc_HOL_Obool)))], (24323 ^ _780478) ^ [_1232773, _1232775] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232773), _1232775) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24324 ^ _780478 : [(24333 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232773), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232775), _1232773))], (24327 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232773)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1232773), _1232775))], (24325 ^ _780478) ^ [] : [_1232775 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (19726 ^ _780478) ^ [_1148627, _1148629, _1148631] : [class_Rings_Olinordered__ring__strict(_1148627), 19729 ^ _780478 : [(19738 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148627), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148627), _1148629), _1148629)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148627), _1148631), _1148631))), c_Groups_Ozero__class_Ozero(_1148627)))), _1148629 = c_Groups_Ozero__class_Ozero(_1148627), _1148631 = c_Groups_Ozero__class_Ozero(_1148627)], (19730 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148627), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148627), _1148629), _1148629)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148627), _1148631), _1148631))), c_Groups_Ozero__class_Ozero(_1148627))), 19733 ^ _780478 : [(19736 ^ _780478) ^ [] : [-(_1148631 = c_Groups_Ozero__class_Ozero(_1148627))], (19734 ^ _780478) ^ [] : [-(_1148629 = c_Groups_Ozero__class_Ozero(_1148627))]]]]], (47091 ^ _780478) ^ [_1727725, _1727727] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1727725), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1727725))), c_List_Otranspose(_1727725, _1727727)))))], (37879 ^ _780478) ^ [_1504570, _1504572, _1504574, _1504576] : [-(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), _1504570), _1504572)), 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), _1504574), _1504576)), 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), _1504570), _1504574)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504572), _1504576))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (45673 ^ _780478) ^ [_1697482, _1697484, _1697486, _1697488] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1697482)), _1697484), hAPP(c_List_Oset(tc_List_Olist(_1697482)), c_Enum_On__lists(_1697482, _1697486, _1697488)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697482)), _1697484) = _1697486)], (13092 ^ _780478) ^ [_1012494, _1012496, _1012498] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1012494), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012494, tc_HOL_Obool)), _1012496), _1012498))), 13095 ^ _780478 : [(13098 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012494), _1012498)))], (13096 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1012494), _1012496)))]]], (42738 ^ _780478) ^ [_1632401, _1632403] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632401)), c_List_Obutlast(_1632401, _1632403)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632401)), _1632403)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (17440 ^ _780478) ^ [_1103847, _1103849, _1103851, _1103853, _1103855, _1103857] : [class_Complete__Lattice_Ocomplete__lattice(_1103847), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103849, tc_fun(_1103851, _1103847)), _1103853), _1103855), _1103857) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103849, _1103847), _1103853), hAPP(hAPP(c_COMBC(_1103849, _1103851, _1103847), _1103855), _1103857)))], (16386 ^ _780478) ^ [_1078777, _1078779, _1078781, _1078783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1078777, tc_HOL_Obool)), _1078783), _1078779)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078777, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078777, tc_HOL_Obool)), _1078779), _1078781)), _1078783) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078777, tc_HOL_Obool)), _1078779), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078777, tc_HOL_Obool)), _1078781), _1078783)))], (25657 ^ _780478) ^ [_1256506, _1256508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256506)), _1256508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1256506), hAPP(c_Int_Onat, _1256508))))], (50277 ^ _780478) ^ [_1797561, _1797563, _1797565, _1797567, _1797569, _1797571] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1797561, _1797563, _1797565, _1797567), _1797569), _1797571) = hAPP(_1797567, hAPP(hAPP(c_Product__Type_OPair(_1797561, _1797563), _1797569), _1797571)))], (13190 ^ _780478) ^ [_1014646, _1014648, _1014650, _1014652, _1014654] : [c_Fun_Oinj__on(_1014646, _1014648, _1014650, c_Orderings_Otop__class_Otop(tc_fun(_1014646, tc_HOL_Obool))), 13193 ^ _780478 : [(13200 ^ _780478) ^ [] : [_1014652 = _1014654, -(hAPP(_1014650, _1014652) = hAPP(_1014650, _1014654))], (13194 ^ _780478) ^ [] : [hAPP(_1014650, _1014652) = hAPP(_1014650, _1014654), -(_1014652 = _1014654)]]], (33863 ^ _780478) ^ [_1420320, _1420322] : [-(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), _1420320)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1420322), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1420320))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (21093 ^ _780478) ^ [_1172601, _1172603] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1172601), _1172603) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1172601 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172603 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44953 ^ _780478) ^ [_1681459, _1681461, _1681463, _1681465, _1681467] : [class_Groups_Ocomm__monoid__add(_1681459), hBOOL(hAPP(hAPP(c_member(_1681461), _1681463), hAPP(c_List_Oset(_1681461), _1681465))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1681459), hAPP(hAPP(c_List_Omap(_1681461, _1681459), _1681467), _1681465)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1681459), hAPP(_1681467, _1681463)), hAPP(c_List_Omonoid__add__class_Olistsum(_1681459), hAPP(hAPP(c_List_Omap(_1681461, _1681459), _1681467), c_List_Oremove1(_1681461, _1681463, _1681465)))))], (29488 ^ _780478) ^ [_1327952] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1327952), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7561 ^ _780478) ^ [_907639, _907641, _907643, _907645] : [-(c_Nitpick_Ofold__graph_H(_907639, _907641, _907643, _907645, c_Orderings_Obot__class_Obot(tc_fun(_907639, tc_HOL_Obool)), _907645))], (42918 ^ _780478) ^ [_1636578, _1636580, _1636582, _1636584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1636578), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636580)), _1636582))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1636578), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636580)), _1636584))), 42928 ^ _780478 : [(42931 ^ _780478) ^ [] : [hAPP(hAPP(c_List_Onth(_1636580), _1636582), 42927 ^ [_1636578, _1636580, _1636582, _1636584]) = hAPP(hAPP(c_List_Onth(_1636580), _1636584), 42927 ^ [_1636578, _1636580, _1636582, _1636584])], (42929 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42927 ^ [_1636578, _1636580, _1636582, _1636584]), _1636578)))]], -(hAPP(hAPP(c_List_Otake(_1636580), _1636578), _1636582) = hAPP(hAPP(c_List_Otake(_1636580), _1636578), _1636584))], (38287 ^ _780478) ^ [_1515865, _1515867, _1515869] : [c_Wellfounded_Owf(_1515865, _1515867), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515865, _1515865)), hAPP(hAPP(c_Product__Type_OPair(_1515865, _1515865), _1515869), _1515869)), _1515867))], (46113 ^ _780478) ^ [_1707314, _1707316] : [-(c_List_Otranspose(_1707314, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1707314)), c_List_Olist_ONil(_1707314)), _1707316)) = c_List_Otranspose(_1707314, _1707316))], (28448 ^ _780478) ^ [_1306943, _1306945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1306943), _1306945)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1306945, _1306943) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (1134 ^ _780478) ^ [_797517, _797519] : [-(class_Rings_Olinordered__ring__strict(_797517)), _797519 = _797517, class_Rings_Olinordered__ring__strict(_797519)], (41790 ^ _780478) ^ [_1605878, _1605880, _1605882, _1605884, _1605886, _1605888] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605878), tc_List_Olist(_1605878))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605878), tc_List_Olist(_1605878)), hAPP(hAPP(c_List_Olist_OCons(_1605878), _1605880), _1605882)), hAPP(hAPP(c_List_Olist_OCons(_1605878), _1605884), _1605886))), c_List_Olexord(_1605878, _1605888))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605878, _1605878)), hAPP(hAPP(c_Product__Type_OPair(_1605878, _1605878), _1605880), _1605884)), _1605888))), 41797 ^ _780478 : [(41800 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605878), tc_List_Olist(_1605878))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605878), tc_List_Olist(_1605878)), _1605882), _1605886)), c_List_Olexord(_1605878, _1605888))))], (41798 ^ _780478) ^ [] : [-(_1605880 = _1605884)]]], (5012 ^ _780478) ^ [_856949, _856951, _856953, _856955, _856957, _856959] : [-(c_Finite__Set_Ofold__image(_856959, _856955, _856951) = c_Finite__Set_Ofold__image(_856957, _856953, _856949)), _856959 = _856957, _856955 = _856953, _856951 = _856949], (40973 ^ _780478) ^ [_1583627, _1583629, _1583631] : [c_Relation_Orefl__on(_1583627, _1583629, _1583631), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1583627, _1583627), tc_HOL_Obool)), _1583631), hAPP(hAPP(c_Relation_Orel__comp(_1583627, _1583627, _1583627), hAPP(c_Relation_Oconverse(_1583627, _1583627), _1583631)), _1583631))))], (48848 ^ _780478) ^ [_1765967, _1765969, _1765971, _1765973, _1765975, _1765977] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1765967, _1765969, _1765971, _1765973, c_Lazy__Sequence_Olazy__sequence_OInsert(_1765969, _1765975, _1765977)) = hAPP(hAPP(_1765973, _1765975), _1765977))], (3006 ^ _780478) ^ [_825006, _825008] : [_825008 = _825006, -(c_HOL_Obool_Obool__size(_825008) = c_HOL_Obool_Obool__size(_825006))], (50895 ^ _780478) ^ [_1812073, _1812075, _1812077] : [-(c_Lazy__Sequence_Oflat(_1812073, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1812073), _1812075, _1812077)) = c_Lazy__Sequence_Oappend(_1812073, _1812075, c_Lazy__Sequence_Oflat(_1812073, _1812077)))], (30494 ^ _780478) ^ [_1346349, _1346351] : [class_Groups_Oordered__ab__group__add__abs(_1346349), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346349), hAPP(c_Groups_Oabs__class_Oabs(_1346349), _1346351)), c_Groups_Ozero__class_Ozero(_1346349)))], (46123 ^ _780478) ^ [_1707673, _1707675, _1707677] : [-(hAPP(c_List_Oset(_1707673), hAPP(c_List_Ofilter(_1707673, _1707675), _1707677)) = hAPP(c_Set_OCollect(_1707673), hAPP(hAPP(c_COMBS(_1707673, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1707673), c_fconj), hAPP(hAPP(c_COMBC(_1707673, tc_fun(_1707673, tc_HOL_Obool), tc_HOL_Obool), c_member(_1707673)), hAPP(c_List_Oset(_1707673), _1707677)))), _1707675)))], (41017 ^ _780478) ^ [_1584944, _1584946, _1584948, _1584950] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584944, _1584944)), hAPP(hAPP(c_Product__Type_OPair(_1584944, _1584944), _1584948), _1584950)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584944, _1584944), tc_HOL_Obool)), _1584946), c_Relation_OId(_1584944)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1584944, tc_fun(_1584944, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1584944, tc_fun(tc_prod(_1584944, _1584944), tc_HOL_Obool), tc_fun(_1584944, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584944, tc_fun(tc_fun(tc_prod(_1584944, _1584944), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1584944, _1584944), tc_HOL_Obool), tc_fun(_1584944, tc_HOL_Obool)), _1584944), c_COMBC(_1584944, tc_fun(tc_prod(_1584944, _1584944), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584944, tc_prod(_1584944, _1584944)), tc_fun(_1584944, tc_fun(tc_fun(tc_prod(_1584944, _1584944), tc_HOL_Obool), tc_HOL_Obool)), _1584944), hAPP(c_COMBB(tc_prod(_1584944, _1584944), tc_fun(tc_fun(tc_prod(_1584944, _1584944), tc_HOL_Obool), tc_HOL_Obool), _1584944), c_member(tc_prod(_1584944, _1584944)))), c_Product__Type_OPair(_1584944, _1584944)))), _1584946)), c_fequal), _1584948), _1584950)))], (45375 ^ _780478) ^ [_1690145, _1690147, _1690149] : [hBOOL(hAPP(c_List_Olistsp(_1690145, hAPP(hAPP(c_COMBC(_1690145, tc_fun(_1690145, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690145)), _1690147)), _1690149)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1690145)), _1690149), c_List_Olists(_1690145, _1690147))))], (24749 ^ _780478) ^ [_1240303, _1240305, _1240307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1240303, tc_HOL_Obool)), _1240305), _1240307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1240303, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1240303, _1240305)), c_Predicate_OPowp(_1240303, _1240307))))], (15391 ^ _780478) ^ [_1057766, _1057768] : [class_Groups_Omonoid__mult(_1057766), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1057766), c_Groups_Oone__class_Oone(_1057766)), _1057768) = c_Groups_Oone__class_Oone(_1057766))], (18834 ^ _780478) ^ [_1134045, _1134047] : [class_Lattices_Olattice(_1134045), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134045), _1134047)), -(_1134047 = c_Orderings_Obot__class_Obot(tc_fun(_1134045, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134045), c_Big__Operators_Olattice__class_OInf__fin(_1134045, _1134047)), c_Big__Operators_Olattice__class_OSup__fin(_1134045, _1134047))))], (44143 ^ _780478) ^ [_1663944, _1663946, _1663948] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663944)), hAPP(c_List_Orotate(_1663944, _1663946), _1663948)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663944)), _1663948))], (11833 ^ _780478) ^ [_988327, _988329, _988331] : [class_Orderings_Olinorder(_988327), hBOOL(hAPP(c_Finite__Set_Ofinite(_988327), _988329)), hBOOL(hAPP(hAPP(c_member(_988327), _988331), _988329)), 11844 ^ _780478 : [(11851 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_988327, tc_HOL_Obool)), _988329), hAPP(hAPP(c_Set_Oinsert(_988327), _988331), c_Orderings_Obot__class_Obot(tc_fun(_988327, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_988327, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_988327, c_Orderings_Oord__class_Omin(_988327), _988329) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_988327), _988331), c_Big__Operators_Olattice_OInf__fin(_988327, c_Orderings_Oord__class_Omin(_988327), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_988327, tc_HOL_Obool)), _988329), hAPP(hAPP(c_Set_Oinsert(_988327), _988331), c_Orderings_Obot__class_Obot(tc_fun(_988327, tc_HOL_Obool)))))))], (11845 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_988327, tc_HOL_Obool)), _988329), hAPP(hAPP(c_Set_Oinsert(_988327), _988331), c_Orderings_Obot__class_Obot(tc_fun(_988327, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_988327, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_988327, c_Orderings_Oord__class_Omin(_988327), _988329) = _988331)]]], (43107 ^ _780478) ^ [_1640052, _1640054, _1640056] : [-(hAPP(hAPP(c_List_Olist__update(_1640052, c_List_Olist_ONil(_1640052)), _1640054), _1640056) = c_List_Olist_ONil(_1640052))], (46750 ^ _780478) ^ [_1720671, _1720673, _1720675, _1720677, _1720679, _1720681] : [class_Orderings_Olinorder(_1720671), c_List_Olinorder__class_Osorted(_1720671, hAPP(hAPP(c_List_Omap(_1720673, _1720671), _1720675), _1720677)), hBOOL(hAPP(_1720679, _1720681)), -(hAPP(c_List_Ofilter(_1720673, _1720679), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720673, _1720671, _1720675), _1720681), _1720677)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1720673, _1720671, _1720675), _1720681), hAPP(c_List_Ofilter(_1720673, _1720679), _1720677)))], (16278 ^ _780478) ^ [_1076318, _1076320, _1076322, _1076324] : [class_Lattices_Olattice(_1076318), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076318), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076318), _1076320), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076318), _1076322), _1076324))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076318), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076318), _1076320), _1076322)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076318), _1076320), _1076324)))))], (36998 ^ _780478) ^ [_1484150, _1484152, _1484154] : [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), _1484150), _1484152))), -(hBOOL(hAPP(hAPP(_1484154, _1484150), _1484152))), 37005 ^ _780478 : [(37008 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1484154, 37003 ^ [_1484150, _1484152, _1484154]), 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)))), 37004 ^ [_1484150, _1484152, _1484154])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37003 ^ [_1484150, _1484152, _1484154]), 37004 ^ [_1484150, _1484152, _1484154]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 37004 ^ [_1484150, _1484152, _1484154]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37018 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1484154, 37003 ^ [_1484150, _1484152, _1484154]), 37004 ^ [_1484150, _1484152, _1484154]))], (37006 ^ _780478) ^ [] : [-(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), 37003 ^ [_1484150, _1484152, _1484154]), 37004 ^ [_1484150, _1484152, _1484154]))))]]], (50153 ^ _780478) ^ [_1794629, _1794631, _1794633, _1794635, _1794637, _1794639, _1794641] : [c_Fun_Oinj__on(_1794629, _1794631, _1794633, hAPP(c_Set_Oimage(_1794635, _1794629, _1794637), _1794639)), c_Fun_Oinj__on(_1794635, _1794629, _1794637, _1794639), hBOOL(hAPP(hAPP(c_member(_1794631), _1794641), hAPP(c_Set_Oimage(_1794629, _1794631, _1794633), hAPP(c_Set_Oimage(_1794635, _1794629, _1794637), _1794639)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1794635, _1794631, _1794639, hAPP(c_Fun_Ocomp(_1794629, _1794631, _1794635, _1794633), _1794637)), _1794641) = hAPP(hAPP(c_Fun_Ocomp(_1794629, _1794635, _1794631, c_Hilbert__Choice_Oinv__into(_1794635, _1794629, _1794639, _1794637)), c_Hilbert__Choice_Oinv__into(_1794629, _1794631, hAPP(c_Set_Oimage(_1794635, _1794629, _1794637), _1794639), _1794633)), _1794641))], (22353 ^ _780478) ^ [_1196174] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1196174)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1196174), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1196174)))], (38883 ^ _780478) ^ [_1531837, _1531839, _1531841, _1531843] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1531837, _1531839)), hAPP(hAPP(c_Product__Type_OSigma(_1531837, _1531839), hAPP(hAPP(c_Set_Oinsert(_1531837), _1531841), c_Orderings_Obot__class_Obot(tc_fun(_1531837, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1531839, tc_HOL_Obool), _1531837), _1531843))) = hAPP(c_Finite__Set_Ocard(_1531839), _1531843))], (48575 ^ _780478) ^ [_1760548, _1760550, _1760552, _1760554] : [48583 ^ _780478 : [(48586 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1760554, 48582 ^ [_1760548, _1760550, _1760552, _1760554])))], (48584 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760548), 48582 ^ [_1760548, _1760550, _1760552, _1760554]), hAPP(c_List_Oset(_1760548), c_List_Oreplicate(_1760548, _1760550, _1760552)))))]], hBOOL(hAPP(_1760554, _1760552)), -(_1760550 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43031 ^ _780478) ^ [_1638716, _1638718, _1638720] : [43032 ^ _780478 : [(43035 ^ _780478) ^ [] : [_1638720 = c_List_Olist_ONil(_1638716)], (43033 ^ _780478) ^ [] : [_1638718 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1638716), _1638718), _1638720) = c_List_Olist_ONil(_1638716))], (25098 ^ _780478) ^ [_1246702, _1246704, _1246706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1246702)), 25101 ^ _780478 : [(25102 ^ _780478) ^ [] : [-(_1246704 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1246706), _1246702)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246702), _1246704)), _1246706)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246702), hAPP(c_Nat_OSuc, _1246704))))], (25112 ^ _780478) ^ [] : [_1246704 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1246706), _1246702), 25115 ^ _780478 : [(25118 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246702), hAPP(c_Nat_OSuc, _1246704)))))], (25116 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246702), _1246704)), _1246706)))]]]]], (17989 ^ _780478) ^ [_1115397, _1115399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115397)), hAPP(c_Nat_OSuc, _1115399))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115397), _1115399)))], (33266 ^ _780478) ^ [_1408949, _1408951] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408949))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408949)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408951)) = 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), _1408951)))], (22572 ^ _780478) ^ [_1200921, _1200923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200921)), 22575 ^ _780478 : [(22584 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200921), _1200923) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1200921 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1200923 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (22576 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1200921), _1200923) = c_Groups_Oone__class_Oone(tc_Int_Oint), 22579 ^ _780478 : [(22582 ^ _780478) ^ [] : [-(_1200923 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (22580 ^ _780478) ^ [] : [-(_1200921 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (9624 ^ _780478) ^ [_945933, _945935] : [class_Orderings_Olinorder(_945933), hBOOL(hAPP(c_Finite__Set_Ofinite(_945933), _945935)), -(_945935 = c_Orderings_Obot__class_Obot(tc_fun(_945933, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_945933), c_Big__Operators_Olinorder__class_OMin(_945933, _945935)), _945935)))], (35780 ^ _780478) ^ [_1458391, _1458393, _1458395, _1458397, _1458399, _1458401] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458391, tc_fun(_1458393, tc_fun(_1458395, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1458391, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1458393, _1458395), tc_HOL_Obool), tc_fun(_1458393, tc_fun(_1458395, tc_HOL_Obool)), _1458391), hAPP(c_COMBC(_1458393, tc_fun(tc_prod(_1458393, _1458395), tc_HOL_Obool), tc_fun(_1458395, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458395, tc_fun(tc_fun(tc_prod(_1458393, _1458395), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1458393, _1458395), tc_HOL_Obool), tc_fun(_1458395, tc_HOL_Obool)), _1458393), c_COMBC(_1458395, tc_fun(tc_prod(_1458393, _1458395), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1458395, tc_prod(_1458393, _1458395)), tc_fun(_1458395, tc_fun(tc_fun(tc_prod(_1458393, _1458395), tc_HOL_Obool), tc_HOL_Obool)), _1458393), hAPP(c_COMBB(tc_prod(_1458393, _1458395), tc_fun(tc_fun(tc_prod(_1458393, _1458395), tc_HOL_Obool), tc_HOL_Obool), _1458395), c_member(tc_prod(_1458393, _1458395)))), c_Product__Type_OPair(_1458393, _1458395))))), _1458397)), _1458399), _1458401)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1458393, _1458395)), hAPP(hAPP(c_Product__Type_OPair(_1458393, _1458395), _1458399), _1458401)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1458391, tc_fun(tc_prod(_1458393, _1458395), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1458391, tc_HOL_Obool))), _1458397))))], (30468 ^ _780478) ^ [_1345979, _1345981] : [class_Groups_Oordered__ab__group__add__abs(_1345979), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345979), c_Groups_Ozero__class_Ozero(_1345979)), _1345981)), -(hAPP(c_Groups_Oabs__class_Oabs(_1345979), _1345981) = _1345981)], (39805 ^ _780478) ^ [_1555792, _1555794, _1555796, _1555798, _1555800, _1555802] : [class_Groups_Ocomm__monoid__mult(_1555792), c_Fun_Oinj__on(_1555794, _1555796, _1555798, _1555800), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555796, _1555792), _1555802), hAPP(c_Set_Oimage(_1555794, _1555796, _1555798), _1555800)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1555794, _1555792), hAPP(c_Fun_Ocomp(_1555796, _1555792, _1555794, _1555802), _1555798)), _1555800))], (21103 ^ _780478) ^ [_1172759, _1172761] : [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), _1172759), _1172761))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1172761), _1172759)))], (49622 ^ _780478) ^ [_1784086, _1784088, _1784090, _1784092] : [c_Relation_Oantisym(_1784086, _1784088), hBOOL(hAPP(hAPP(c_member(tc_prod(_1784086, _1784086)), hAPP(hAPP(c_Product__Type_OPair(_1784086, _1784086), _1784090), _1784092)), _1784088)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1784086, _1784086)), hAPP(hAPP(c_Product__Type_OPair(_1784086, _1784086), _1784092), _1784090)), _1784088)), -(_1784090 = _1784092)], (2288 ^ _780478) ^ [_813941, _813943, _813945, _813947, _813949, _813951] : [-(c_Nat_Onat_Onat__rec(_813951, _813947, _813943) = c_Nat_Onat_Onat__rec(_813949, _813945, _813941)), _813951 = _813949, _813947 = _813945, _813943 = _813941], (39995 ^ _780478) ^ [_1560247, _1560249, _1560251, _1560253, _1560255, _1560257] : [c_Finite__Set_Ofolding(_1560247, _1560249, _1560251, _1560253), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560247), _1560255)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560247), _1560257)), -(hAPP(c_Fun_Ocomp(_1560249, _1560249, _1560249, hAPP(_1560253, _1560257)), hAPP(_1560253, _1560255)) = hAPP(c_Fun_Ocomp(_1560249, _1560249, _1560249, hAPP(_1560253, _1560255)), hAPP(_1560253, _1560257)))], (7970 ^ _780478) ^ [_915981, _915983, _915985, _915987, _915989] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_915981, _915981, _915983, _915985, _915987), _915989)), -(hBOOL(hAPP(hAPP(c_member(_915981), _915985), _915987))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_915981, _915983, hAPP(hAPP(c_Set_Oinsert(_915981), _915985), _915987)), _915989)))], (28556 ^ _780478) ^ [_1309161, _1309163, _1309165] : [class_Orderings_Olinorder(_1309161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309161), _1309163), _1309165)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309161, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1309161, _1309163, _1309165)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1309161), _1309165)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1309161), _1309163))], (30354 ^ _780478) ^ [_1343629] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1343629)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1343629))], (40632 ^ _780478) ^ [_1575775, _1575777, _1575779, _1575781] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575775, _1575775)), hAPP(hAPP(c_Product__Type_OPair(_1575775, _1575775), _1575777), _1575779)), c_Transitive__Closure_Ortrancl(_1575775, _1575781))), -(_1575777 = _1575779), 40639 ^ _780478 : [(40642 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575775, _1575775)), hAPP(hAPP(c_Product__Type_OPair(_1575775, _1575775), _1575777), _1575779)), c_Transitive__Closure_Otrancl(_1575775, _1575781))))], (40640 ^ _780478) ^ [] : [_1575777 = _1575779]]], (48296 ^ _780478) ^ [_1753910, _1753912, _1753914] : [48298 ^ _780478 : [(48301 ^ _780478) ^ [] : [hBOOL(hAPP(_1753912, 48297 ^ [_1753910, _1753912, _1753914]))], (48299 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1753910), 48297 ^ [_1753910, _1753912, _1753914]), hAPP(c_List_Oset(_1753910), _1753914))))]], -(c_List_Olist__all(_1753910, _1753912, _1753914))], (31140 ^ _780478) ^ [_1359982] : [-(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)), _1359982)))))], (35121 ^ _780478) ^ [_1442350] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1442350)), -(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), _1442350), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (22245 ^ _780478) ^ [_1194042, _1194044, _1194046, _1194048, _1194050, _1194052] : [class_Rings_Olinordered__semiring__1__strict(_1194042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194042), _1194044), _1194046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194042), _1194048), _1194046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194042), c_Groups_Ozero__class_Ozero(_1194042)), _1194050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1194042), c_Groups_Ozero__class_Ozero(_1194042)), _1194052)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194042), _1194050), _1194052) = c_Groups_Oone__class_Oone(_1194042), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194042), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194042), _1194050), _1194044)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1194042), _1194052), _1194048))), _1194046)))], (33586 ^ _780478) ^ [_1413923, _1413925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413923), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413923)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413925)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413925))], (2580 ^ _780478) ^ [_818465, _818467] : [_818467 = _818465, -(c_Int_Oint__ge__less__than(_818467) = c_Int_Oint__ge__less__than(_818465))], (52305 ^ _780478) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (50885 ^ _780478) ^ [_1811815, _1811817, _1811819, _1811821] : [50888 ^ _780478 : [(50891 ^ _780478) ^ [] : [hAPP(_1811819, 50886 ^ [_1811815, _1811817, _1811819, _1811821]) = hAPP(_1811819, 50887 ^ [_1811815, _1811817, _1811819, _1811821])], (50889 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1811815, _1811815)), hAPP(hAPP(c_Product__Type_OPair(_1811815, _1811815), 50886 ^ [_1811815, _1811817, _1811819, _1811821]), 50887 ^ [_1811815, _1811817, _1811819, _1811821])), _1811817)))]], -(c_Equiv__Relations_Ocongruent(_1811815, _1811821, _1811817, _1811819))], (49129 ^ _780478) ^ [_1772392, _1772394, _1772396] : [-(c_Random__Sequence_Oempty(_1772392, _1772394, _1772396) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1772392)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1772392)))], (52045 ^ _780478) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (17341 ^ _780478) ^ [_1100737, _1100739, _1100741, _1100743] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1100737, tc_fun(_1100739, tc_HOL_Obool)), _1100741), _1100743) = c_Orderings_Obot__class_Obot(tc_fun(_1100739, tc_HOL_Obool)), 17344 ^ _780478 : [(17345 ^ _780478) ^ [_1100853] : [hBOOL(hAPP(hAPP(c_member(_1100737), _1100853), _1100741)), -(hAPP(_1100743, _1100853) = c_Orderings_Obot__class_Obot(tc_fun(_1100739, tc_HOL_Obool)))]]], (35623 ^ _780478) ^ [_1451176, _1451178, _1451180, _1451182, _1451184, _1451186] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1451176, tc_fun(_1451178, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1451176, tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_fun(_1451178, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451178, tc_fun(tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_fun(_1451178, tc_HOL_Obool)), _1451176), c_COMBC(_1451178, tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451178, tc_prod(_1451176, _1451178)), tc_fun(_1451178, tc_fun(tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_HOL_Obool)), _1451176), hAPP(c_COMBB(tc_prod(_1451176, _1451178), tc_fun(tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_HOL_Obool), _1451178), c_member(tc_prod(_1451176, _1451178)))), c_Product__Type_OPair(_1451176, _1451178)))), _1451180)), hAPP(hAPP(c_COMBC(_1451176, tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_fun(_1451178, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451178, tc_fun(tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_fun(_1451178, tc_HOL_Obool)), _1451176), c_COMBC(_1451178, tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1451178, tc_prod(_1451176, _1451178)), tc_fun(_1451178, tc_fun(tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_HOL_Obool)), _1451176), hAPP(c_COMBB(tc_prod(_1451176, _1451178), tc_fun(tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool), tc_HOL_Obool), _1451178), c_member(tc_prod(_1451176, _1451178)))), c_Product__Type_OPair(_1451176, _1451178)))), _1451182)), _1451184), _1451186)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1451176, _1451178)), hAPP(hAPP(c_Product__Type_OPair(_1451176, _1451178), _1451184), _1451186)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1451176, _1451178), tc_HOL_Obool)), _1451180), _1451182))))], (43346 ^ _780478) ^ [_1645401, _1645403, _1645405, _1645407, _1645409] : [-(hAPP(hAPP(c_List_Oappend(_1645401), _1645403), _1645405) = hAPP(hAPP(c_List_Olist_OCons(_1645401), _1645407), _1645409)), 43347 ^ _780478 : [(43354 ^ _780478) ^ [_1645584] : [_1645403 = hAPP(hAPP(c_List_Olist_OCons(_1645401), _1645407), _1645584), hAPP(hAPP(c_List_Oappend(_1645401), _1645584), _1645405) = _1645409], (43348 ^ _780478) ^ [] : [_1645403 = c_List_Olist_ONil(_1645401), _1645405 = hAPP(hAPP(c_List_Olist_OCons(_1645401), _1645407), _1645409)]]], (7371 ^ _780478) ^ [_903905, _903907] : [-(c_Fun_Oinj__on(_903905, _903905, c_COMBI(_903905), _903907))], (52295 ^ _780478) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (1494 ^ _780478) ^ [_802017, _802019] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_802017)), _802019 = _802017, class_Groups_Oordered__cancel__ab__semigroup__add(_802019)], (40580 ^ _780478) ^ [_1574394, _1574396, _1574398, _1574400, _1574402] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574394, _1574394)), hAPP(hAPP(c_Product__Type_OPair(_1574394, _1574394), _1574396), _1574398)), c_Transitive__Closure_Ortrancl(_1574394, _1574400))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574394, _1574394)), hAPP(hAPP(c_Product__Type_OPair(_1574394, _1574394), _1574398), _1574402)), _1574400)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574394, _1574394)), hAPP(hAPP(c_Product__Type_OPair(_1574394, _1574394), _1574396), _1574402)), c_Transitive__Closure_Ortrancl(_1574394, _1574400))))], (21848 ^ _780478) ^ [_1186106, _1186108] : [-(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), _1186106), _1186108)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1186106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1186108))], (43021 ^ _780478) ^ [_1638604, _1638606, _1638608] : [hAPP(hAPP(c_List_Otake(_1638604), _1638606), _1638608) = c_List_Olist_ONil(_1638604), -(_1638606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1638608 = c_List_Olist_ONil(_1638604))], (6498 ^ _780478) ^ [_886471, _886473] : [-(hAPP(c_Set_Oimage(_886471, _886471, c_COMBI(_886471)), _886473) = _886473)], (35459 ^ _780478) ^ [_1448401] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1448401)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1448401)))], (41654 ^ _780478) ^ [_1601422, _1601424, _1601426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1601422), c_Nitpick_Oplus__frac(_1601422, _1601424, c_Nitpick_Ouminus__frac(_1601422, _1601426)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1601422, _1601424, _1601426))], (52037 ^ _780478) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (37820 ^ _780478) ^ [_1503193, _1503195, _1503197, _1503199] : [c_FunDef_Oreduction__pair(_1503193, _1503195), -(c_FunDef_Oreduction__pair(_1503197, hAPP(hAPP(c_FunDef_Orp__inv__image(_1503193, _1503197), _1503195), _1503199)))], (47035 ^ _780478) ^ [_1726665, _1726667, _1726669] : [_1726667 = hAPP(c_List_Orev(_1726665), _1726669), -(hAPP(c_List_Orev(_1726665), _1726667) = _1726669)], (47282 ^ _780478) ^ [_1731815, _1731817] : [-(_1731815 = c_List_Olist_ONil(_1731817)), hBOOL(hAPP(c_List_Odistinct(_1731817), _1731815)), -(c_List_OtakeWhile(_1731817, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1731817), c_fNot), hAPP(hAPP(c_COMBC(_1731817, _1731817, tc_HOL_Obool), c_fequal), c_List_Olast(_1731817, _1731815))), _1731815) = c_List_Obutlast(_1731817, _1731815))], (12788 ^ _780478) ^ [_1007054, _1007056] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1007054, _1007056)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1007054, _1007056), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1007056), c_Orderings_Otop__class_Otop(tc_fun(_1007056, tc_HOL_Obool)))))], (48341 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45351 ^ _780478) ^ [_1689562, _1689564, _1689566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1689562, tc_HOL_Obool)), _1689564), _1689566)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1689562), tc_HOL_Obool)), c_List_Olistsp(_1689562, _1689564)), c_List_Olistsp(_1689562, _1689566))))], (29003 ^ _780478) ^ [_1317928, _1317930] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1317928, tc_HOL_Obool)), _1317930), hAPP(c_Set_OPow(_1317928), _1317930))))], (14519 ^ _780478) ^ [_1039902, _1039904, _1039906] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039902), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039904), _1039906)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039902), _1039904)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039902), _1039906)))], (18892 ^ _780478) ^ [_1135061, _1135063, _1135065] : [class_Lattices_Olattice(_1135061), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135061), _1135063)), 18899 ^ _780478 : [(18906 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1135061, tc_HOL_Obool)), _1135063), hAPP(hAPP(c_Set_Oinsert(_1135061), _1135065), c_Orderings_Obot__class_Obot(tc_fun(_1135061, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1135061, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1135061, hAPP(hAPP(c_Set_Oinsert(_1135061), _1135065), _1135063)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1135061), _1135065), c_Big__Operators_Olattice__class_OInf__fin(_1135061, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1135061, tc_HOL_Obool)), _1135063), hAPP(hAPP(c_Set_Oinsert(_1135061), _1135065), c_Orderings_Obot__class_Obot(tc_fun(_1135061, tc_HOL_Obool)))))))], (18900 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1135061, tc_HOL_Obool)), _1135063), hAPP(hAPP(c_Set_Oinsert(_1135061), _1135065), c_Orderings_Obot__class_Obot(tc_fun(_1135061, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1135061, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1135061, hAPP(hAPP(c_Set_Oinsert(_1135061), _1135065), _1135063)) = _1135065)]]], (15461 ^ _780478) ^ [_1059064, _1059066] : [class_Lattices_Olattice(_1059064), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059064), _1059066)), -(_1059066 = c_Orderings_Obot__class_Obot(tc_fun(_1059064, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1059064), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1059064), 15474 ^ [_1059064, _1059066]), 15475 ^ [_1059064, _1059066])), hAPP(hAPP(c_Set_Oinsert(_1059064), 15474 ^ [_1059064, _1059066]), hAPP(hAPP(c_Set_Oinsert(_1059064), 15475 ^ [_1059064, _1059066]), c_Orderings_Obot__class_Obot(tc_fun(_1059064, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1059064), c_Big__Operators_Olattice__class_OSup__fin(_1059064, _1059066)), _1059066)))], (6758 ^ _780478) ^ [_892322, _892324, _892326, _892328, _892330, _892332] : [-(c_Fun_Ofun__upd(_892322, _892324, c_Fun_Ofun__upd(_892322, _892324, _892326, _892328, _892330), _892328, _892332) = c_Fun_Ofun__upd(_892322, _892324, _892326, _892328, _892332))], (42298 ^ _780478) ^ [_1620701, _1620703, _1620705, _1620707] : [hBOOL(hAPP(hAPP(c_member(_1620701), _1620703), hAPP(c_List_Oset(_1620701), hAPP(hAPP(c_List_Otake(_1620701), _1620705), _1620707)))), -(hBOOL(hAPP(hAPP(c_member(_1620701), _1620703), hAPP(c_List_Oset(_1620701), _1620707))))], (10901 ^ _780478) ^ [_970576, _970578, _970580] : [class_Groups_Oordered__ab__group__add(_970576), 10904 ^ _780478 : [(10911 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970576), _970580), hAPP(c_Groups_Ouminus__class_Ouminus(_970576), _970578))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970576), _970578), hAPP(c_Groups_Ouminus__class_Ouminus(_970576), _970580))))], (10905 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970576), _970578), hAPP(c_Groups_Ouminus__class_Ouminus(_970576), _970580))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970576), _970580), hAPP(c_Groups_Ouminus__class_Ouminus(_970576), _970578))))]]], (19032 ^ _780478) ^ [_1137774, _1137776] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1137774, tc_HOL_Obool), _1137776) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1137774, tc_HOL_Obool), tc_fun(_1137774, tc_HOL_Obool)), _1137776), c_COMBI(tc_fun(_1137774, tc_HOL_Obool))))], (45121 ^ _780478) ^ [_1684864, _1684866, _1684868] : [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, _1684864), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1684864)), _1684866)))), -(hBOOL(hAPP(hAPP(c_member(_1684864), hAPP(c_Product__Type_Ofst(_1684864, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1684864, _1684866), _1684868))), hAPP(c_List_Oset(_1684864), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1684864), _1684864), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1684864)), _1684866)))))], (47061 ^ _780478) ^ [_1727129, _1727131, _1727133, _1727135, _1727137] : [-(c_List_Ofoldr(_1727129, _1727131, _1727133, _1727135, _1727137) = hAPP(c_List_Ofoldl(_1727131, _1727129, hAPP(c_COMBC(_1727129, _1727131, _1727131), _1727133), _1727137), hAPP(c_List_Orev(_1727129), _1727135)))], (46170 ^ _780478) ^ [_1708962, _1708964, _1708966, _1708968] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1708962)), c_List_Otranspose__rel(_1708962)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708962)), hAPP(hAPP(c_List_Olist_OCons(_1708962), _1708964), _1708966)), _1708968))), -(c_List_Otranspose(_1708962, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708962)), hAPP(hAPP(c_List_Olist_OCons(_1708962), _1708964), _1708966)), _1708968)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708962)), hAPP(hAPP(c_List_Olist_OCons(_1708962), _1708964), c_List_Oconcat(_1708962, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1708962), tc_List_Olist(_1708962)), c_List_Olist_Olist__case(tc_List_Olist(_1708962), _1708962, c_List_Olist_ONil(_1708962), hAPP(hAPP(c_COMBB(tc_List_Olist(_1708962), tc_fun(tc_List_Olist(_1708962), tc_List_Olist(_1708962)), _1708962), c_COMBK(tc_List_Olist(_1708962), tc_List_Olist(_1708962))), hAPP(hAPP(c_COMBC(_1708962, tc_List_Olist(_1708962), tc_List_Olist(_1708962)), c_List_Olist_OCons(_1708962)), c_List_Olist_ONil(_1708962))))), _1708968)))), c_List_Otranspose(_1708962, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1708962)), _1708966), c_List_Oconcat(tc_List_Olist(_1708962), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1708962), tc_List_Olist(tc_List_Olist(_1708962))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1708962)), _1708962, c_List_Olist_ONil(tc_List_Olist(_1708962)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1708962), tc_List_Olist(tc_List_Olist(_1708962))), _1708962), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708962), tc_List_Olist(tc_List_Olist(_1708962)), tc_List_Olist(tc_List_Olist(_1708962))), c_List_Olist_OCons(tc_List_Olist(_1708962))), c_List_Olist_ONil(tc_List_Olist(_1708962)))))), _1708968))))))], (29572 ^ _780478) ^ [_1329624, _1329626] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329624, _1329626) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329624, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1329626)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35537 ^ _780478) ^ [_1449534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449534)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1449534) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (38570 ^ _780478) ^ [_1522491, _1522493, _1522495, _1522497] : [hBOOL(hAPP(c_Predicate_ORangeP(_1522491, _1522493, hAPP(hAPP(c_COMBC(_1522491, tc_fun(tc_prod(_1522491, _1522493), tc_HOL_Obool), tc_fun(_1522493, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522493, tc_fun(tc_fun(tc_prod(_1522491, _1522493), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1522491, _1522493), tc_HOL_Obool), tc_fun(_1522493, tc_HOL_Obool)), _1522491), c_COMBC(_1522493, tc_fun(tc_prod(_1522491, _1522493), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522493, tc_prod(_1522491, _1522493)), tc_fun(_1522493, tc_fun(tc_fun(tc_prod(_1522491, _1522493), tc_HOL_Obool), tc_HOL_Obool)), _1522491), hAPP(c_COMBB(tc_prod(_1522491, _1522493), tc_fun(tc_fun(tc_prod(_1522491, _1522493), tc_HOL_Obool), tc_HOL_Obool), _1522493), c_member(tc_prod(_1522491, _1522493)))), c_Product__Type_OPair(_1522491, _1522493)))), _1522495)), _1522497)), -(hBOOL(hAPP(hAPP(c_member(_1522493), _1522497), hAPP(c_Relation_ORange(_1522491, _1522493), _1522495))))], (25757 ^ _780478) ^ [_1258278, _1258280] : [hAPP(c_Int_Onat, _1258278) = _1258280, 25760 ^ _780478 : [(25767 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258278))), -(_1258280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25761 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258278)), -(_1258278 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258280))]]], (9700 ^ _780478) ^ [_947610, _947612, _947614, _947616, _947618, _947620] : [class_Rings_Oordered__ring(_947610), 9703 ^ _780478 : [(9710 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947610), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947610), _947612), _947618)), _947614)), _947616)), _947620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947610), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947610), _947612), _947614)), _947616)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947610), _947618), _947614)), _947620))))], (9704 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947610), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947610), _947612), _947614)), _947616)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947610), _947618), _947614)), _947620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947610), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947610), _947612), _947618)), _947614)), _947616)), _947620)))]]], (4718 ^ _780478) ^ [_852342, _852344] : [_852344 = _852342, -(c_DSequence_Ounion(_852344) = c_DSequence_Ounion(_852342))], (14909 ^ _780478) ^ [_1048294, _1048296, _1048298, _1048300] : [hBOOL(hAPP(hAPP(_1048298, _1048300), _1048296)), -(hBOOL(hAPP(hAPP(c_member(_1048294), _1048296), c_SetInterval_Oord_OatLeast(_1048294, _1048298, _1048300))))], (38973 ^ _780478) ^ [_1534321, _1534323, _1534325, _1534327] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1534321, _1534323), _1534325), _1534327) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534321, tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool)), _1534325), hAPP(hAPP(c_COMBS(_1534321, tc_fun(_1534323, tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool)), tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534323, tc_HOL_Obool), tc_fun(tc_fun(_1534323, tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool)), tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool)), _1534321), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534323, tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool))), _1534327)), hAPP(hAPP(c_COMBC(_1534321, tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool), tc_fun(_1534323, tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534323, tc_fun(tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool), tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool), tc_fun(_1534323, tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool))), _1534321), c_COMBC(_1534323, tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool), tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1534323, tc_prod(_1534321, _1534323)), tc_fun(_1534323, tc_fun(tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool), tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool))), _1534321), hAPP(c_COMBB(tc_prod(_1534321, _1534323), tc_fun(tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool), tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool)), _1534323), c_Set_Oinsert(tc_prod(_1534321, _1534323)))), c_Product__Type_OPair(_1534321, _1534323)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1534321, _1534323), tc_HOL_Obool))))))], (34647 ^ _780478) ^ [_1433671, _1433673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433671), _1433673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1433671)), c_Int_OBit0(_1433673))))], (49218 ^ _780478) ^ [_1774836, _1774838] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1774836, tc_HOL_Obool), _1774838) = hAPP(c_Set_OCollect(_1774836), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774836, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1774836), c_HOL_OEx(tc_fun(_1774836, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774836, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1774836, tc_HOL_Obool), tc_HOL_Obool), _1774836), hAPP(c_COMBS(tc_fun(_1774836, 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(_1774836, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1774836, tc_HOL_Obool), tc_fun(tc_fun(_1774836, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1774836, tc_HOL_Obool))), _1774838)))), c_member(_1774836)))))], (9582 ^ _780478) ^ [_945239, _945241, _945243, _945245, _945247] : [class_Groups_Oab__semigroup__mult(_945239), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_945239, _945239, c_Groups_Otimes__class_Otimes(_945239), _945241, _945243), _945245)), -(hBOOL(hAPP(hAPP(c_member(_945239), _945241), _945243))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_945239, _945239, c_Groups_Otimes__class_Otimes(_945239), _945247, hAPP(hAPP(c_Set_Oinsert(_945239), _945241), _945243)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_945239), _945247), _945245))))], (15741 ^ _780478) ^ [_1064990, _1064992, _1064994] : [class_Lattices_Osemilattice__inf(_1064990), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064990), _1064992), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064990), _1064992), _1064994)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064990), _1064992), _1064994))], (25539 ^ _780478) ^ [] : [-(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))))], (52129 ^ _780478) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (24779 ^ _780478) ^ [_1240871, _1240873, _1240875] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1240873), _1240875)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240871), _1240873)), _1240875))], (37752 ^ _780478) ^ [] : [-(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)))))], (29427 ^ _780478) ^ [_1326950, _1326952, _1326954] : [class_Divides_Osemiring__div(_1326950), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1326950), c_Divides_Odiv__class_Omod(_1326950, _1326952, _1326954)), _1326954) = c_Groups_Ozero__class_Ozero(_1326950))], (32170 ^ _780478) ^ [_1388100, _1388102, _1388104, _1388106] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388100), hAPP(c_Int_Onumber__class_Onumber__of(_1388100), _1388102)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388100), _1388104), _1388106)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388100), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388100), hAPP(c_Int_Onumber__class_Onumber__of(_1388100), _1388102)), _1388104)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388100), hAPP(c_Int_Onumber__class_Onumber__of(_1388100), _1388102)), _1388106))), class_Int_Onumber(_1388100), class_Rings_Oring(_1388100)], (43127 ^ _780478) ^ [_1640374, _1640376, _1640378, _1640380] : [-(hBOOL(hAPP(hAPP(c_member(_1640374), _1640376), hAPP(c_List_Oset(_1640374), _1640378)))), hBOOL(hAPP(hAPP(c_member(_1640374), _1640376), hAPP(c_List_Oset(_1640374), c_List_Oremove1(_1640374, _1640380, _1640378))))], (51469 ^ _780478) ^ [_1822783, _1822785] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822783), _1822785)), -(c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822785, _1822783) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (30260 ^ _780478) ^ [_1341913, _1341915] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1341913, tc_HOL_Obool), hAPP(c_Set_OPow(_1341913), _1341915)) = _1341915)], (23689 ^ _780478) ^ [_1220824, _1220826, _1220828] : [-(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)), _1220824)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220826), _1220828)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220826), _1220824)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220828), _1220824)))], (45775 ^ _780478) ^ [_1699618, _1699620] : [c_List_Olist_ONil(_1699618) = c_List_Oremdups(_1699618, _1699620), -(_1699620 = c_List_Olist_ONil(_1699618))], (13236 ^ _780478) ^ [_1015623, _1015625, _1015627, _1015629, _1015631] : [-(hAPP(c_Set_Oimage(_1015623, _1015625, hAPP(hAPP(c_COMBB(_1015627, _1015625, _1015623), _1015629), _1015631)), c_Orderings_Otop__class_Otop(tc_fun(_1015623, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1015627, _1015625, _1015629), hAPP(c_Set_Oimage(_1015623, _1015627, _1015631), c_Orderings_Otop__class_Otop(tc_fun(_1015623, tc_HOL_Obool)))))], (49070 ^ _780478) ^ [_1771081, _1771083, _1771085] : [c_List_Olist__all(tc_Int_Oint, _1771081, c_List_Oupto(_1771083, _1771085)), -(c_List_Oall__interval__int(_1771081, _1771083, _1771085))], (15669 ^ _780478) ^ [_1063652, _1063654, _1063656, _1063658, _1063660] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1063652, _1063654, _1063656), _1063658), _1063660)), -(hBOOL(hAPP(_1063658, hAPP(_1063656, _1063660))))], (27762 ^ _780478) ^ [_1293630, _1293632, _1293634] : [27764 ^ _780478 : [(27767 ^ _780478) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1293634, 27763 ^ [_1293630, _1293632, _1293634]))], (27765 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1293630), 27763 ^ [_1293630, _1293632, _1293634]), _1293632)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293630, tc_Int_Oint), _1293634), _1293632) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293630, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1293630), c_Int_Onat), _1293634)), _1293632)))], (29397 ^ _780478) ^ [_1326395, _1326397, _1326399] : [class_Divides_Osemiring__div(_1326395), -(c_Divides_Odiv__class_Omod(_1326395, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326395), _1326397), _1326399), _1326397) = c_Groups_Ozero__class_Ozero(_1326395))], (33807 ^ _780478) ^ [_1419186, _1419188, _1419190, _1419192] : [-(hAPP(c_Nat_Onat_Onat__rec(_1419186, _1419188, _1419190), hAPP(c_Nat_OSuc, _1419192)) = hAPP(hAPP(_1419190, _1419192), hAPP(c_Nat_Onat_Onat__rec(_1419186, _1419188, _1419190), _1419192)))], (33626 ^ _780478) ^ [_1414670, _1414672] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414670), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414670)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414672)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1414670), _1414672)))], (52079 ^ _780478) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (17061 ^ _780478) ^ [_1094210, _1094212, _1094214] : [class_Orderings_Olinorder(_1094210), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094210), _1094212)), -(_1094212 = c_Orderings_Obot__class_Obot(tc_fun(_1094210, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094210), _1094214)), -(_1094214 = c_Orderings_Obot__class_Obot(tc_fun(_1094210, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1094210, tc_HOL_Obool)), _1094212), _1094214) = c_Orderings_Obot__class_Obot(tc_fun(_1094210, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1094210, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1094210, tc_HOL_Obool)), _1094212), _1094214)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094210), c_Big__Operators_Olinorder__class_OMax(_1094210, _1094212)), c_Big__Operators_Olinorder__class_OMax(_1094210, _1094214)))], (31623 ^ _780478) ^ [_1376565, _1376567] : [31624 ^ _780478 : [(31625 ^ _780478) ^ [_1376629, _1376631] : [_1376567 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1376565, _1376629), 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)), _1376631)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1376565), _1376567)))], (16434 ^ _780478) ^ [_1080327, _1080329, _1080331, _1080333] : [class_Lattices_Osemilattice__inf(_1080327), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080327), _1080329)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1080327, _1080327, c_Lattices_Osemilattice__inf__class_Oinf(_1080327)), _1080331), hAPP(hAPP(c_Set_Oinsert(_1080327), _1080333), _1080329)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1080327), _1080333), hAPP(hAPP(c_Finite__Set_Ofold(_1080327, _1080327, c_Lattices_Osemilattice__inf__class_Oinf(_1080327)), _1080331), _1080329)))], (44570 ^ _780478) ^ [_1672548, _1672550, _1672552] : [-(_1672548 = c_List_Olist_ONil(_1672550)), -(c_List_Olast(_1672550, hAPP(hAPP(c_List_Oappend(_1672550), _1672552), _1672548)) = c_List_Olast(_1672550, _1672548))], (3936 ^ _780478) ^ [_839675, _839677, _839679, _839681, _839683, _839685, _839687, _839689, _839691, _839693, _839695, _839697, _839699, _839701] : [-(c_New__Random__Sequence_Opos__decr__bind(_839701, _839697, _839693, _839689, _839685, _839681, _839677) = c_New__Random__Sequence_Opos__decr__bind(_839699, _839695, _839691, _839687, _839683, _839679, _839675)), _839701 = _839699, _839697 = _839695, _839693 = _839691, _839689 = _839687, _839685 = _839683, _839681 = _839679, _839677 = _839675], (6956 ^ _780478) ^ [_896409, _896411, _896413, _896415, _896417] : [class_Groups_Oab__group__add(_896409), hBOOL(hAPP(c_Finite__Set_Ofinite(_896411), _896413)), 6963 ^ _780478 : [(6970 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_896411), _896415), _896413))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896411, _896409), _896417), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896411, tc_HOL_Obool)), _896413), hAPP(hAPP(c_Set_Oinsert(_896411), _896415), c_Orderings_Obot__class_Obot(tc_fun(_896411, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896411, _896409), _896417), _896413))], (6964 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_896411), _896415), _896413)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896411, _896409), _896417), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896411, tc_HOL_Obool)), _896413), hAPP(hAPP(c_Set_Oinsert(_896411), _896415), c_Orderings_Obot__class_Obot(tc_fun(_896411, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_896409), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_896411, _896409), _896417), _896413)), hAPP(_896417, _896415)))]]], (39412 ^ _780478) ^ [_1545923, _1545925] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1545923, _1545923)), _1545925)), c_Wellfounded_Oacyclic(_1545923, _1545925), -(c_Wellfounded_Owf(_1545923, _1545925))], (18247 ^ _780478) ^ [_1121729, _1121731, _1121733] : [class_Rings_Ocomm__semiring__1(_1121729), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1121729), _1121731), hAPP(c_Nat_OSuc, _1121733)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121729), _1121731), hAPP(hAPP(c_Power_Opower__class_Opower(_1121729), _1121731), _1121733)))], (24693 ^ _780478) ^ [_1239335, _1239337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1239337)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1239335, _1239337))))], (43271 ^ _780478) ^ [_1643201, _1643203, _1643205, _1643207, _1643209] : [-(hAPP(hAPP(c_List_Ozip(_1643201, _1643203), _1643205), hAPP(hAPP(c_List_Olist_OCons(_1643203), _1643207), _1643209)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1643201, _1643203)), _1643201, c_List_Olist_ONil(tc_prod(_1643201, _1643203)), hAPP(hAPP(c_COMBC(_1643201, tc_fun(tc_List_Olist(_1643201), tc_List_Olist(tc_prod(_1643201, _1643203))), tc_fun(tc_List_Olist(_1643201), tc_List_Olist(tc_prod(_1643201, _1643203)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1643201, _1643203)), tc_List_Olist(tc_prod(_1643201, _1643203))), tc_fun(tc_fun(tc_List_Olist(_1643201), tc_List_Olist(tc_prod(_1643201, _1643203))), tc_fun(tc_List_Olist(_1643201), tc_List_Olist(tc_prod(_1643201, _1643203)))), _1643201), c_COMBB(tc_List_Olist(tc_prod(_1643201, _1643203)), tc_List_Olist(tc_prod(_1643201, _1643203)), tc_List_Olist(_1643201))), hAPP(hAPP(c_COMBB(tc_prod(_1643201, _1643203), tc_fun(tc_List_Olist(tc_prod(_1643201, _1643203)), tc_List_Olist(tc_prod(_1643201, _1643203))), _1643201), c_List_Olist_OCons(tc_prod(_1643201, _1643203))), hAPP(hAPP(c_COMBC(_1643201, _1643203, tc_prod(_1643201, _1643203)), c_Product__Type_OPair(_1643201, _1643203)), _1643207)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1643201), tc_List_Olist(_1643203), tc_List_Olist(tc_prod(_1643201, _1643203))), c_List_Ozip(_1643201, _1643203)), _1643209))), _1643205))], (36288 ^ _780478) ^ [_1470616, _1470618, _1470620, _1470622, _1470624, _1470626] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470616, tc_fun(_1470618, tc_HOL_Obool))), _1470620), _1470622), _1470624), _1470626)), -(hBOOL(hAPP(hAPP(_1470620, _1470624), _1470626)))], (26116 ^ _780478) ^ [_1264608, _1264610, _1264612, _1264614] : [class_Fields_Olinordered__field(_1264608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264608), c_Groups_Ozero__class_Ozero(_1264608)), _1264610)), 26123 ^ _780478 : [(26130 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264608), _1264612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264608), _1264614), _1264610))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264608), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264608), _1264612), _1264610)), _1264614)))], (26124 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264608), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264608), _1264612), _1264610)), _1264614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264608), _1264612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264608), _1264614), _1264610))))]]], (5002 ^ _780478) ^ [_856800, _856802, _856804, _856806] : [-(c_Hilbert__Choice_OEps(_856806, _856802) = c_Hilbert__Choice_OEps(_856804, _856800)), _856806 = _856804, _856802 = _856800], (10885 ^ _780478) ^ [_970293, _970295, _970297] : [class_Groups_Oordered__ab__group__add(_970293), 10888 ^ _780478 : [(10895 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970293), hAPP(c_Groups_Ouminus__class_Ouminus(_970293), _970297)), _970295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970293), hAPP(c_Groups_Ouminus__class_Ouminus(_970293), _970295)), _970297)))], (10889 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970293), hAPP(c_Groups_Ouminus__class_Ouminus(_970293), _970295)), _970297)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_970293), hAPP(c_Groups_Ouminus__class_Ouminus(_970293), _970297)), _970295)))]]], (12832 ^ _780478) ^ [_1007888, _1007890, _1007892] : [class_Lattices_Olattice(_1007888), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007888), _1007890), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007888), _1007892), _1007890))))], (43734 ^ _780478) ^ [_1654051, _1654053, _1654055, _1654057, _1654059] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1654051), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654053)), _1654055)))), -(hAPP(hAPP(c_List_Olist__update(_1654053, hAPP(hAPP(c_List_Oappend(_1654053), _1654055), _1654057)), _1654051), _1654059) = hAPP(hAPP(c_List_Oappend(_1654053), _1654055), hAPP(hAPP(c_List_Olist__update(_1654053, _1654057), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1654051), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654053)), _1654055))), _1654059)))], (39707 ^ _780478) ^ [_1553606, _1553608] : [-(c_Hilbert__Choice_OEps(_1553606, hAPP(hAPP(c_COMBC(_1553606, _1553606, tc_HOL_Obool), c_fequal), _1553608)) = _1553608)], (1124 ^ _780478) ^ [_797392, _797394] : [-(class_Rings_Oring__1__no__zero__divisors(_797392)), _797394 = _797392, class_Rings_Oring__1__no__zero__divisors(_797394)], (22680 ^ _780478) ^ [_1202743] : [_1202743 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202743) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (12335 ^ _780478) ^ [_997931, _997933, _997935, _997937] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_997931), _997933)), hBOOL(hAPP(hAPP(c_member(_997931), _997935), _997933)), hBOOL(hAPP(hAPP(c_member(_997931), _997937), _997933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_997931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_997931, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_997931, tc_HOL_Obool)), _997933), hAPP(hAPP(c_Set_Oinsert(_997931), _997935), c_Orderings_Obot__class_Obot(tc_fun(_997931, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_997931), _997937), c_Orderings_Obot__class_Obot(tc_fun(_997931, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_997931), _997933))))], (2258 ^ _780478) ^ [_813486, _813488, _813490, _813492] : [-(c_Com_Ocom_OSemi(_813492, _813488) = c_Com_Ocom_OSemi(_813490, _813486)), _813492 = _813490, _813488 = _813486], (48421 ^ _780478) ^ [_1756667, _1756669, _1756671, _1756673, _1756675] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1756667), _1756669), _1756671), _1756673), _1756675) = c_New__DSequence_Oneg__single(_1756667, _1756669))], (25627 ^ _780478) ^ [_1256033, _1256035] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256033) = _1256035, 25630 ^ _780478 : [(25633 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256035)))], (25631 ^ _780478) ^ [] : [-(_1256033 = hAPP(c_Int_Onat, _1256035))]]], (40859 ^ _780478) ^ [_1580613, _1580615, _1580617, _1580619] : [-(hAPP(c_Relation_Oconverse(_1580613, _1580615), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1580613, _1580615), tc_HOL_Obool)), _1580617), _1580619)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1580615, _1580613), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1580613, _1580615), _1580617)), hAPP(c_Relation_Oconverse(_1580613, _1580615), _1580619)))], (23819 ^ _780478) ^ [_1223501, _1223503] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223501)), -(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), _1223501), _1223503))))], (37708 ^ _780478) ^ [_1500090, _1500092, _1500094, _1500096] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1500090), _1500092)), 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)), _1500090), _1500094)), 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)), _1500092), _1500096)), 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)), _1500092), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1500094), _1500096))), c_FunDef_Omin__weak)))], (8412 ^ _780478) ^ [_924890, _924892, _924894, _924896, _924898] : [class_Groups_Ocomm__monoid__add(_924890), hBOOL(hAPP(c_Finite__Set_Ofinite(_924892), _924894)), -(hBOOL(hAPP(hAPP(c_member(_924892), _924896), _924894))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_924892, _924890), _924898), hAPP(hAPP(c_Set_Oinsert(_924892), _924896), _924894)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924890), hAPP(_924898, _924896)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_924892, _924890), _924898), _924894)))], (18970 ^ _780478) ^ [_1136570, _1136572] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1136570), hAPP(c_Nat_OSuc, _1136572)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1136570), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1136572))], (21694 ^ _780478) ^ [_1183361, _1183363, _1183365, _1183367] : [class_Rings_Olinordered__semidom(_1183361), hAPP(hAPP(c_Power_Opower__class_Opower(_1183361), _1183363), hAPP(c_Nat_OSuc, _1183365)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1183361), _1183367), hAPP(c_Nat_OSuc, _1183365)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183361), c_Groups_Ozero__class_Ozero(_1183361)), _1183363)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183361), c_Groups_Ozero__class_Ozero(_1183361)), _1183367)), -(_1183363 = _1183367)], (38513 ^ _780478) ^ [_1521063, _1521065, _1521067, _1521069, _1521071] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1521063, _1521065)), hAPP(hAPP(c_Product__Type_OPair(_1521063, _1521065), _1521067), _1521069)), _1521071)), -(hBOOL(hAPP(hAPP(c_member(_1521065), _1521069), hAPP(c_Relation_ORange(_1521063, _1521065), _1521071))))], (30817 ^ _780478) ^ [_1352959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1352959)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1352959 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6132 ^ _780478) ^ [_878366, _878368, _878370, _878372, _878374] : [hAPP(hAPP(c_Set_Oinsert(_878366), _878368), hAPP(hAPP(c_Set_Oinsert(_878366), _878370), c_Orderings_Obot__class_Obot(tc_fun(_878366, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_878366), _878372), hAPP(hAPP(c_Set_Oinsert(_878366), _878374), c_Orderings_Obot__class_Obot(tc_fun(_878366, tc_HOL_Obool)))), 6137 ^ _780478 : [(6140 ^ _780478) ^ [] : [-(_878370 = _878374)], (6138 ^ _780478) ^ [] : [-(_878368 = _878372)]], 6141 ^ _780478 : [(6144 ^ _780478) ^ [] : [-(_878370 = _878372)], (6142 ^ _780478) ^ [] : [-(_878368 = _878374)]]], (43855 ^ _780478) ^ [_1657476, _1657478] : [hBOOL(hAPP(c_List_Odistinct(_1657476), _1657478)), -(hBOOL(hAPP(c_List_Odistinct(_1657476), hAPP(c_List_Orotate1(_1657476), _1657478))))], (18025 ^ _780478) ^ [_1115949, _1115951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115951)), _1115949)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115949), _1115951))], (19416 ^ _780478) ^ [_1143932] : [hAPP(c_Nat_OSuc, _1143932) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (34261 ^ _780478) ^ [_1426624, _1426626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1426624)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1426626)), _1426624) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1426626), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1426624), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (38153 ^ _780478) ^ [_1513477, _1513479, _1513481, _1513483] : [-(c_Wellfounded_Omax__extp(_1513477, _1513479, _1513481, _1513483)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513477), _1513481)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513477), _1513483)), -(_1513483 = c_Orderings_Obot__class_Obot(tc_fun(_1513477, tc_HOL_Obool))), 38167 ^ _780478 : [(38170 ^ _780478) ^ [_1513822] : [hBOOL(hAPP(hAPP(c_member(_1513477), _1513822), _1513483)), hBOOL(hAPP(hAPP(_1513479, 38166 ^ [_1513477, _1513479, _1513481, _1513483]), _1513822))], (38168 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513477), 38166 ^ [_1513477, _1513479, _1513481, _1513483]), _1513481)))]]], (43861 ^ _780478) ^ [_1657581, _1657583, _1657585] : [-(c_List_Obutlast(_1657581, hAPP(hAPP(c_List_Odrop(_1657581), _1657583), _1657585)) = hAPP(hAPP(c_List_Odrop(_1657581), _1657583), c_List_Obutlast(_1657581, _1657585)))], (35073 ^ _780478) ^ [_1441373, _1441375, _1441377] : [class_Rings_Olinordered__idom(_1441373), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1441373), c_Groups_Ozero__class_Ozero(_1441373)), hAPP(hAPP(c_Power_Opower__class_Opower(_1441373), _1441375), 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)))), _1441377)))))], (17418 ^ _780478) ^ [_1102737, _1102739, _1102741, _1102743, _1102745] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102737, tc_fun(_1102739, tc_HOL_Obool)), _1102741), hAPP(hAPP(c_COMBS(_1102737, tc_fun(_1102739, tc_HOL_Obool), tc_fun(_1102739, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1102739, tc_HOL_Obool), tc_fun(tc_fun(_1102739, tc_HOL_Obool), tc_fun(_1102739, tc_HOL_Obool)), _1102737), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102739, tc_HOL_Obool))), _1102743)), _1102745)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102739, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102737, tc_fun(_1102739, tc_HOL_Obool)), _1102741), _1102743)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102737, tc_fun(_1102739, tc_HOL_Obool)), _1102741), _1102745)))], (47829 ^ _780478) ^ [_1744169, _1744171, _1744173, _1744175, _1744177] : [hAPP(hAPP(c_List_Olist_OCons(_1744169), _1744171), _1744173) = hAPP(c_List_Ofilter(_1744169, _1744175), _1744177), 47834 ^ _780478 : [(47843 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1744175, _1744171)))], (47845 ^ _780478) ^ [] : [-(_1744173 = hAPP(c_List_Ofilter(_1744169, _1744175), 47833 ^ [_1744169, _1744171, _1744173, _1744175, _1744177]))], (47837 ^ _780478) ^ [_1744483] : [hBOOL(hAPP(hAPP(c_member(_1744169), _1744483), hAPP(c_List_Oset(_1744169), 47832 ^ [_1744169, _1744171, _1744173, _1744175, _1744177]))), hBOOL(hAPP(_1744175, _1744483))], (47835 ^ _780478) ^ [] : [-(_1744177 = hAPP(hAPP(c_List_Oappend(_1744169), 47832 ^ [_1744169, _1744171, _1744173, _1744175, _1744177]), hAPP(hAPP(c_List_Olist_OCons(_1744169), _1744171), 47833 ^ [_1744169, _1744171, _1744173, _1744175, _1744177])))]]], (21660 ^ _780478) ^ [_1182696] : [class_Rings_Olinordered__semidom(_1182696), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182696), c_Groups_Ozero__class_Ozero(_1182696)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182696), c_Groups_Oone__class_Oone(_1182696)), c_Groups_Oone__class_Oone(_1182696)))))], (49762 ^ _780478) ^ [_1786835, _1786837] : [-(c_Relation_Osym(_1786835, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1786835, _1786835), tc_HOL_Obool)), _1786837), hAPP(c_Relation_Oconverse(_1786835, _1786835), _1786837))))], (48982 ^ _780478) ^ [_1768852, _1768854, _1768856] : [-(c_FunDef_OTHE__default(_1768854, _1768856, _1768852) = _1768856), 48984 ^ _780478 : [(48987 ^ _780478) ^ [_1768974] : [hBOOL(hAPP(_1768852, _1768974)), -(_1768974 = 48983 ^ [_1768852, _1768854, _1768856])], (48985 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1768852, 48983 ^ [_1768852, _1768854, _1768856])))]]], (33040 ^ _780478) ^ [_1404894] : [-(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), _1404894)) = 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), _1404894))))], (33224 ^ _780478) ^ [_1408151, _1408153, _1408155, _1408157, _1408159, _1408161, _1408163, _1408165, _1408167] : [c_Equiv__Relations_Oequiv(_1408151, _1408153, _1408155), c_Equiv__Relations_Oequiv(_1408157, _1408159, _1408161), c_Equiv__Relations_Ocongruent2(_1408151, _1408157, tc_fun(_1408163, tc_HOL_Obool), _1408155, _1408161, _1408165), hBOOL(hAPP(hAPP(c_member(_1408157), _1408167), _1408159)), -(c_Equiv__Relations_Ocongruent(_1408151, tc_fun(_1408163, tc_HOL_Obool), _1408155, hAPP(hAPP(c_COMBB(tc_fun(_1408157, tc_fun(_1408163, tc_HOL_Obool)), tc_fun(_1408163, tc_HOL_Obool), _1408151), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408157, tc_fun(_1408163, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1408157, _1408157, _1408161), hAPP(hAPP(c_Set_Oinsert(_1408157), _1408167), c_Orderings_Obot__class_Obot(tc_fun(_1408157, tc_HOL_Obool)))))), _1408165)))], (9826 ^ _780478) ^ [_950479, _950481, _950483, _950485] : [class_Rings_Ocomm__semiring__1(_950479), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950479), _950481), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950479), _950483), _950485)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950479), _950483), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950479), _950481), _950485)))], (48491 ^ _780478) ^ [_1758278, _1758280, _1758282, _1758284, _1758286] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1758278, _1758280, _1758282), _1758284), _1758286)), -(hBOOL(hAPP(hAPP(_1758282, _1758286), _1758284)))], (47499 ^ _780478) ^ [_1736562, _1736564] : [class_Orderings_Olinorder(_1736562), 47502 ^ _780478 : [(47523 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1736562, _1736564)), 47524 ^ _780478 : [(47527 ^ _780478) ^ [_1737122, _1737124] : [_1736564 = hAPP(hAPP(c_List_Olist_OCons(_1736562), _1737122), _1737124), 47533 ^ _780478 : [(47536 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1736562), _1737122), 47532 ^ [_1736562, _1736564, _1737122, _1737124]))], (47534 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736562), 47532 ^ [_1736562, _1736564, _1737122, _1737124]), hAPP(c_List_Oset(_1736562), _1737124))))]], c_List_Olinorder__class_Osorted(_1736562, _1737124)], (47525 ^ _780478) ^ [] : [_1736564 = c_List_Olist_ONil(_1736562)]]], (47503 ^ _780478) ^ [] : [c_List_Olinorder__class_Osorted(_1736562, _1736564), -(_1736564 = c_List_Olist_ONil(_1736562)), 47512 ^ _780478 : [(47515 ^ _780478) ^ [_1736896] : [hBOOL(hAPP(hAPP(c_member(_1736562), _1736896), hAPP(c_List_Oset(_1736562), 47510 ^ [_1736562, _1736564]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1736562), 47511 ^ [_1736562, _1736564]), _1736896)))], (47521 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1736562, 47510 ^ [_1736562, _1736564]))], (47513 ^ _780478) ^ [] : [-(_1736564 = hAPP(hAPP(c_List_Olist_OCons(_1736562), 47511 ^ [_1736562, _1736564]), 47510 ^ [_1736562, _1736564]))]]]]], (22622 ^ _780478) ^ [_1201808, _1201810, _1201812] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201808), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201810), _1201812)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201808), _1201810)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201808), _1201812)))], (2242 ^ _780478) ^ [_813252, _813254, _813256, _813258] : [-(c_Nitpick_Onat__lcm(_813258, _813254) = c_Nitpick_Onat__lcm(_813256, _813252)), _813258 = _813256, _813254 = _813252], (3156 ^ _780478) ^ [_827375, _827377, _827379, _827381] : [-(c_Big__Operators_Olattice__class_OSup__fin(_827381, _827377) = c_Big__Operators_Olattice__class_OSup__fin(_827379, _827375)), _827381 = _827379, _827377 = _827375], (5759 ^ _780478) ^ [_871514, _871516] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_871514, _871516, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871514), tc_HOL_Obool))))], (37287 ^ _780478) ^ [_1489989, _1489991, _1489993, _1489995, _1489997] : [hBOOL(hAPP(hAPP(_1489989, _1489991), _1489993)), -(hBOOL(hAPP(hAPP(_1489989, hAPP(c_Product__Type_Osnd(_1489995, _1489997), hAPP(hAPP(c_Product__Type_OPair(_1489995, _1489997), _1489993), _1489991))), hAPP(c_Product__Type_Ofst(_1489995, _1489997), hAPP(hAPP(c_Product__Type_OPair(_1489995, _1489997), _1489993), _1489991)))))], (16290 ^ _780478) ^ [_1076596, _1076598] : [class_Lattices_Oboolean__algebra(_1076596), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076596), hAPP(c_Groups_Ouminus__class_Ouminus(_1076596), _1076598)), _1076598) = c_Orderings_Obot__class_Obot(_1076596))], (40830 ^ _780478) ^ [_1579797, _1579799, _1579801, _1579803, _1579805] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579797, _1579797)), hAPP(hAPP(c_Product__Type_OPair(_1579797, _1579797), hAPP(_1579799, hAPP(c_Nat_OSuc, 40831 ^ [_1579797, _1579799, _1579801, _1579803, _1579805]))), hAPP(_1579799, 40831 ^ [_1579797, _1579799, _1579801, _1579803, _1579805]))), c_Transitive__Closure_Ortrancl(_1579797, _1579801))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579797, _1579797)), hAPP(hAPP(c_Product__Type_OPair(_1579797, _1579797), hAPP(_1579799, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1579803), _1579805))), hAPP(_1579799, _1579803))), c_Transitive__Closure_Ortrancl(_1579797, _1579801))))], (22688 ^ _780478) ^ [_1202859, _1202861] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202859)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202861), 22691 ^ _780478 : [(22694 ^ _780478) ^ [] : [-(_1202861 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22692 ^ _780478) ^ [] : [-(_1202859 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (52287 ^ _780478) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (16817 ^ _780478) ^ [_1088969, _1088971, _1088973, _1088975, _1088977] : [class_Groups_Oab__group__add(_1088969), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088971), _1088973)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088971), _1088975)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088971, _1088969), _1088977), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088971, tc_HOL_Obool)), _1088973), _1088975)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1088969), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088969), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088971, _1088969), _1088977), _1088973)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088971, _1088969), _1088977), _1088975))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088971, _1088969), _1088977), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088971, tc_HOL_Obool)), _1088973), _1088975))))], (17087 ^ _780478) ^ [_1094687, _1094689, _1094691] : [class_Orderings_Olinorder(_1094687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094687), _1094689)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1094687), _1094691)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1094687, tc_HOL_Obool)), _1094689), _1094691) = c_Orderings_Obot__class_Obot(tc_fun(_1094687, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094687), c_Big__Operators_Olattice_OInf__fin(_1094687, c_Orderings_Oord__class_Omin(_1094687), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1094687, tc_HOL_Obool)), _1094689), _1094691))), c_Big__Operators_Olattice_OInf__fin(_1094687, c_Orderings_Oord__class_Omin(_1094687), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1094687, tc_HOL_Obool)), _1094689), _1094691))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094687), c_Big__Operators_Olattice_OInf__fin(_1094687, c_Orderings_Oord__class_Omin(_1094687), _1094689)), c_Big__Operators_Olattice_OInf__fin(_1094687, c_Orderings_Oord__class_Omin(_1094687), _1094691)))], (27828 ^ _780478) ^ [_1295303, _1295305] : [27836 ^ _780478 : [(27839 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1295305, 27835 ^ [_1295303, _1295305])))], (27837 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27835 ^ [_1295303, _1295305]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1295303))))]], 27829 ^ _780478 : [(27830 ^ _780478) ^ [_1295372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1295372), _1295303)), hBOOL(hAPP(_1295305, _1295372))]]], (44149 ^ _780478) ^ [_1664084, _1664086, _1664088] : [hAPP(c_List_Orotate(_1664084, _1664086), _1664088) = c_List_Olist_ONil(_1664084), -(_1664088 = c_List_Olist_ONil(_1664084))], (38724 ^ _780478) ^ [_1527080, _1527082, _1527084] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1527080, _1527082), c_Orderings_Obot__class_Obot(tc_fun(_1527080, tc_HOL_Obool))), _1527084) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527080, _1527082), tc_HOL_Obool)))], (4820 ^ _780478) ^ [_853955, _853957, _853959, _853961] : [-(c_Product__Type_Ofst(_853961, _853957) = c_Product__Type_Ofst(_853959, _853955)), _853961 = _853959, _853957 = _853955], (48443 ^ _780478) ^ [_1757272, _1757274] : [c_Wellfounded_Oacyclic(_1757272, hAPP(c_Set_OCollect(tc_prod(_1757272, _1757272)), hAPP(c_Product__Type_Oprod_Oprod__case(_1757272, _1757272, tc_HOL_Obool), c_Predicate_Oconversep(_1757272, _1757272, _1757274)))), -(c_Wellfounded_Oacyclic(_1757272, hAPP(c_Set_OCollect(tc_prod(_1757272, _1757272)), hAPP(c_Product__Type_Oprod_Oprod__case(_1757272, _1757272, tc_HOL_Obool), _1757274))))], (40536 ^ _780478) ^ [_1573315, _1573317, _1573319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573315, _1573315), tc_HOL_Obool)), _1573317), c_Transitive__Closure_Ortrancl(_1573315, _1573319))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1573315, _1573315), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1573315, _1573317)), c_Transitive__Closure_Ortrancl(_1573315, _1573319))))], (43177 ^ _780478) ^ [_1641461, _1641463, _1641465] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641461), tc_List_Olist(_1641461))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641461), tc_List_Olist(_1641461)), _1641463), c_List_Olist_ONil(_1641461))), c_List_Olex(_1641461, _1641465)))], (42388 ^ _780478) ^ [_1622752, _1622754, _1622756] : [42390 ^ _780478 : [(42393 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1622752), 42389 ^ [_1622752, _1622754, _1622756]), _1622756))], (42391 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622752), 42389 ^ [_1622752, _1622754, _1622756]), hAPP(c_List_Oset(_1622752), _1622754))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622752)), _1622754), c_List_Olists(_1622752, _1622756))))], (37915 ^ _780478) ^ [_1505656, _1505658, _1505660, _1505662] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1505656, _1505658, _1505660, c_Code__Numeral_OSuc__code__numeral(_1505662)) = hAPP(_1505660, _1505662))], (2368 ^ _780478) ^ [_815165, _815167, _815169, _815171] : [-(c_Divides_Opdivmod(_815171, _815167) = c_Divides_Opdivmod(_815169, _815165)), _815171 = _815169, _815167 = _815165], (25567 ^ _780478) ^ [_1255124, _1255126] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1255124)), hAPP(c_Int_Onat, _1255126)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255124), _1255126))], (51973 ^ _780478) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (41069 ^ _780478) ^ [_1586209] : [-(hAPP(c_Relation_ODomain(_1586209, _1586209), c_Relation_OId(_1586209)) = c_Orderings_Otop__class_Otop(tc_fun(_1586209, tc_HOL_Obool)))], (9374 ^ _780478) ^ [_941001, _941003, _941005, _941007] : [class_Groups_Oordered__cancel__ab__semigroup__add(_941001), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941001), _941003), _941005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941001), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941001), _941007), _941003)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941001), _941007), _941005))))], (11305 ^ _780478) ^ [_978282, _978284, _978286] : [class_Orderings_Olinorder(_978282), -(_978284 = c_Orderings_Obot__class_Obot(tc_fun(_978282, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978282, tc_HOL_Obool)), _978284), _978286)), hBOOL(hAPP(c_Finite__Set_Ofinite(_978282), _978286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978282), hAPP(c_Finite__Set_Ofold1(_978282, c_Orderings_Oord__class_Omin(_978282)), _978286)), hAPP(c_Finite__Set_Ofold1(_978282, c_Orderings_Oord__class_Omin(_978282)), _978284))))], (46673 ^ _780478) ^ [_1719183, _1719185, _1719187] : [class_Orderings_Olinorder(_1719183), -(c_List_Olinorder__class_Osorted(_1719183, hAPP(c_List_Ofilter(_1719183, hAPP(hAPP(c_COMBC(_1719183, _1719183, tc_HOL_Obool), c_fequal), hAPP(_1719185, _1719187))), _1719187)))], (33752 ^ _780478) ^ [_1417639, _1417641, _1417643, _1417645, _1417647, _1417649, _1417651, _1417653, _1417655, _1417657, _1417659] : [c_Equiv__Relations_Oequiv(_1417639, _1417641, _1417643), c_Equiv__Relations_Oequiv(_1417645, _1417647, _1417649), c_Equiv__Relations_Ocongruent2(_1417639, _1417645, tc_fun(_1417651, tc_HOL_Obool), _1417643, _1417649, _1417653), hBOOL(hAPP(hAPP(c_member(tc_fun(_1417639, tc_HOL_Obool)), _1417655), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1417639), _1417641), _1417643))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1417645, tc_HOL_Obool)), _1417657), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1417645), _1417647), _1417649))), 33774 ^ _780478 : [(33780 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1417651, tc_HOL_Obool)), hAPP(hAPP(_1417653, 33773 ^ [_1417639, _1417641, _1417643, _1417645, _1417647, _1417649, _1417651, _1417653, _1417655, _1417657, _1417659]), 33776 ^ [_1417639, _1417641, _1417643, _1417645, _1417647, _1417649, _1417651, _1417653, _1417655, _1417657, _1417659])), _1417659))], (33778 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417645), 33776 ^ [_1417639, _1417641, _1417643, _1417645, _1417647, _1417649, _1417651, _1417653, _1417655, _1417657, _1417659]), _1417647)))], (33775 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417639), 33773 ^ [_1417639, _1417641, _1417643, _1417645, _1417647, _1417649, _1417651, _1417653, _1417655, _1417657, _1417659]), _1417641)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1417651, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417639, tc_fun(_1417651, tc_HOL_Obool)), _1417655), hAPP(hAPP(c_COMBB(tc_fun(_1417645, tc_fun(_1417651, tc_HOL_Obool)), tc_fun(_1417651, tc_HOL_Obool), _1417639), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417645, tc_fun(_1417651, tc_HOL_Obool)), _1417657)), _1417653))), _1417659)))], (42310 ^ _780478) ^ [_1620983, _1620985, _1620987, _1620989] : [hBOOL(hAPP(hAPP(c_member(_1620983), _1620985), hAPP(c_List_Oset(_1620983), hAPP(hAPP(c_List_Olist_OCons(_1620983), _1620987), _1620989)))), -(_1620985 = _1620987), -(hBOOL(hAPP(hAPP(c_member(_1620983), _1620985), hAPP(c_List_Oset(_1620983), _1620989))))], (10651 ^ _780478) ^ [_966275, _966277, _966279, _966281, _966283] : [class_Orderings_Olinorder(_966275), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966275), _966277), _966279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966275), _966281), _966283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_966275), hAPP(hAPP(c_Orderings_Oord__class_Omin(_966275), _966277), _966281)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_966275), _966279), _966283))))], (10415 ^ _780478) ^ [_962185, _962187, _962189, _962191] : [class_Orderings_Olinorder(_962185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962185), _962187), _962189)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962185), _962191), _962189)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962185), hAPP(hAPP(c_Orderings_Oord__class_Omax(_962185), _962187), _962191)), _962189)))], (39047 ^ _780478) ^ [_1537333, _1537335, _1537337, _1537339] : [class_Groups_Ocomm__monoid__mult(_1537333), c_Fun_Oinj__on(_1537335, _1537333, _1537337, _1537339), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1537335, _1537333), _1537337), _1537339) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1537333, _1537333), c_Fun_Oid(_1537333)), hAPP(c_Set_Oimage(_1537335, _1537333, _1537337), _1537339)))], (48455 ^ _780478) ^ [_1757578, _1757580, _1757582] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757578, _1757578, hAPP(hAPP(c_COMBB(tc_fun(_1757578, tc_HOL_Obool), tc_fun(_1757578, tc_HOL_Obool), _1757578), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1757578), c_fNot)), c_fequal)), _1757580), _1757582)), _1757580 = _1757582], (30407 ^ _780478) ^ [_1344947, _1344949, _1344951] : [class_Complete__Lattice_Ocomplete__lattice(_1344947), class_Orderings_Olinorder(_1344947), 30414 ^ _780478 : [(30424 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344947), _1344949), c_Complete__Lattice_OSup__class_OSup(_1344947, _1344951)))), 30425 ^ _780478 : [(30426 ^ _780478) ^ [_1345253] : [hBOOL(hAPP(hAPP(c_member(_1344947), _1345253), _1344951)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344947), _1344949), _1345253))]]], (30415 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344947), _1344949), c_Complete__Lattice_OSup__class_OSup(_1344947, _1344951))), 30419 ^ _780478 : [(30422 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344947), _1344949), 30418 ^ [_1344947, _1344949, _1344951])))], (30420 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344947), 30418 ^ [_1344947, _1344949, _1344951]), _1344951)))]]]]], (45430 ^ _780478) ^ [_1692092, _1692094, _1692096, _1692098, _1692100, _1692102, _1692104] : [c_List_Olist__all2(_1692092, _1692094, _1692096, _1692098, hAPP(hAPP(c_List_Omap(_1692100, _1692094), _1692102), _1692104)), -(c_List_Olist__all2(_1692092, _1692100, hAPP(hAPP(c_COMBC(_1692092, tc_fun(_1692100, _1692094), tc_fun(_1692100, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1692094, tc_HOL_Obool), tc_fun(tc_fun(_1692100, _1692094), tc_fun(_1692100, tc_HOL_Obool)), _1692092), c_COMBB(_1692094, tc_HOL_Obool, _1692100)), _1692096)), _1692102), _1692098, _1692104))], (4618 ^ _780478) ^ [_850734, _850736, _850738, _850740] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850740, _850736) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_850738, _850734)), _850740 = _850738, _850736 = _850734], (20778 ^ _780478) ^ [_1167613, _1167615, _1167617] : [class_Groups_Ogroup__add(_1167613), 20781 ^ _780478 : [(20788 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167613), _1167615), _1167617) = c_Groups_Ozero__class_Ozero(_1167613), -(_1167615 = hAPP(c_Groups_Ouminus__class_Ouminus(_1167613), _1167617))], (20782 ^ _780478) ^ [] : [_1167615 = hAPP(c_Groups_Ouminus__class_Ouminus(_1167613), _1167617), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167613), _1167615), _1167617) = c_Groups_Ozero__class_Ozero(_1167613))]]], (14044 ^ _780478) ^ [_1031536, _1031538] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031536), _1031538) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1031536 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1031538 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (27235 ^ _780478) ^ [_1284700, _1284702] : [c_Nat__Transfer_Onat__set(_1284700), c_Nat__Transfer_Onat__set(_1284702), 27242 ^ _780478 : [(27249 ^ _780478) ^ [] : [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), _1284700)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1284702))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1284700), _1284702)))], (27243 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1284700), _1284702)), -(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), _1284700)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1284702))))]]], (47029 ^ _780478) ^ [_1726570, _1726572, _1726574] : [hAPP(c_List_Orev(_1726570), _1726572) = _1726574, -(_1726572 = hAPP(c_List_Orev(_1726570), _1726574))], (6069 ^ _780478) ^ [_877088, _877090, _877092, _877094] : [hBOOL(hAPP(hAPP(c_member(_877088), _877090), hAPP(hAPP(c_Set_Oinsert(_877088), _877092), _877094))), -(_877090 = _877092), -(hBOOL(hAPP(hAPP(c_member(_877088), _877090), _877094)))], (41047 ^ _780478) ^ [_1585784] : [-(c_Relation_Osingle__valued(_1585784, _1585784, c_Relation_OId(_1585784)))], (20086 ^ _780478) ^ [_1155109, _1155111, _1155113, _1155115] : [class_Rings_Oordered__ring(_1155109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155109), _1155111), _1155113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155109), _1155115), c_Groups_Ozero__class_Ozero(_1155109))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155109), _1155113), _1155115)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155109), _1155111), _1155115))))], (28106 ^ _780478) ^ [_1300418, _1300420, _1300422, _1300424] : [class_Orderings_Oorder(_1300418), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300418, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300418, _1300420, _1300422)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1300418, _1300422, _1300424)) = c_Orderings_Obot__class_Obot(tc_fun(_1300418, tc_HOL_Obool)))], (38998 ^ _780478) ^ [_1536163, _1536165, _1536167, _1536169] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1536165, _1536163), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1536163, tc_prod(_1536165, _1536163), 38994 ^ [_1536163, _1536165, _1536167, _1536169]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1536165, tc_fun(_1536163, tc_HOL_Obool)), _1536167), _1536169))), hAPP(hAPP(c_Product__Type_OSigma(_1536165, _1536163), _1536167), _1536169))))], (39688 ^ _780478) ^ [_1553282, _1553284] : [39689 ^ _780478 : [(39690 ^ _780478) ^ [_1553328] : [hBOOL(hAPP(_1553282, _1553328))]], -(hBOOL(hAPP(_1553282, c_Hilbert__Choice_OEps(_1553284, _1553282))))], (20498 ^ _780478) ^ [_1162712, _1162714, _1162716, _1162718] : [class_Rings_Olinordered__semiring__strict(_1162712), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162712), _1162714), _1162716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162712), c_Groups_Ozero__class_Ozero(_1162712)), _1162718)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162712), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162712), _1162718), _1162714)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162712), _1162718), _1162716))))], (40889 ^ _780478) ^ [_1581386, _1581388, _1581390, _1581392, _1581394] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581386, _1581388)), hAPP(hAPP(c_Product__Type_OPair(_1581386, _1581388), _1581390), _1581392)), _1581394)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581388, _1581386)), hAPP(hAPP(c_Product__Type_OPair(_1581388, _1581386), _1581392), _1581390)), hAPP(c_Relation_Oconverse(_1581386, _1581388), _1581394))))], (51731 ^ _780478) ^ [_1827114, _1827116, _1827118] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827114), _1827116)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827116), _1827114))), 51746 ^ _780478 : [(51749 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827118), _1827114))], (51747 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827114), _1827118)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827116), _1827118)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1827118), _1827116)))], (4228 ^ _780478) ^ [_844457, _844459] : [_844459 = _844457, -(c_List_Otake(_844459) = c_List_Otake(_844457))], (42603 ^ _780478) ^ [_1629411] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1629411)), -(c_List_Onat__list(_1629411))], (18118 ^ _780478) ^ [_1118147, _1118149, _1118151, _1118153, _1118155] : [18120 ^ _780478 : [(18123 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1118147, tc_HOL_Obool)), _1118149), hAPP(_1118155, 18119 ^ [_1118147, _1118149, _1118151, _1118153, _1118155])))], (18121 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1118151), 18119 ^ [_1118147, _1118149, _1118151, _1118153, _1118155]), _1118153)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1118147, tc_HOL_Obool)), _1118149), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1118151, tc_fun(_1118147, tc_HOL_Obool)), _1118153), _1118155))))], (7633 ^ _780478) ^ [_908980, _908982, _908984] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_908980), _908982)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908980, tc_HOL_Obool)), _908984), _908982)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_908980), _908984)))], (39257 ^ _780478) ^ [_1542688, _1542690, _1542692] : [c_Wellfounded_OwfP(_1542688, _1542690), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1542688, _1542690), _1542692)))], (11057 ^ _780478) ^ [_973456, _973458, _973460, _973462] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_973456), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973456), hAPP(hAPP(c_Orderings_Oord__class_Omin(_973456), _973458), _973460)), _973462) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_973456), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973456), _973458), _973462)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973456), _973460), _973462)))], (42017 ^ _780478) ^ [_1613273, _1613275, _1613277, _1613279, _1613281] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613273), tc_List_Olist(_1613273))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613273), tc_List_Olist(_1613273)), _1613275), hAPP(hAPP(c_List_Olist_OCons(_1613273), _1613277), _1613279))), c_List_Olistrel(_1613273, _1613281))), 42022 ^ _780478 : [(42027 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1613273), tc_List_Olist(_1613273))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1613273), tc_List_Olist(_1613273)), 42021 ^ [_1613273, _1613275, _1613277, _1613279, _1613281]), _1613279)), c_List_Olistrel(_1613273, _1613281))))], (42025 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1613273, _1613273)), hAPP(hAPP(c_Product__Type_OPair(_1613273, _1613273), 42020 ^ [_1613273, _1613275, _1613277, _1613279, _1613281]), _1613277)), _1613281)))], (42023 ^ _780478) ^ [] : [-(_1613275 = hAPP(hAPP(c_List_Olist_OCons(_1613273), 42020 ^ [_1613273, _1613275, _1613277, _1613279, _1613281]), 42021 ^ [_1613273, _1613275, _1613277, _1613279, _1613281]))]]], (46224 ^ _780478) ^ [_1710903, _1710905] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1710903))), c_List_Otranspose(_1710903, _1710905)) = c_List_Ofoldr(tc_List_Olist(_1710903), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1710903)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1710903))), _1710905, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6818 ^ _780478) ^ [_893268, _893270, _893272, _893274] : [c_Com_Ocom_OWhile(_893268, _893270) = c_Com_Ocom_OWhile(_893272, _893274), 6821 ^ _780478 : [(6824 ^ _780478) ^ [] : [-(_893270 = _893274)], (6822 ^ _780478) ^ [] : [-(_893268 = _893272)]]], (40159 ^ _780478) ^ [_1564098, _1564100, _1564102, _1564104, _1564106, _1564108] : [c_Finite__Set_Ofolding__idem(_1564098, _1564100, _1564102, _1564104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1564098), _1564106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564098, tc_HOL_Obool)), _1564108), _1564106)), -(hAPP(c_Fun_Ocomp(_1564100, _1564100, _1564100, hAPP(_1564104, _1564106)), hAPP(_1564104, _1564108)) = hAPP(_1564104, _1564106))], (50285 ^ _780478) ^ [_1797742, _1797744] : [-(c_Fun_Obij__betw(_1797742, _1797742, c_Fun_Oid(_1797742), _1797744, _1797744))], (51505 ^ _780478) ^ [_1823291, _1823293] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823293, _1823291) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823291), _1823293)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823293), _1823291)))], (45711 ^ _780478) ^ [_1698403, _1698405, _1698407, _1698409, _1698411] : [c_Fun_Oinj__on(_1698403, _1698405, _1698407, hAPP(hAPP(c_Set_Oinsert(_1698403), _1698409), hAPP(c_List_Oset(_1698403), _1698411))), -(hAPP(hAPP(c_List_Omap(_1698403, _1698405), _1698407), hAPP(c_List_OremoveAll(_1698403, _1698409), _1698411)) = hAPP(c_List_OremoveAll(_1698405, hAPP(_1698407, _1698409)), hAPP(hAPP(c_List_Omap(_1698403, _1698405), _1698407), _1698411)))], (48163 ^ _780478) ^ [_1751462, _1751464, _1751466] : [48165 ^ _780478 : [(48168 ^ _780478) ^ [] : [hBOOL(hAPP(_1751464, hAPP(hAPP(c_List_Onth(_1751462), _1751466), 48164 ^ [_1751462, _1751464, _1751466])))], (48166 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48164 ^ [_1751462, _1751464, _1751466]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751462)), _1751466))))]], -(c_List_Olist__all(_1751462, _1751464, _1751466))], (24627 ^ _780478) ^ [_1238152, _1238154, _1238156] : [-(hBOOL(hAPP(_1238152, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1238154), _1238156)))), 24630 ^ _780478 : [(24633 ^ _780478) ^ [] : [hBOOL(hAPP(_1238152, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24631 ^ _780478) ^ [] : [-(_1238156 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 24636 ^ _780478 : [(24637 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238156)))], (24643 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 24639 ^ [_1238152, _1238154, _1238156]), _1238156)))], (24647 ^ _780478) ^ [] : [hBOOL(hAPP(_1238152, 24638 ^ [_1238152, _1238154, _1238156]))], (24645 ^ _780478) ^ [] : [-(_1238154 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1238156), 24638 ^ [_1238152, _1238154, _1238156])), 24639 ^ [_1238152, _1238154, _1238156]))], (24641 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24639 ^ [_1238152, _1238154, _1238156])))]], 24648 ^ _780478 : [(24649 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238156), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24655 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 24651 ^ [_1238152, _1238154, _1238156]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24659 ^ _780478) ^ [] : [hBOOL(hAPP(_1238152, 24650 ^ [_1238152, _1238154, _1238156]))], (24657 ^ _780478) ^ [] : [-(_1238154 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1238156), 24650 ^ [_1238152, _1238154, _1238156])), 24651 ^ [_1238152, _1238154, _1238156]))], (24653 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238156), 24651 ^ [_1238152, _1238154, _1238156])))]]], (23001 ^ _780478) ^ [_1208574, _1208576, _1208578] : [class_Rings_Oring__1(_1208574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1208576), _1208578)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208574), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1208578), _1208576)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1208574), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208574), _1208578)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1208574), _1208576)))], (9652 ^ _780478) ^ [_946293, _946295, _946297, _946299, _946301, _946303] : [class_Rings_Oordered__ring(_946293), 9655 ^ _780478 : [(9662 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946293), _946299), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946293), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_946293), _946301), _946295)), _946297)), _946303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946293), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946293), _946295), _946297)), _946299)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946293), _946301), _946297)), _946303))))], (9656 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946293), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946293), _946295), _946297)), _946299)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946293), _946301), _946297)), _946303))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946293), _946299), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946293), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_946293), _946301), _946295)), _946297)), _946303))))]]], (22057 ^ _780478) ^ [_1190410, _1190412, _1190414, _1190416, _1190418, _1190420] : [class_Rings_Olinordered__semiring__1(_1190410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190410), _1190412), _1190414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190410), _1190416), _1190414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190410), c_Groups_Ozero__class_Ozero(_1190410)), _1190418)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190410), c_Groups_Ozero__class_Ozero(_1190410)), _1190420)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190410), _1190418), _1190420) = c_Groups_Oone__class_Oone(_1190410), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1190410), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1190410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190410), _1190418), _1190412)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1190410), _1190420), _1190416))), _1190414)))], (23118 ^ _780478) ^ [_1210810, _1210812] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210810)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210812)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1210810), _1210812)))], (41128 ^ _780478) ^ [_1587599, _1587601] : [-(c_Transitive__Closure_Otrancl(_1587599, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587599, _1587599), tc_HOL_Obool)), _1587601), c_Relation_OId(_1587599))) = c_Transitive__Closure_Ortrancl(_1587599, _1587601))], (2940 ^ _780478) ^ [_824011, _824013, _824015, _824017] : [-(c_Nitpick_OAbs__Frac(_824017, _824013) = c_Nitpick_OAbs__Frac(_824015, _824011)), _824017 = _824015, _824013 = _824011], (17965 ^ _780478) ^ [_1115009, _1115011] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1115009)), _1115011) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115009), hAPP(c_Nat_OSuc, _1115011)))], (44077 ^ _780478) ^ [_1662922, _1662924, _1662926] : [_1662922 = c_List_Olist_ONil(_1662924), -(hAPP(c_List_Ohd(_1662924), hAPP(hAPP(c_List_Oappend(_1662924), _1662922), _1662926)) = hAPP(c_List_Ohd(_1662924), _1662926))], (5334 ^ _780478) ^ [_862020, _862022, _862024, _862026] : [-(c_Lazy__Sequence_Oflat(_862026, _862022) = c_Lazy__Sequence_Oflat(_862024, _862020)), _862026 = _862024, _862022 = _862020], (5456 ^ _780478) ^ [_863909, _863911, _863913, _863915, _863917, _863919, _863921, _863923] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_863923, _863919, _863915, _863911) = c_SetInterval_Oord_OgreaterThanLessThan(_863921, _863917, _863913, _863909)), _863923 = _863921, _863919 = _863917, _863915 = _863913, _863911 = _863909], (47944 ^ _780478) ^ [_1746924, _1746926] : [class_Enum_Oenum(_1746924), 47947 ^ _780478 : [(47954 ^ _780478) ^ [] : [hBOOL(hAPP(_1746926, 47955 ^ [_1746924, _1746926])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746924), _1746926)))], (47948 ^ _780478) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746924), _1746926)), 47951 ^ _780478 : [(47952 ^ _780478) ^ [_1747050] : [-(hBOOL(hAPP(_1746926, _1747050)))]]]]], (44312 ^ _780478) ^ [_1667448, _1667450, _1667452] : [class_Orderings_Olinorder(_1667448), -(c_Big__Operators_Olinorder__class_OMax(_1667448, hAPP(c_List_Oset(_1667448), hAPP(hAPP(c_List_Olist_OCons(_1667448), _1667450), _1667452))) = hAPP(c_List_Ofoldl(_1667448, _1667448, c_Orderings_Oord__class_Omax(_1667448), _1667450), _1667452))], (52115 ^ _780478) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (15117 ^ _780478) ^ [_1052712, _1052714, _1052716, _1052718] : [class_Groups_Ocomm__monoid__mult(_1052712), hBOOL(hAPP(c_Finite__Set_Ofinite(_1052714), _1052716)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1052714, _1052712), hAPP(c_COMBK(_1052712, _1052714), _1052718)), _1052716) = hAPP(hAPP(c_Power_Opower__class_Opower(_1052712), _1052718), hAPP(c_Finite__Set_Ocard(_1052714), _1052716)))], (19148 ^ _780478) ^ [_1139942, _1139944] : [class_Groups_Omonoid__add(_1139942), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139942), c_Groups_Ozero__class_Ozero(_1139942)), _1139944) = _1139944)], (41239 ^ _780478) ^ [_1590452, _1590454, _1590456] : [c_Relation_Ototal__on(_1590452, _1590454, hAPP(c_Relation_Oconverse(_1590452, _1590452), _1590456)), -(c_Relation_Ototal__on(_1590452, _1590454, _1590456))], (51979 ^ _780478) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (49636 ^ _780478) ^ [_1784370, _1784372] : [c_Relation_Oantisym(_1784370, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1784370, _1784370), tc_HOL_Obool)), _1784372), c_Relation_OId(_1784370))), -(c_Relation_Oantisym(_1784370, _1784372))], (35842 ^ _780478) ^ [_1460873, _1460875, _1460877] : [class_Rings_Osemiring__1(_1460873), hBOOL(hAPP(hAPP(c_member(_1460873), _1460875), c_Nat_Osemiring__1__class_ONats(_1460873))), hBOOL(hAPP(hAPP(c_member(_1460873), _1460877), c_Nat_Osemiring__1__class_ONats(_1460873))), -(hBOOL(hAPP(hAPP(c_member(_1460873), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460873), _1460875), _1460877)), c_Nat_Osemiring__1__class_ONats(_1460873))))], (6932 ^ _780478) ^ [_895790, _895792, _895794, _895796] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895790, tc_HOL_Obool)), _895792), hAPP(hAPP(c_Set_Oinsert(_895790), _895794), _895796)))), 6935 ^ _780478 : [(6938 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895790, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895790, tc_HOL_Obool)), _895792), hAPP(hAPP(c_Set_Oinsert(_895790), _895794), c_Orderings_Obot__class_Obot(tc_fun(_895790, tc_HOL_Obool))))), _895796))], (6936 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_895790), _895794), _895792)))]], 6939 ^ _780478 : [(6942 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895790, tc_HOL_Obool)), _895792), _895796))], (6940 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895790), _895794), _895792))]]], (45005 ^ _780478) ^ [_1682575, _1682577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1682575)), hAPP(c_Code__Numeral_Oof__nat, _1682577))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682575), _1682577)))], (42324 ^ _780478) ^ [_1621260, _1621262, _1621264, _1621266] : [-(hAPP(hAPP(c_List_Otake(_1621260), _1621262), hAPP(hAPP(c_List_Otake(_1621260), _1621264), _1621266)) = hAPP(hAPP(c_List_Otake(_1621260), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1621262), _1621264)), _1621266))], (38242 ^ _780478) ^ [_1515047, _1515049, _1515051, _1515053, _1515055, _1515057, _1515059] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1515047, _1515049, _1515051, _1515053, _1515055), _1515057), _1515059)), 38246 ^ _780478 : [(38249 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1515055, 38245 ^ [_1515047, _1515049, _1515051, _1515053, _1515055, _1515057, _1515059]), _1515059)))], (38247 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1515053, _1515057), 38245 ^ [_1515047, _1515049, _1515051, _1515053, _1515055, _1515057, _1515059])))]]], (1154 ^ _780478) ^ [_797767, _797769] : [-(class_Rings_Olinordered__semiring__1(_797767)), _797769 = _797767, class_Rings_Olinordered__semiring__1(_797769)], (39021 ^ _780478) ^ [_1536869, _1536871] : [-(hAPP(c_Set_Ovimage(_1536869, _1536869, c_Fun_Oid(_1536869)), _1536871) = _1536871)], (19500 ^ _780478) ^ [_1145165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1145165), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2992 ^ _780478) ^ [_824785, _824787, _824789, _824791, _824793, _824795] : [-(c_Product__Type_Ointernal__split(_824795, _824791, _824787) = c_Product__Type_Ointernal__split(_824793, _824789, _824785)), _824795 = _824793, _824791 = _824789, _824787 = _824785], (14124 ^ _780478) ^ [_1032913, _1032915] : [class_Groups_Omonoid__mult(_1032913), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032913), c_Groups_Oone__class_Oone(_1032913)), _1032915) = _1032915)], (2706 ^ _780478) ^ [_820386, _820388, _820390, _820392, _820394, _820396, _820398, _820400] : [-(c_Product__Type_Oapsnd(_820400, _820396, _820392, _820388) = c_Product__Type_Oapsnd(_820398, _820394, _820390, _820386)), _820400 = _820398, _820396 = _820394, _820392 = _820390, _820388 = _820386], (14965 ^ _780478) ^ [_1049432, _1049434, _1049436, _1049438, _1049440] : [-(hBOOL(hAPP(hAPP(c_member(_1049432), _1049434), c_SetInterval_Oord_OgreaterThanLessThan(_1049432, _1049436, _1049438, _1049440)))), hBOOL(hAPP(hAPP(_1049436, _1049438), _1049434)), hBOOL(hAPP(hAPP(_1049436, _1049434), _1049440))], (49113 ^ _780478) ^ [_1771788, _1771790, _1771792, _1771794] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1771788, _1771790, _1771792, c_Code__Numeral_OSuc__code__numeral(_1771794)) = hAPP(hAPP(_1771792, _1771794), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1771788, _1771790, _1771792, _1771794)))], (36156 ^ _780478) ^ [_1467936, _1467938] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467936), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1467938, _1467936) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1467938), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1467936)))], (21722 ^ _780478) ^ [_1183858, _1183860] : [21723 ^ _780478 : [(21726 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1183858), _1183860)))], (21724 ^ _780478) ^ [] : [_1183860 = c_Orderings_Obot__class_Obot(tc_fun(_1183858, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1183858), _1183860) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45803 ^ _780478) ^ [_1700091, _1700093, _1700095, _1700097] : [-(c_List_Oremdups(_1700091, hAPP(hAPP(c_List_Omap(_1700093, _1700091), _1700095), c_List_Oremdups(_1700093, _1700097))) = c_List_Oremdups(_1700091, hAPP(hAPP(c_List_Omap(_1700093, _1700091), _1700095), _1700097)))], (22686 ^ _780478) ^ [] : [-(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))], (22355 ^ _780478) ^ [] : [-(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)))], (48513 ^ _780478) ^ [_1758777, _1758779, _1758781, _1758783, _1758785] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1758777, _1758779, hAPP(hAPP(c_COMBC(_1758777, tc_fun(tc_prod(_1758777, _1758779), tc_HOL_Obool), tc_fun(_1758779, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1758779, tc_fun(tc_fun(tc_prod(_1758777, _1758779), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1758777, _1758779), tc_HOL_Obool), tc_fun(_1758779, tc_HOL_Obool)), _1758777), c_COMBC(_1758779, tc_fun(tc_prod(_1758777, _1758779), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1758779, tc_prod(_1758777, _1758779)), tc_fun(_1758779, tc_fun(tc_fun(tc_prod(_1758777, _1758779), tc_HOL_Obool), tc_HOL_Obool)), _1758777), hAPP(c_COMBB(tc_prod(_1758777, _1758779), tc_fun(tc_fun(tc_prod(_1758777, _1758779), tc_HOL_Obool), tc_HOL_Obool), _1758779), c_member(tc_prod(_1758777, _1758779)))), c_Product__Type_OPair(_1758777, _1758779)))), _1758781)), _1758783), _1758785)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1758779, _1758777)), hAPP(hAPP(c_Product__Type_OPair(_1758779, _1758777), _1758783), _1758785)), hAPP(c_Relation_Oconverse(_1758777, _1758779), _1758781))))], (29031 ^ _780478) ^ [_1318606, _1318608, _1318610] : [-(c_Nat_Onat_Onat__case(_1318606, _1318608, _1318610, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1318608)], (25695 ^ _780478) ^ [_1257229] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1257229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257229)))], (34765 ^ _780478) ^ [_1435910, _1435912] : [class_Groups_Omonoid__mult(_1435910), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435910), _1435912), 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(_1435910), _1435912), _1435912))], (31897 ^ _780478) ^ [_1382846, _1382848, _1382850, _1382852, _1382854] : [c_Com_Ocom_OCond(_1382846, _1382848, _1382850) = c_Com_Ocom_OSemi(_1382852, _1382854)], (46537 ^ _780478) ^ [_1716817] : [class_Orderings_Olinorder(_1716817), -(c_List_Olinorder__class_Osorted(_1716817, c_List_Olist_ONil(_1716817)))], (32160 ^ _780478) ^ [_1387857, _1387859, _1387861, _1387863] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387857), _1387859), _1387861)), hAPP(c_Int_Onumber__class_Onumber__of(_1387857), _1387863)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1387857), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387857), _1387859), hAPP(c_Int_Onumber__class_Onumber__of(_1387857), _1387863))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387857), _1387861), hAPP(c_Int_Onumber__class_Onumber__of(_1387857), _1387863)))), class_Int_Onumber(_1387857), class_Rings_Osemiring(_1387857)], (27964 ^ _780478) ^ [_1297533, _1297535, _1297537] : [class_Groups_Oordered__ab__group__add(_1297533), -(hAPP(c_Set_Oimage(_1297533, _1297533, c_Groups_Ouminus__class_Ouminus(_1297533)), c_SetInterval_Oord__class_OatLeastAtMost(_1297533, _1297535, _1297537)) = c_SetInterval_Oord__class_OatLeastAtMost(_1297533, hAPP(c_Groups_Ouminus__class_Ouminus(_1297533), _1297537), hAPP(c_Groups_Ouminus__class_Ouminus(_1297533), _1297535)))], (43716 ^ _780478) ^ [_1653626, _1653628, _1653630, _1653632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653626), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653628)), _1653630))), -(hAPP(hAPP(c_List_Onth(_1653628), hAPP(hAPP(c_List_Oappend(_1653628), _1653630), _1653632)), _1653626) = hAPP(hAPP(c_List_Onth(_1653628), _1653630), _1653626))], (16755 ^ _780478) ^ [_1087684, _1087686, _1087688, _1087690, _1087692] : [c_Finite__Set_Ofolding__one(_1087684, _1087686, _1087688), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087684), _1087690)), -(_1087690 = c_Orderings_Obot__class_Obot(tc_fun(_1087684, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087684), _1087692)), -(_1087692 = c_Orderings_Obot__class_Obot(tc_fun(_1087684, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1087684, tc_HOL_Obool)), _1087690), _1087692) = c_Orderings_Obot__class_Obot(tc_fun(_1087684, tc_HOL_Obool)), -(hAPP(_1087688, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1087684, tc_HOL_Obool)), _1087690), _1087692)) = hAPP(hAPP(_1087686, hAPP(_1087688, _1087690)), hAPP(_1087688, _1087692)))], (33248 ^ _780478) ^ [_1408692, _1408694] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408692)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408692)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408694)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408692)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408694))))], (48200 ^ _780478) ^ [_1752100, _1752102] : [-(c_FunDef_Ois__measure(_1752100, _1752102))], (20676 ^ _780478) ^ [_1165890, _1165892] : [class_Groups_Olinordered__ab__group__add(_1165890), 20679 ^ _780478 : [(20686 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165890), c_Groups_Ozero__class_Ozero(_1165890)), _1165892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165890), hAPP(c_Groups_Ouminus__class_Ouminus(_1165890), _1165892)), _1165892)))], (20680 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165890), hAPP(c_Groups_Ouminus__class_Ouminus(_1165890), _1165892)), _1165892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165890), c_Groups_Ozero__class_Ozero(_1165890)), _1165892)))]]], (20740 ^ _780478) ^ [_1166974, _1166976] : [class_Groups_Olinordered__ab__group__add(_1166974), 20743 ^ _780478 : [(20750 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166974), c_Groups_Ozero__class_Ozero(_1166974)), _1166976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166974), hAPP(c_Groups_Ouminus__class_Ouminus(_1166974), _1166976)), _1166976)))], (20744 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166974), hAPP(c_Groups_Ouminus__class_Ouminus(_1166974), _1166976)), _1166976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166974), c_Groups_Ozero__class_Ozero(_1166974)), _1166976)))]]], (16184 ^ _780478) ^ [_1073697, _1073699, _1073701] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073697, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073697, tc_HOL_Obool)), _1073699), _1073701)), _1073701)))], (16422 ^ _780478) ^ [_1080043, _1080045, _1080047, _1080049, _1080051] : [hBOOL(hAPP(hAPP(c_member(_1080043), _1080045), hAPP(c_Set_Ovimage(_1080043, _1080047, _1080049), hAPP(hAPP(c_Set_Oinsert(_1080047), _1080051), c_Orderings_Obot__class_Obot(tc_fun(_1080047, tc_HOL_Obool)))))), -(hAPP(_1080049, _1080045) = _1080051)], (23599 ^ _780478) ^ [_1219112, _1219114, _1219116] : [class_Orderings_Oorder(_1219112), 23602 ^ _780478 : [(23609 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219112), _1219114), _1219116))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219112, _1219114), _1219116) = c_Orderings_Obot__class_Obot(tc_fun(_1219112, tc_HOL_Obool)))], (23603 ^ _780478) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219112, _1219114), _1219116) = c_Orderings_Obot__class_Obot(tc_fun(_1219112, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219112), _1219114), _1219116))]]], (18716 ^ _780478) ^ [_1131944, _1131946] : [class_Lattices_Olattice(_1131944), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131944), _1131946)), -(c_Big__Operators_Olattice__class_OInf__fin(_1131944, _1131946) = hAPP(c_Finite__Set_Ofold1(_1131944, c_Lattices_Osemilattice__inf__class_Oinf(_1131944)), _1131946))], (34859 ^ _780478) ^ [_1437561, _1437563] : [class_Rings_Olinordered__idom(_1437561), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437561), c_Groups_Ozero__class_Ozero(_1437561)), hAPP(hAPP(c_Power_Opower__class_Opower(_1437561), _1437563), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (1714 ^ _780478) ^ [_804767, _804769] : [-(class_Rings_Ocomm__semiring(_804767)), _804769 = _804767, class_Rings_Ocomm__semiring(_804769)], (12486 ^ _780478) ^ [_1000830, _1000832, _1000834, _1000836] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1000830, tc_HOL_Obool)), _1000832), _1000834), _1000836)), -(hBOOL(hAPP(_1000832, _1000836))), -(hBOOL(hAPP(_1000834, _1000836)))], (30374 ^ _780478) ^ [_1344122, _1344124, _1344126, _1344128] : [-(hAPP(c_Set_Oimage(_1344122, _1344124, _1344126), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1344122, tc_HOL_Obool), _1344128)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1344122, tc_HOL_Obool), tc_fun(_1344124, tc_HOL_Obool)), _1344128), c_Set_Oimage(_1344122, _1344124, _1344126)))], (3092 ^ _780478) ^ [_826393, _826395, _826397, _826399] : [-(c_List_Olistset(_826399, _826395) = c_List_Olistset(_826397, _826393)), _826399 = _826397, _826395 = _826393], (29534 ^ _780478) ^ [_1328980, _1328982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328980), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29537 ^ _780478 : [(29540 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328980), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328982, _1328980))))], (29538 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328982, _1328980)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (46949 ^ _780478) ^ [_1724802, _1724804] : [c_List_Olist_ONil(_1724802) = hAPP(c_List_Orev(_1724802), _1724804), -(_1724804 = c_List_Olist_ONil(_1724802))], (52087 ^ _780478) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (46937 ^ _780478) ^ [_1724599, _1724601] : [hAPP(c_List_Orev(_1724599), _1724601) = c_List_Olist_ONil(_1724599), -(_1724601 = c_List_Olist_ONil(_1724599))], (41011 ^ _780478) ^ [_1584523, _1584525, _1584527, _1584529] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1584523, tc_fun(_1584523, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1584523, tc_fun(tc_prod(_1584523, _1584523), tc_HOL_Obool), tc_fun(_1584523, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584523, tc_fun(tc_fun(tc_prod(_1584523, _1584523), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1584523, _1584523), tc_HOL_Obool), tc_fun(_1584523, tc_HOL_Obool)), _1584523), c_COMBC(_1584523, tc_fun(tc_prod(_1584523, _1584523), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1584523, tc_prod(_1584523, _1584523)), tc_fun(_1584523, tc_fun(tc_fun(tc_prod(_1584523, _1584523), tc_HOL_Obool), tc_HOL_Obool)), _1584523), hAPP(c_COMBB(tc_prod(_1584523, _1584523), tc_fun(tc_fun(tc_prod(_1584523, _1584523), tc_HOL_Obool), tc_HOL_Obool), _1584523), c_member(tc_prod(_1584523, _1584523)))), c_Product__Type_OPair(_1584523, _1584523)))), _1584525)), c_fequal), _1584527), _1584529)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584523, _1584523)), hAPP(hAPP(c_Product__Type_OPair(_1584523, _1584523), _1584527), _1584529)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584523, _1584523), tc_HOL_Obool)), _1584525), c_Relation_OId(_1584523)))))], (20586 ^ _780478) ^ [_1164354, _1164356, _1164358, _1164360, _1164362, _1164364] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1164354), -(_1164356 = c_Groups_Ozero__class_Ozero(_1164354)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164354), _1164358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164354), _1164356), _1164362)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164354), _1164360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164354), _1164356), _1164364)), _1164358 = _1164360, -(_1164362 = _1164364)], (8302 ^ _780478) ^ [_922685, _922687, _922689, _922691, _922693] : [c_Finite__Set_Ofun__left__comm(_922685, _922687, _922689), -(c_Finite__Set_Ofun__left__comm(_922691, _922687, hAPP(hAPP(c_COMBB(_922685, tc_fun(_922687, _922687), _922691), _922689), _922693)))], (35243 ^ _780478) ^ [_1445178] : [c_Int_OMin = c_Int_OBit0(_1445178)], (1314 ^ _780478) ^ [_799767, _799769] : [-(class_Rings_Oring(_799767)), _799769 = _799767, class_Rings_Oring(_799769)], (17229 ^ _780478) ^ [_1097646, _1097648, _1097650, _1097652, _1097654] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097646, tc_fun(_1097648, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1097646), _1097650), _1097652)), _1097654) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1097648, tc_HOL_Obool)), hAPP(_1097654, _1097650)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097646, tc_fun(_1097648, tc_HOL_Obool)), _1097652), _1097654)))], (41900 ^ _780478) ^ [_1609376, _1609378, _1609380, _1609382, _1609384] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609376, _1609376)), hAPP(hAPP(c_Product__Type_OPair(_1609376, _1609376), _1609378), _1609380)), _1609382)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609376), tc_List_Olist(_1609376))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609376), tc_List_Olist(_1609376)), hAPP(hAPP(c_List_Olist_OCons(_1609376), _1609378), _1609384)), hAPP(hAPP(c_List_Olist_OCons(_1609376), _1609380), _1609384))), c_List_Olistrel1(_1609376, _1609382))))], (22233 ^ _780478) ^ [_1193862, _1193864] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1193862), _1193864))), -(hAPP(c_Finite__Set_Ocard(_1193862), _1193864) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45647 ^ _780478) ^ [_1696929, _1696931, _1696933] : [-(hAPP(c_List_Oset(tc_List_Olist(_1696929)), c_Enum_On__lists(_1696929, _1696931, _1696933)) = hAPP(c_Set_OCollect(tc_List_Olist(_1696929)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1696929), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1696929)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1696929), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1696929)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1696929)))), _1696931))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1696929), tc_fun(_1696929, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1696929, tc_HOL_Obool), tc_fun(tc_fun(_1696929, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1696929)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1696929, tc_HOL_Obool))), c_List_Oset(_1696929))), hAPP(c_List_Oset(_1696929), _1696933)))))], (43175 ^ _780478) ^ [_1641387, _1641389, _1641391] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641387), tc_List_Olist(_1641387))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641387), tc_List_Olist(_1641387)), c_List_Olist_ONil(_1641387)), _1641389)), c_List_Olex(_1641387, _1641391)))], (1234 ^ _780478) ^ [_798767, _798769] : [-(class_Groups_Ogroup__add(_798767)), _798769 = _798767, class_Groups_Ogroup__add(_798769)], (46137 ^ _780478) ^ [_1708004, _1708006, _1708008] : [-(c_List_Opartition(_1708004, _1708006, _1708008) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1708004), tc_List_Olist(_1708004)), hAPP(c_List_Ofilter(_1708004, _1708006), _1708008)), hAPP(c_List_Ofilter(_1708004, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1708004, c_fNot), _1708006)), _1708008)))], (46294 ^ _780478) ^ [_1712332, _1712334] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712332), _1712334)), -(c_List_Oupt(_1712334, _1712332) = c_List_Olist_ONil(tc_Nat_Onat))], (14018 ^ _780478) ^ [_1031156, _1031158] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031156), _1031158) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1031158), _1031156))], (18490 ^ _780478) ^ [_1126894, _1126896, _1126898, _1126900] : [_1126894 = c_Orderings_Obot__class_Obot(tc_fun(_1126896, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1126896, tc_fun(_1126898, tc_HOL_Obool)), _1126894), hAPP(c_COMBK(tc_fun(_1126898, tc_HOL_Obool), _1126896), _1126900)) = c_Orderings_Otop__class_Otop(tc_fun(_1126898, tc_HOL_Obool)))], (17199 ^ _780478) ^ [_1097112, _1097114, _1097116, _1097118, _1097120] : [class_Complete__Lattice_Ocomplete__lattice(_1097112), hBOOL(hAPP(hAPP(c_member(_1097114), _1097116), _1097118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097112), hAPP(_1097120, _1097116)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097114, _1097112), _1097118), _1097120))))], (1094 ^ _780478) ^ [_797017, _797019] : [-(class_Rings_Olinordered__semiring__1__strict(_797017)), _797019 = _797017, class_Rings_Olinordered__semiring__1__strict(_797019)], (24903 ^ _780478) ^ [_1243001, _1243003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1243001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1243003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1243003), _1243001)), _1243003)))], (21528 ^ _780478) ^ [_1180282, _1180284, _1180286, _1180288] : [class_Rings_Olinordered__semiring(_1180282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180282), _1180284), _1180286)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180282), _1180288), _1180286))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180282), c_Groups_Ozero__class_Ozero(_1180282)), _1180286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180282), _1180284), _1180288)))], (37634 ^ _780478) ^ [_1498756, _1498758, _1498760, _1498762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1498756), _1498758)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1498760), _1498762)), -(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), _1498756), _1498760)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1498758), _1498762))), c_FunDef_Opair__leq)))], (25277 ^ _780478) ^ [_1250401, _1250403, _1250405, _1250407] : [class_Rings_Odivision__ring(_1250401), -(_1250403 = c_Groups_Ozero__class_Ozero(_1250401)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250401), _1250405), _1250403) = _1250407, -(_1250405 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250401), _1250407), _1250403))], (4634 ^ _780478) ^ [_850968, _850970, _850972, _850974, _850976, _850978, _850980, _850982, _850984, _850986] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_850986, _850982, _850978, _850974, _850970) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_850984, _850980, _850976, _850972, _850968)), _850986 = _850984, _850982 = _850980, _850978 = _850976, _850974 = _850972, _850970 = _850968], (10533 ^ _780478) ^ [_964213, _964215, _964217, _964219] : [class_Orderings_Olinorder(_964213), 10536 ^ _780478 : [(10537 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964213), _964215), hAPP(hAPP(c_Orderings_Oord__class_Omax(_964213), _964217), _964219))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964213), _964215), _964217))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964213), _964215), _964219)))], (10547 ^ _780478) ^ [] : [10548 ^ _780478 : [(10551 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964213), _964215), _964219))], (10549 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964213), _964215), _964217))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964213), _964215), hAPP(hAPP(c_Orderings_Oord__class_Omax(_964213), _964217), _964219))))]]], (5580 ^ _780478) ^ [_865935, _865937, _865939, _865941] : [-(tc_sum(_865941, _865937) = tc_sum(_865939, _865935)), _865941 = _865939, _865937 = _865935], (38762 ^ _780478) ^ [_1528071, _1528073, _1528075, _1528077] : [38763 ^ _780478 : [(38766 ^ _780478) ^ [] : [_1528077 = c_Orderings_Obot__class_Obot(tc_fun(_1528073, tc_HOL_Obool))], (38764 ^ _780478) ^ [] : [_1528075 = c_Orderings_Obot__class_Obot(tc_fun(_1528071, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1528071, _1528073), _1528075), hAPP(c_COMBK(tc_fun(_1528073, tc_HOL_Obool), _1528071), _1528077)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528071, _1528073), tc_HOL_Obool)))], (17448 ^ _780478) ^ [_1104107, _1104109, _1104111, _1104113, _1104115] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1104107, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104109, tc_fun(_1104107, tc_HOL_Obool)), _1104111), _1104113)), _1104115) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104109, tc_fun(_1104107, tc_HOL_Obool)), _1104111), hAPP(hAPP(c_COMBC(_1104109, tc_fun(_1104107, tc_HOL_Obool), tc_fun(_1104107, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1104107, tc_HOL_Obool), tc_fun(tc_fun(_1104107, tc_HOL_Obool), tc_fun(_1104107, tc_HOL_Obool)), _1104109), c_Groups_Ominus__class_Ominus(tc_fun(_1104107, tc_HOL_Obool))), _1104113)), _1104115)))], (24891 ^ _780478) ^ [_1242791, _1242793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1242791)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1242791), _1242793)), _1242791) = _1242793)], (51515 ^ _780478) ^ [_1823453, _1823455, _1823457] : [class_Divides_Oring__div(_1823453), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823453), _1823455), _1823457)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1823453), _1823457), hAPP(c_Groups_Ouminus__class_Ouminus(_1823453), _1823455)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1823453), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1823453), _1823457), _1823455)))], (15625 ^ _780478) ^ [_1062641, _1062643, _1062645, _1062647] : [hBOOL(hAPP(hAPP(c_member(_1062641), _1062643), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062641, tc_HOL_Obool)), _1062645), _1062647))), 15628 ^ _780478 : [(15631 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062641), _1062643), _1062647)))], (15629 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1062641), _1062643), _1062645)))]]], (6624 ^ _780478) ^ [_889275, _889277, _889279, _889281] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_889275), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889275, tc_HOL_Obool)), _889277), _889281))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_889275), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889275, tc_HOL_Obool)), _889277), hAPP(hAPP(c_Set_Oinsert(_889275), _889279), _889281)))))], (40740 ^ _780478) ^ [_1578244, _1578246, _1578248, _1578250] : [-(c_Wellfounded_Oacyclic(_1578244, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1578244, _1578244)), hAPP(hAPP(c_Product__Type_OPair(_1578244, _1578244), _1578246), _1578248)), _1578250))), c_Wellfounded_Oacyclic(_1578244, _1578250), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1578244, _1578244)), hAPP(hAPP(c_Product__Type_OPair(_1578244, _1578244), _1578248), _1578246)), c_Transitive__Closure_Ortrancl(_1578244, _1578250))))], (42652 ^ _780478) ^ [_1630482, _1630484, _1630486, _1630488] : [-(_1630482 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630484)), _1630486)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1630484, hAPP(hAPP(c_List_Olist__update(_1630484, _1630486), _1630482), _1630488)) = hAPP(hAPP(c_List_Olist__update(_1630484, c_List_Obutlast(_1630484, _1630486)), _1630482), _1630488))], (24469 ^ _780478) ^ [_1235112, _1235114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1235112), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235114), _1235112)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235112), _1235114) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (46869 ^ _780478) ^ [_1722999, _1723001, _1723003, _1723005, _1723007] : [class_Orderings_Olinorder(_1722999), c_Fun_Oinj__on(_1723001, _1722999, _1723003, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1723001, tc_HOL_Obool)), hAPP(c_List_Oset(_1723001), _1723005)), hAPP(c_List_Oset(_1723001), _1723007))), c_List_Olinorder__class_Osorted(_1722999, hAPP(hAPP(c_List_Omap(_1723001, _1722999), _1723003), _1723005)), hBOOL(hAPP(c_List_Odistinct(_1722999), hAPP(hAPP(c_List_Omap(_1723001, _1722999), _1723003), _1723005))), c_List_Olinorder__class_Osorted(_1722999, hAPP(hAPP(c_List_Omap(_1723001, _1722999), _1723003), _1723007)), hBOOL(hAPP(c_List_Odistinct(_1722999), hAPP(hAPP(c_List_Omap(_1723001, _1722999), _1723003), _1723007))), hAPP(c_List_Oset(_1723001), _1723005) = hAPP(c_List_Oset(_1723001), _1723007), -(_1723005 = _1723007)], (8020 ^ _780478) ^ [_917123, _917125, _917127, _917129, _917131, _917133, _917135] : [-(c_Nitpick_Ofold__graph_H(_917123, _917125, _917127, _917129, _917131, hAPP(hAPP(_917127, _917133), _917135))), 8021 ^ _780478 : [(8028 ^ _780478) ^ [_917352, _917354] : [hAPP(hAPP(_917127, _917133), _917135) = hAPP(hAPP(_917127, _917354), _917352), hBOOL(hAPP(hAPP(c_member(_917123), _917354), _917131)), c_Nitpick_Ofold__graph_H(_917123, _917125, _917127, _917129, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917123, tc_HOL_Obool)), _917131), hAPP(hAPP(c_Set_Oinsert(_917123), _917354), c_Orderings_Obot__class_Obot(tc_fun(_917123, tc_HOL_Obool)))), _917352)], (8022 ^ _780478) ^ [] : [_917131 = c_Orderings_Obot__class_Obot(tc_fun(_917123, tc_HOL_Obool)), hAPP(hAPP(_917127, _917133), _917135) = _917129]]], (41660 ^ _780478) ^ [_1601539] : [-(c_Nitpick_Onum(_1601539) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1601539, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1601539)))], (41507 ^ _780478) ^ [_1597721, _1597723] : [c_Wellfounded_Owf(_1597721, _1597723), 41510 ^ _780478 : [(41511 ^ _780478) ^ [_1597853] : [41512 ^ _780478 : [(41513 ^ _780478) ^ [_1597958] : [hBOOL(hAPP(hAPP(c_member(_1597721), _1597958), _1597853))]], 41515 ^ _780478 : [(41518 ^ _780478) ^ [_1598080] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597721, _1597721)), hAPP(hAPP(c_Product__Type_OPair(_1597721, _1597721), _1598080), 41514 ^ [_1597721, _1597723, _1597853])), _1597723)), hBOOL(hAPP(hAPP(c_member(_1597721), _1598080), _1597853))], (41516 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1597721), 41514 ^ [_1597721, _1597723, _1597853]), _1597853)))]]]]], (1184 ^ _780478) ^ [_798142, _798144] : [-(class_Rings_Olinordered__ring(_798142)), _798144 = _798142, class_Rings_Olinordered__ring(_798144)], (9420 ^ _780478) ^ [_941909, _941911, _941913, _941915, _941917] : [class_Groups_Oordered__ab__group__add(_941909), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_941909), _941911), _941913) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_941909), _941915), _941917), 9427 ^ _780478 : [(9434 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941909), _941915), _941917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941909), _941911), _941913)))], (9428 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941909), _941911), _941913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941909), _941915), _941917)))]]], (5771 ^ _780478) ^ [_871754, _871756, _871758, _871760, _871762, _871764, _871766] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871754), _871756), _871758), _871760) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871754), _871762), _871764), _871766)), _871756 = _871762, _871758 = _871764, _871760 = _871766], (18462 ^ _780478) ^ [_1126336, _1126338, _1126340, _1126342] : [class_Complete__Lattice_Ocomplete__lattice(_1126336), -(_1126338 = c_Orderings_Obot__class_Obot(tc_fun(_1126340, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1126340, _1126336), _1126338), hAPP(c_COMBK(_1126336, _1126340), _1126342)) = _1126342)], (13920 ^ _780478) ^ [_1029356, _1029358, _1029360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029356), _1029358)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029358), _1029360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029356), _1029360)))], (31182 ^ _780478) ^ [_1360841, _1360843] : [-(hBOOL(hAPP(_1360843, 31183 ^ [_1360841, _1360843]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1360841, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1360841), _1360843))], (40516 ^ _780478) ^ [_1572835, _1572837] : [-(c_Transitive__Closure_Otrancl(_1572835, _1572837) = hAPP(hAPP(c_Relation_Orel__comp(_1572835, _1572835, _1572835), c_Transitive__Closure_Ortrancl(_1572835, _1572837)), _1572837))], (33318 ^ _780478) ^ [_1409781] : [-(c_Int_Osucc(c_Int_Opred(_1409781)) = _1409781)], (38675 ^ _780478) ^ [_1525230, _1525232, _1525234, _1525236, _1525238] : [-(hAPP(c_Relation_ODomain(_1525230, _1525232), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1525230, _1525232)), hAPP(hAPP(c_Product__Type_OPair(_1525230, _1525232), _1525234), _1525236)), _1525238)) = hAPP(hAPP(c_Set_Oinsert(_1525230), _1525234), hAPP(c_Relation_ODomain(_1525230, _1525232), _1525238)))], (49240 ^ _780478) ^ [_1775301] : [-(c_Relation_Otrans(tc_fun(_1775301, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1775301)))], (5676 ^ _780478) ^ [_867347, _867349, _867351, _867353, _867355, _867357] : [-(c_Set_Oimage(_867357, _867353, _867349) = c_Set_Oimage(_867355, _867351, _867347)), _867357 = _867355, _867353 = _867351, _867349 = _867347], (33662 ^ _780478) ^ [_1415281, _1415283] : [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(_1415281))), 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)), _1415283))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415281) = hAPP(c_Nat_OSuc, _1415283))], (23589 ^ _780478) ^ [_1218945, _1218947, _1218949] : [class_Orderings_Oorder(_1218945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1218945), _1218947), _1218949)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1218945, _1218949), _1218947) = c_Orderings_Obot__class_Obot(tc_fun(_1218945, tc_HOL_Obool)))], (22616 ^ _780478) ^ [_1201637, _1201639, _1201641] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201637), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1201639), _1201641)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201637), _1201639)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201637), _1201641)))], (39694 ^ _780478) ^ [_1553401, _1553403] : [hBOOL(hAPP(_1553401, c_Hilbert__Choice_OEps(_1553403, _1553401))), -(hBOOL(hAPP(_1553401, 39697 ^ [_1553401, _1553403])))], (28534 ^ _780478) ^ [_1308680, _1308682] : [class_Orderings_Olinorder(_1308680), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308680, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1308680), _1308682)), hAPP(hAPP(c_Set_Oinsert(_1308680), _1308682), c_Orderings_Obot__class_Obot(tc_fun(_1308680, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1308680), _1308682))], (41694 ^ _780478) ^ [_1602301, _1602303, _1602305] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602301)), _1602303) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602301)), _1602305)), _1602303 = _1602305], (11629 ^ _780478) ^ [_984315, _984317, _984319] : [class_Orderings_Olinorder(_984315), hBOOL(hAPP(c_Finite__Set_Ofinite(_984315), _984317)), -(hBOOL(hAPP(hAPP(c_member(_984315), _984319), _984317))), -(_984317 = c_Orderings_Obot__class_Obot(tc_fun(_984315, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_984315, hAPP(hAPP(c_Set_Oinsert(_984315), _984319), _984317)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_984315), _984319), c_Big__Operators_Olinorder__class_OMin(_984315, _984317)))], (40933 ^ _780478) ^ [_1582377, _1582379, _1582381] : [-(hAPP(c_Relation_ODomain(_1582377, _1582379), hAPP(c_Relation_Oconverse(_1582379, _1582377), _1582381)) = hAPP(c_Relation_ORange(_1582379, _1582377), _1582381))], (45387 ^ _780478) ^ [_1690429, _1690431, _1690433, _1690435] : [-(c_List_Opartition(_1690429, _1690431, hAPP(hAPP(c_List_Olist_OCons(_1690429), _1690433), _1690435)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1690429), tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1690429), tc_fun(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429))), tc_fun(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690429), tc_fun(tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)))), tc_fun(tc_fun(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429))), tc_fun(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)))), tc_List_Olist(_1690429)), c_COMBS(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429))), tc_fun(tc_List_Olist(_1690429), tc_fun(tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)))), tc_List_Olist(_1690429)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)), tc_fun(tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429))), tc_List_Olist(_1690429)), hAPP(c_If(tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429))), hAPP(_1690431, _1690433)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1690429), tc_fun(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429))), tc_List_Olist(_1690429)), c_Product__Type_OPair(tc_List_Olist(_1690429), tc_List_Olist(_1690429))), hAPP(c_List_Olist_OCons(_1690429), _1690433))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690429), tc_fun(tc_List_Olist(_1690429), tc_List_Olist(_1690429)), tc_fun(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429))), tc_fun(tc_fun(tc_List_Olist(_1690429), tc_List_Olist(_1690429)), tc_fun(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)))), tc_List_Olist(_1690429)), c_COMBB(tc_List_Olist(_1690429), tc_prod(tc_List_Olist(_1690429), tc_List_Olist(_1690429)), tc_List_Olist(_1690429))), c_Product__Type_OPair(tc_List_Olist(_1690429), tc_List_Olist(_1690429)))), hAPP(c_List_Olist_OCons(_1690429), _1690433)))), c_List_Opartition(_1690429, _1690431, _1690435)))], (2964 ^ _780478) ^ [_824381, _824383, _824385, _824387] : [-(c_Nitpick_Ouminus__frac(_824387, _824383) = c_Nitpick_Ouminus__frac(_824385, _824381)), _824387 = _824385, _824383 = _824381], (35159 ^ _780478) ^ [_1443181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1443181)), -(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), _1443181), 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)))))))], (40359 ^ _780478) ^ [_1569000, _1569002] : [c_Wellfounded_Owf(_1569000, _1569002), -(c_Wellfounded_Owf(_1569000, c_Transitive__Closure_Otrancl(_1569000, _1569002)))], (5120 ^ _780478) ^ [_858701, _858703] : [_858703 = _858701, -(c_Lattices_Osemilattice__inf__class_Oinf(_858703) = c_Lattices_Osemilattice__inf__class_Oinf(_858701))], (23831 ^ _780478) ^ [_1223730, _1223732] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223730), _1223732))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1223730), hAPP(c_Nat_OSuc, _1223732)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (42286 ^ _780478) ^ [_1620439, _1620441, _1620443, _1620445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1620439), _1620441)), -(hAPP(hAPP(c_List_Onth(_1620443), hAPP(hAPP(c_List_Otake(_1620443), _1620441), _1620445)), _1620439) = hAPP(hAPP(c_List_Onth(_1620443), _1620445), _1620439))], (49094 ^ _780478) ^ [_1771431, _1771433, _1771435] : [c_List_Oall__interval__int(_1771431, _1771433, _1771435), 49097 ^ _780478 : [(49098 ^ _780478) ^ [_1771509] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1771509), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1771433, _1771435))), -(hBOOL(hAPP(_1771431, _1771509)))]]], (39572 ^ _780478) ^ [_1550228, _1550230, _1550232] : [c_Wellfounded_OwfP(_1550228, hAPP(_1550230, 39573 ^ [_1550228, _1550230, _1550232])), 39580 ^ _780478 : [(39583 ^ _780478) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1550228, tc_HOL_Obool)), c_Predicate_ODomainP(_1550228, _1550228, hAPP(_1550230, 39578 ^ [_1550228, _1550230, _1550232]))), c_Predicate_ORangeP(_1550228, _1550228, hAPP(_1550230, 39579 ^ [_1550228, _1550230, _1550232]))) = c_Orderings_Obot__class_Obot(tc_fun(_1550228, tc_HOL_Obool))], (39581 ^ _780478) ^ [] : [hAPP(_1550230, 39578 ^ [_1550228, _1550230, _1550232]) = hAPP(_1550230, 39579 ^ [_1550228, _1550230, _1550232])]], -(c_Wellfounded_OwfP(_1550228, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1550232, tc_fun(_1550228, tc_fun(_1550228, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1550232, tc_HOL_Obool))), _1550230)))], (44336 ^ _780478) ^ [_1668018, _1668020, _1668022, _1668024] : [class_Complete__Lattice_Ocomplete__lattice(_1668018), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1668020, _1668018), hAPP(c_List_Oset(_1668020), _1668022)), _1668024) = hAPP(c_List_Ofoldl(_1668018, _1668020, hAPP(c_COMBC(_1668020, _1668018, _1668018), hAPP(hAPP(c_COMBB(_1668018, tc_fun(_1668018, _1668018), _1668020), c_Lattices_Osemilattice__inf__class_Oinf(_1668018)), _1668024)), c_Orderings_Otop__class_Otop(_1668018)), _1668022))], (17331 ^ _780478) ^ [_1100467, _1100469, _1100471, _1100473, _1100475] : [-(hBOOL(hAPP(hAPP(c_member(_1100467), _1100469), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1100471, tc_fun(_1100467, tc_HOL_Obool)), _1100473), _1100475)))), 17332 ^ _780478 : [(17333 ^ _780478) ^ [_1100549] : [hBOOL(hAPP(hAPP(c_member(_1100471), _1100549), _1100473)), hBOOL(hAPP(hAPP(c_member(_1100467), _1100469), hAPP(_1100475, _1100549)))]]], (16470 ^ _780478) ^ [_1081064, _1081066, _1081068, _1081070, _1081072] : [hAPP(c_Set_Oimage(_1081064, _1081066, _1081068), c_Orderings_Otop__class_Otop(tc_fun(_1081064, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1081066, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081064, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1081064, _1081066, _1081068), _1081070)), _1081072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081066, tc_HOL_Obool)), _1081070), hAPP(c_Set_Oimage(_1081064, _1081066, _1081068), _1081072))))], (6780 ^ _780478) ^ [_892651, _892653, _892655, _892657, _892659, _892661] : [-(_892651 = _892653), -(hAPP(c_Fun_Ofun__upd(_892655, _892657, _892659, _892653, _892661), _892651) = hAPP(_892659, _892651))], (52061 ^ _780478) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (4878 ^ _780478) ^ [_854860, _854862] : [_854862 = _854860, -(c_Set_OBex(_854862) = c_Set_OBex(_854860))], (3390 ^ _780478) ^ [_831008, _831010, _831012, _831014] : [-(c_Enum_Oenum__the(_831014, _831010) = c_Enum_Oenum__the(_831012, _831008)), _831014 = _831012, _831010 = _831008], (22415 ^ _780478) ^ [_1197330, _1197332, _1197334] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1197330), _1197332)), _1197334) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1197330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197332), _1197334)))], (44161 ^ _780478) ^ [_1664280, _1664282, _1664284] : [-(hAPP(c_List_Orotate1(_1664280), hAPP(c_List_Orotate(_1664280, _1664282), _1664284)) = hAPP(c_List_Orotate(_1664280, _1664282), hAPP(c_List_Orotate1(_1664280), _1664284)))], (15972 ^ _780478) ^ [_1069421, _1069423, _1069425, _1069427] : [class_Lattices_Osemilattice__inf(_1069421), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069421), _1069423), _1069425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1069421), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069421), _1069423), _1069427)), _1069425)))], (25011 ^ _780478) ^ [_1245072, _1245074, _1245076, _1245078] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1245072, _1245074)), c_Sum__Type_OPlus(_1245072, _1245074, _1245076, _1245078))), 25014 ^ _780478 : [(25017 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1245074), _1245078)))], (25015 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1245072), _1245076)))]]], (37873 ^ _780478) ^ [_1504444, _1504446] : [-(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), _1504444), _1504446)), 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), _1504446), _1504444)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (20244 ^ _780478) ^ [_1158066, _1158068, _1158070] : [class_Groups_Oordered__comm__monoid__add(_1158066), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158066), _1158068), c_Groups_Ozero__class_Ozero(_1158066))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158066), _1158070), c_Groups_Ozero__class_Ozero(_1158066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158066), _1158068), _1158070)), c_Groups_Ozero__class_Ozero(_1158066))))], (41126 ^ _780478) ^ [_1587552, _1587554] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587552, _1587552), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1587552, _1587554)), c_Relation_OId(_1587552)) = c_Transitive__Closure_Ortrancl(_1587552, _1587554))], (13288 ^ _780478) ^ [_1016690, _1016692, _1016694, _1016696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1016690), hAPP(c_Set_Oimage(_1016692, _1016690, _1016694), _1016696))), hAPP(c_Finite__Set_Ocard(_1016692), _1016696))), c_Fun_Oinj__on(_1016692, _1016690, _1016694, _1016696)], (45733 ^ _780478) ^ [_1698874, _1698876] : [c_List_Oremdups(_1698874, _1698876) = _1698876, -(hBOOL(hAPP(c_List_Odistinct(_1698874), _1698876)))], (22397 ^ _780478) ^ [_1196981, _1196983, _1196985] : [class_Orderings_Olinorder(_1196981), 22400 ^ _780478 : [(22407 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196981), _1196983), _1196985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1196981, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196981), _1196983)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196981), _1196985))))], (22401 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1196981, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196981), _1196983)), hAPP(c_SetInterval_Oord__class_OlessThan(_1196981), _1196985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196981), _1196983), _1196985)))]]], (45001 ^ _780478) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (47340 ^ _780478) ^ [_1733147, _1733149, _1733151] : [class_Orderings_Olinorder(_1733147), c_List_Olinorder__class_Osorted(_1733147, _1733149), -(c_List_Olinorder__class_Osorted(_1733147, c_List_OdropWhile(_1733147, _1733151, _1733149)))], (11725 ^ _780478) ^ [_986085] : [class_Orderings_Olinorder(_986085), -(c_Orderings_Oord_Omin(_986085, hAPP(c_COMBC(_986085, _986085, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_986085))) = c_Orderings_Oord__class_Omax(_986085))], (15253 ^ _780478) ^ [_1055066, _1055068, _1055070] : [class_Lattices_Olattice(_1055066), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055066), _1055068)), -(hBOOL(hAPP(hAPP(c_member(_1055066), _1055070), _1055068))), -(c_Big__Operators_Olattice__class_OSup__fin(_1055066, hAPP(hAPP(c_Set_Oinsert(_1055066), _1055070), _1055068)) = hAPP(hAPP(c_Finite__Set_Ofold(_1055066, _1055066, c_Lattices_Osemilattice__sup__class_Osup(_1055066)), _1055070), _1055068))], (38539 ^ _780478) ^ [_1521683, _1521685, _1521687, _1521689] : [-(hAPP(c_Relation_ORange(_1521683, _1521685), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1521683, _1521685), tc_HOL_Obool)), _1521687), _1521689)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521685, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521683, _1521685), _1521687)), hAPP(c_Relation_ORange(_1521683, _1521685), _1521689)))], (49327 ^ _780478) ^ [_1777055, _1777057] : [c_Relation_Otrans(_1777055, _1777057), -(c_Relation_Otrans(_1777055, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1777055, _1777055), tc_HOL_Obool)), _1777057), c_Relation_OId(_1777055))))], (40812 ^ _780478) ^ [_1579457, _1579459] : [-(_1579457 = _1579459), -(c_Random_Oinc__shift(_1579457, _1579459) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1579459), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (48467 ^ _780478) ^ [_1757788, _1757790, _1757792, _1757794, _1757796] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1757788, _1757790, _1757792), _1757794), _1757796)), -(hBOOL(hAPP(hAPP(_1757792, _1757796), _1757794)))], (40408 ^ _780478) ^ [_1570070] : [-(c_Transitive__Closure_Otrancl(_1570070, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1570070, _1570070), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1570070, _1570070), tc_HOL_Obool)))], (37505 ^ _780478) ^ [_1496047, _1496049, _1496051, _1496053, _1496055, _1496057] : [-(hAPP(c_Product__Type_Oapfst(_1496047, _1496049, _1496051, _1496053), hAPP(hAPP(c_Product__Type_OPair(_1496047, _1496051), _1496055), _1496057)) = hAPP(hAPP(c_Product__Type_OPair(_1496049, _1496051), hAPP(_1496053, _1496055)), _1496057))], (28878 ^ _780478) ^ [_1315367, _1315369, _1315371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1315367)), 28884 ^ _780478 : [(28887 ^ _780478) ^ [] : [hBOOL(hAPP(_1315369, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28883 ^ [_1315367, _1315369, _1315371]), _1315367)))], (28885 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1315369, 28883 ^ [_1315367, _1315369, _1315371])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1315371)), 28892 ^ _780478 : [(28893 ^ _780478) ^ [_1315656] : [hBOOL(hAPP(_1315369, _1315656)), -(hBOOL(hAPP(_1315369, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1315656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1315371), _1315367)))))]]], (38412 ^ _780478) ^ [_1518631, _1518633] : [-(c_FunDef_Oreduction__pair(_1518631, _1518633)), c_Wellfounded_Owf(_1518631, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518631, _1518631), tc_HOL_Obool), tc_fun(tc_prod(_1518631, _1518631), tc_HOL_Obool)), _1518633)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518631, _1518631), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518631, _1518631, _1518631), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518631, _1518631), tc_HOL_Obool), tc_fun(tc_prod(_1518631, _1518631), tc_HOL_Obool)), _1518633)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1518631, _1518631), tc_HOL_Obool), tc_fun(tc_prod(_1518631, _1518631), tc_HOL_Obool)), _1518633))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518631, _1518631), tc_HOL_Obool), tc_fun(tc_prod(_1518631, _1518631), tc_HOL_Obool)), _1518633)))], (44632 ^ _780478) ^ [_1673529, _1673531, _1673533] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1673529)), _1673531), c_List_Olists(_1673529, _1673533))), -(_1673531 = c_List_Olist_ONil(_1673529)), 44641 ^ _780478 : [(44646 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1673529)), 44640 ^ [_1673529, _1673531, _1673533]), c_List_Olists(_1673529, _1673533))))], (44644 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1673529), 44639 ^ [_1673529, _1673531, _1673533]), _1673533)))], (44642 ^ _780478) ^ [] : [-(_1673531 = hAPP(hAPP(c_List_Olist_OCons(_1673529), 44639 ^ [_1673529, _1673531, _1673533]), 44640 ^ [_1673529, _1673531, _1673533]))]]], (35273 ^ _780478) ^ [_1445566] : [c_Int_OMin = _1445566, -(c_Int_OMin = c_Int_OBit1(_1445566))], (7066 ^ _780478) ^ [_898466, _898468, _898470] : [class_Orderings_Oorder(_898466), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898466), _898468), _898470)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898466), _898470), _898468)), -(_898470 = _898468)], (15559 ^ _780478) ^ [_1061261, _1061263, _1061265, _1061267, _1061269] : [class_Groups_Ocomm__monoid__mult(_1061261), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061263), _1061265)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061263), _1061267)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1061263, tc_HOL_Obool)), _1061265), _1061267) = c_Orderings_Obot__class_Obot(tc_fun(_1061263, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1061261, _1061263, c_Groups_Otimes__class_Otimes(_1061261)), _1061269), c_Groups_Oone__class_Oone(_1061261)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061263, tc_HOL_Obool)), _1061265), _1061267)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061261), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1061261, _1061263, c_Groups_Otimes__class_Otimes(_1061261)), _1061269), c_Groups_Oone__class_Oone(_1061261)), _1061265)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1061261, _1061263, c_Groups_Otimes__class_Otimes(_1061261)), _1061269), c_Groups_Oone__class_Oone(_1061261)), _1061267)))], (22805 ^ _780478) ^ [_1205003, _1205005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205003), _1205005)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1205005)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1205003)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1205005), _1205003)))], (23395 ^ _780478) ^ [_1215541, _1215543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215541), _1215543)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215543), _1215541)), -(_1215541 = _1215543)], (41636 ^ _780478) ^ [_1601065, _1601067, _1601069] : [c_Nitpick_Oless__frac(_1601065, _1601067, _1601069), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1601065), c_Nitpick_Oplus__frac(_1601065, _1601067, c_Nitpick_Ouminus__frac(_1601065, _1601069)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (42378 ^ _780478) ^ [_1622525, _1622527, _1622529] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1622525)), _1622527), c_List_Olists(_1622525, _1622529))), 42381 ^ _780478 : [(42382 ^ _780478) ^ [_1622633] : [hBOOL(hAPP(hAPP(c_member(_1622525), _1622633), hAPP(c_List_Oset(_1622525), _1622527))), -(hBOOL(hAPP(hAPP(c_member(_1622525), _1622633), _1622529)))]]], (18536 ^ _780478) ^ [_1127973, _1127975, _1127977, _1127979, _1127981] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127973, tc_HOL_Obool)), _1127975), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127977, tc_fun(_1127973, tc_HOL_Obool)), _1127979), _1127981)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1127977, tc_fun(_1127973, tc_HOL_Obool)), _1127979), hAPP(hAPP(c_COMBB(tc_fun(_1127973, tc_HOL_Obool), tc_fun(_1127973, tc_HOL_Obool), _1127977), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1127973, tc_HOL_Obool)), _1127975)), _1127981)))], (37850 ^ _780478) ^ [_1503896, _1503898, _1503900] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1503896, _1503896)), _1503898), c_Relation_OId__on(_1503896, _1503900))), 37854 ^ _780478 : [(37857 ^ _780478) ^ [] : [-(_1503898 = hAPP(hAPP(c_Product__Type_OPair(_1503896, _1503896), 37853 ^ [_1503896, _1503898, _1503900]), 37853 ^ [_1503896, _1503898, _1503900]))], (37855 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503896), 37853 ^ [_1503896, _1503898, _1503900]), _1503900)))]]], (45141 ^ _780478) ^ [_1685427, _1685429] : [hAPP(c_Code__Numeral_Onat__of, _1685427) = hAPP(c_Code__Numeral_Onat__of, _1685429), -(_1685427 = _1685429)], (46435 ^ _780478) ^ [_1715344] : [class_Orderings_Olinorder(_1715344), -(c_List_Olinorder__class_Osorted(_1715344, c_List_Olist_ONil(_1715344)))], (8848 ^ _780478) ^ [_933300, _933302, _933304] : [class_Orderings_Opreorder(_933300), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933300), _933302), _933304)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933300), _933304), _933302))], (33718 ^ _780478) ^ [_1416691, _1416693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416691)), hAPP(c_Nat_OSuc, _1416693))), -(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(_1416691))), 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)), _1416693)))))], (27751 ^ _780478) ^ [_1293353] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1293353)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1293353)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1293353)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (23483 ^ _780478) ^ [_1217035, _1217037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217035), _1217037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1217035), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1217037)))], (31260 ^ _780478) ^ [_1362641, _1362643, _1362645] : [hBOOL(hAPP(_1362641, _1362643)), -(hAPP(c_Set_OCollect(_1362645), hAPP(hAPP(c_COMBS(_1362645, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1362645), c_fconj), hAPP(c_fequal, _1362643))), _1362641)) = hAPP(hAPP(c_Set_Oinsert(_1362645), _1362643), c_Orderings_Obot__class_Obot(tc_fun(_1362645, tc_HOL_Obool))))], (33408 ^ _780478) ^ [_1411111] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411111), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411111)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1411111)))], (8308 ^ _780478) ^ [_922798, _922800, _922802, _922804, _922806] : [class_Groups_Ocomm__monoid__add(_922798), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_922800, _922798), hAPP(hAPP(c_COMBS(_922800, _922798, _922798), hAPP(hAPP(c_COMBB(_922798, tc_fun(_922798, _922798), _922800), c_Groups_Oplus__class_Oplus(_922798)), _922802)), _922804)), _922806) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922798), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_922800, _922798), _922802), _922806)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_922800, _922798), _922804), _922806)))], (17817 ^ _780478) ^ [_1112606] : [_1112606 = hAPP(c_Nat_OSuc, _1112606)], (7894 ^ _780478) ^ [_914449, _914451, _914453, _914455, _914457, _914459] : [c_Finite__Set_Ofun__left__comm__idem(_914449, _914451, _914453), hBOOL(hAPP(c_Finite__Set_Ofinite(_914449), _914455)), -(hAPP(hAPP(c_Finite__Set_Ofold(_914449, _914451, _914453), _914457), hAPP(hAPP(c_Set_Oinsert(_914449), _914459), _914455)) = hAPP(hAPP(_914453, _914459), hAPP(hAPP(c_Finite__Set_Ofold(_914449, _914451, _914453), _914457), _914455)))], (13206 ^ _780478) ^ [_1014903, _1014905, _1014907, _1014909, _1014911] : [c_Fun_Oinj__on(_1014903, _1014905, _1014907, c_Orderings_Otop__class_Otop(tc_fun(_1014903, tc_HOL_Obool))), hAPP(_1014907, _1014909) = hAPP(_1014907, _1014911), -(_1014909 = _1014911)], (13700 ^ _780478) ^ [_1025218, _1025220, _1025222] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1025218), _1025220)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025218, tc_HOL_Obool)), _1025220), _1025222)), -(hAPP(c_Finite__Set_Ocard(_1025218), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1025218, tc_HOL_Obool)), _1025222), _1025220)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1025218), _1025222)), hAPP(c_Finite__Set_Ocard(_1025218), _1025220)))], (18996 ^ _780478) ^ [_1137121, _1137123] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1137121, _1137123)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1137121, _1137123), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1137123), c_Orderings_Otop__class_Otop(tc_fun(_1137123, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1137121), c_Orderings_Otop__class_Otop(tc_fun(_1137121, tc_HOL_Obool)))))], (48723 ^ _780478) ^ [_1763164, _1763166, _1763168] : [-(_1763164 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1763166), c_List_Oreplicate(_1763166, _1763164, _1763168)) = hAPP(hAPP(c_Set_Oinsert(_1763166), _1763168), c_Orderings_Obot__class_Obot(tc_fun(_1763166, tc_HOL_Obool))))], (42987 ^ _780478) ^ [_1638042, _1638044, _1638046] : [_1638042 = c_List_Olist_ONil(_1638044), -(c_List_Obutlast(_1638044, hAPP(hAPP(c_List_Olist_OCons(_1638044), _1638046), _1638042)) = c_List_Olist_ONil(_1638044))], (38032 ^ _780478) ^ [_1509867, _1509869, _1509871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509867, _1509867), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509867, _1509867, _1509867), _1509869), _1509871)), _1509869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1509867, tc_HOL_Obool), tc_fun(_1509867, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1509867, tc_HOL_Obool), tc_fun(_1509867, tc_HOL_Obool), tc_fun(_1509867, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1509867, _1509869)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1509867, tc_HOL_Obool), tc_fun(_1509867, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1509867, _1509871)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1509867, tc_HOL_Obool), tc_fun(_1509867, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1509867, tc_HOL_Obool), tc_fun(_1509867, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1509867, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1509867, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1509867, tc_HOL_Obool), tc_fun(_1509867, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1509867, _1509869))))], (52091 ^ _780478) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (52227 ^ _780478) ^ [_1832507, _1832509] : [-(class_Nat_Osize(tc_prod(_1832507, _1832509)))], (33058 ^ _780478) ^ [_1405224, _1405226] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405224)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405226)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1405224), _1405226)))], (52029 ^ _780478) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (50507 ^ _780478) ^ [_1802300, _1802302, _1802304, _1802306] : [c_Fun_Obij__betw(_1802300, _1802302, _1802304, c_Orderings_Obot__class_Obot(tc_fun(_1802300, tc_HOL_Obool)), _1802306), -(_1802306 = c_Orderings_Obot__class_Obot(tc_fun(_1802302, tc_HOL_Obool)))], (31490 ^ _780478) ^ [_1370936, _1370938, _1370940] : [class_Groups_Olinordered__ab__semigroup__add(_1370936), hBOOL(hAPP(c_Finite__Set_Ofinite(_1370936), _1370938)), -(_1370938 = c_Orderings_Obot__class_Obot(tc_fun(_1370936, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1370936), _1370940), c_Big__Operators_Olinorder__class_OMax(_1370936, _1370938)) = c_Big__Operators_Olinorder__class_OMax(_1370936, hAPP(c_Set_OCollect(_1370936), hAPP(hAPP(c_COMBB(tc_fun(_1370936, tc_HOL_Obool), tc_HOL_Obool, _1370936), c_HOL_OEx(_1370936)), hAPP(hAPP(c_COMBC(_1370936, tc_fun(_1370936, tc_HOL_Obool), tc_fun(_1370936, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370936, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1370936, tc_HOL_Obool), tc_fun(_1370936, tc_HOL_Obool)), _1370936), c_COMBS(_1370936, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370936, tc_HOL_Obool), tc_fun(_1370936, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1370936), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1370936), c_fconj)), hAPP(hAPP(c_COMBC(_1370936, tc_fun(_1370936, _1370936), tc_fun(_1370936, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1370936, tc_HOL_Obool), tc_fun(tc_fun(_1370936, _1370936), tc_fun(_1370936, tc_HOL_Obool)), _1370936), c_COMBB(_1370936, tc_HOL_Obool, _1370936)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1370936), _1370940))))), hAPP(hAPP(c_COMBC(_1370936, tc_fun(_1370936, tc_HOL_Obool), tc_HOL_Obool), c_member(_1370936)), _1370938))))))], (33320 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (23085 ^ _780478) ^ [_1210102, _1210104, _1210106] : [-(hBOOL(hAPP(_1210102, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1210104), _1210106))))), 23088 ^ _780478 : [(23091 ^ _780478) ^ [] : [hBOOL(hAPP(_1210102, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210104)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210106))))], (23089 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1210106), _1210104)))]], 23092 ^ _780478 : [(23095 ^ _780478) ^ [] : [hBOOL(hAPP(_1210102, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23093 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1210104), _1210106)))]]], (14106 ^ _780478) ^ [_1032628, _1032630] : [class_Groups_Ocomm__monoid__mult(_1032628), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032628), _1032630), c_Groups_Oone__class_Oone(_1032628)) = _1032630)], (34789 ^ _780478) ^ [_1436316] : [-(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)))), _1436316) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1436316), _1436316))], (13865 ^ _780478) ^ [_1028399, _1028401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028399), _1028401)), -(_1028401 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028399), 13868 ^ [_1028399, _1028401]))], (42322 ^ _780478) ^ [_1621205, _1621207, _1621209] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621205)), hAPP(hAPP(c_List_Otake(_1621205), _1621207), _1621209)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621205)), _1621209)), _1621207))], (46210 ^ _780478) ^ [_1710584, _1710586, _1710588, _1710590, _1710592, _1710594, _1710596] : [-(c_List_Ofoldr(_1710584, _1710586, _1710588, hAPP(hAPP(c_List_Omap(_1710590, _1710584), _1710592), _1710594), _1710596) = c_List_Ofoldr(_1710590, _1710586, hAPP(c_Fun_Ocomp(_1710584, tc_fun(_1710586, _1710586), _1710590, _1710588), _1710592), _1710594, _1710596))], (46042 ^ _780478) ^ [_1706043, _1706045, _1706047, _1706049] : [-(hAPP(c_List_Ofilter(_1706043, _1706045), hAPP(c_List_Ofilter(_1706043, _1706047), _1706049)) = hAPP(c_List_Ofilter(_1706043, hAPP(hAPP(c_COMBS(_1706043, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1706043), c_fconj), _1706047)), _1706045)), _1706049))], (35513 ^ _780478) ^ [_1449138] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1449138), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1449138))], (13956 ^ _780478) ^ [_1029970, _1029972, _1029974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1029970), _1029972)), _1029974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029970), _1029974)))], (25494 ^ _780478) ^ [_1253753] : [-(hBOOL(hAPP(_1253753, 25501 ^ [_1253753]))), 25495 ^ _780478 : [(25496 ^ _780478) ^ [_1253805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253805)), hBOOL(hAPP(_1253753, hAPP(c_Int_Onat, _1253805)))]]], (21484 ^ _780478) ^ [_1179436, _1179438, _1179440, _1179442, _1179444] : [class_Rings_Olinordered__semiring__strict(_1179436), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179436), _1179438), _1179440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179436), _1179442), _1179444)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1179436), c_Groups_Ozero__class_Ozero(_1179436)), _1179438)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179436), c_Groups_Ozero__class_Ozero(_1179436)), _1179442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1179436), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179436), _1179438), _1179442)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1179436), _1179440), _1179444))))], (39560 ^ _780478) ^ [_1549760, _1549762] : [class_Complete__Lattice_Ocomplete__lattice(_1549760), -(c_Complete__Lattice_OSup__class_OSup(_1549760, _1549762) = c_Complete__Lattice_OInf__class_OInf(_1549760, hAPP(c_Set_OCollect(_1549760), hAPP(hAPP(c_COMBB(tc_fun(_1549760, tc_HOL_Obool), tc_HOL_Obool, _1549760), c_HOL_OAll(_1549760)), hAPP(hAPP(c_COMBB(tc_fun(_1549760, tc_HOL_Obool), tc_fun(_1549760, tc_HOL_Obool), _1549760), hAPP(c_COMBS(_1549760, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549760), c_fimplies), hAPP(hAPP(c_COMBC(_1549760, tc_fun(_1549760, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549760)), _1549762)))), hAPP(c_COMBC(_1549760, _1549760, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1549760)))))))], (1040 ^ _780478) ^ [_796178, _796180, _796182, _796184, _796186, _796188] : [-(c_List_Oall__interval__nat(_796186, _796182, _796178)), c_List_Oall__interval__nat(_796188, _796184, _796180), _796188 = _796186, _796184 = _796182, _796180 = _796178], (46807 ^ _780478) ^ [_1721707, _1721709, _1721711] : [class_Orderings_Olinorder(_1721707), hBOOL(hAPP(hAPP(c_member(_1721707), _1721709), hAPP(c_List_Oset(_1721707), _1721711))), c_List_Olinorder__class_Osorted(_1721707, _1721711), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1721707, _1721707, c_COMBI(_1721707)), _1721709), c_List_Oremove1(_1721707, _1721709, _1721711)) = _1721711)], (34249 ^ _780478) ^ [_1426376, _1426378] : [class_Int_Onumber__ring(_1426376), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426376), c_Groups_Oone__class_Oone(_1426376)), hAPP(c_Int_Onumber__class_Onumber__of(_1426376), _1426378)) = hAPP(c_Int_Onumber__class_Onumber__of(_1426376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1426378)))], (50315 ^ _780478) ^ [_1798370, _1798372, _1798374, _1798376, _1798378] : [c_Fun_Obij__betw(_1798370, _1798372, _1798374, c_Orderings_Otop__class_Otop(tc_fun(_1798370, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1798372, tc_HOL_Obool))), c_Fun_Obij__betw(_1798376, _1798370, _1798378, c_Orderings_Otop__class_Otop(tc_fun(_1798376, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1798370, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1798376, _1798372, c_Orderings_Otop__class_Otop(tc_fun(_1798376, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1798370, _1798372, _1798376, _1798374), _1798378)) = hAPP(c_Fun_Ocomp(_1798370, _1798376, _1798372, c_Hilbert__Choice_Oinv__into(_1798376, _1798370, c_Orderings_Otop__class_Otop(tc_fun(_1798376, tc_HOL_Obool)), _1798378)), c_Hilbert__Choice_Oinv__into(_1798370, _1798372, c_Orderings_Otop__class_Otop(tc_fun(_1798370, tc_HOL_Obool)), _1798374)))], (42804 ^ _780478) ^ [_1634030, _1634032, _1634034, _1634036] : [hBOOL(hAPP(c_List_Odistinct(_1634030), _1634032)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1634034, _1634030)), hAPP(hAPP(c_List_Ozip(_1634034, _1634030), _1634036), _1634032))))], (43756 ^ _780478) ^ [_1654612, _1654614, _1654616, _1654618, _1654620, _1654622, _1654624] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1654612, _1654612)), hAPP(hAPP(c_Product__Type_OPair(_1654612, _1654612), _1654614), _1654616)), _1654618)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1654612), tc_List_Olist(_1654612))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1654612), tc_List_Olist(_1654612)), hAPP(hAPP(c_List_Oappend(_1654612), _1654620), hAPP(hAPP(c_List_Olist_OCons(_1654612), _1654614), _1654622))), hAPP(hAPP(c_List_Oappend(_1654612), _1654620), hAPP(hAPP(c_List_Olist_OCons(_1654612), _1654616), _1654624)))), c_List_Olexord(_1654612, _1654618))))], (13863 ^ _780478) ^ [_1028354, _1028356] : [-(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)), _1028354), _1028356))], (4844 ^ _780478) ^ [_854325, _854327, _854329, _854331, _854333, _854335, _854337, _854339] : [-(c_Wellfounded_Olex__prod(_854339, _854335, _854331, _854327) = c_Wellfounded_Olex__prod(_854337, _854333, _854329, _854325)), _854339 = _854337, _854335 = _854333, _854331 = _854329, _854327 = _854325], (9036 ^ _780478) ^ [_935944, _935946, _935948, _935950] : [class_Orderings_Oorder(_935944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935944), _935946), _935948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935944), _935950), _935946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935944), _935950), _935948)))], (10565 ^ _780478) ^ [_964741, _964743, _964745] : [class_Lattices_Oboolean__algebra(_964741), 10568 ^ _780478 : [(10575 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964741), _964745), _964743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964741), hAPP(c_Groups_Ouminus__class_Ouminus(_964741), _964743)), hAPP(c_Groups_Ouminus__class_Ouminus(_964741), _964745))))], (10569 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964741), hAPP(c_Groups_Ouminus__class_Ouminus(_964741), _964743)), hAPP(c_Groups_Ouminus__class_Ouminus(_964741), _964745))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964741), _964745), _964743)))]]], (48339 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51917 ^ _780478) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (51941 ^ _780478) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (16138 ^ _780478) ^ [_1072676, _1072678, _1072680] : [-(hAPP(c_Set_Ovimage(_1072676, _1072678, _1072680), c_Orderings_Obot__class_Obot(tc_fun(_1072678, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1072676, tc_HOL_Obool)))], (43199 ^ _780478) ^ [_1641918, _1641920, _1641922] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1641918))), -(c_List_Osublist(_1641920, hAPP(hAPP(c_List_Olist_OCons(_1641920), _1641922), c_List_Olist_ONil(_1641920)), _1641918) = c_List_Olist_ONil(_1641920))], (23315 ^ _780478) ^ [_1214195, _1214197, _1214199] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214195), _1214197)), _1214199) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214195), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214197), _1214199)))], (17833 ^ _780478) ^ [_1112858, _1112860] : [hAPP(c_Nat_OSuc, _1112858) = hAPP(c_Nat_OSuc, _1112860), -(_1112858 = _1112860)], (4762 ^ _780478) ^ [_853034, _853036] : [_853036 = _853034, -(c_DSequence_Osingle(_853036) = c_DSequence_Osingle(_853034))], (6836 ^ _780478) ^ [_893555, _893557, _893559, _893561] : [c_Com_Ocom_OSemi(_893555, _893557) = c_Com_Ocom_OSemi(_893559, _893561), 6839 ^ _780478 : [(6842 ^ _780478) ^ [] : [-(_893557 = _893561)], (6840 ^ _780478) ^ [] : [-(_893555 = _893559)]]], (1334 ^ _780478) ^ [_800017, _800019] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_800017)), _800019 = _800017, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_800019)], (18434 ^ _780478) ^ [_1125459, _1125461, _1125463, _1125465, _1125467] : [hBOOL(hAPP(hAPP(c_member(_1125459), _1125461), _1125463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1125465, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125459, tc_fun(_1125465, tc_HOL_Obool)), _1125463), _1125467)), hAPP(_1125467, _1125461))))], (22333 ^ _780478) ^ [_1195886, _1195888, _1195890] : [class_Orderings_Olinorder(_1195886), 22336 ^ _780478 : [(22343 ^ _780478) ^ [] : [_1195888 = _1195890, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1195886), _1195888) = hAPP(c_SetInterval_Oord__class_OlessThan(_1195886), _1195890))], (22337 ^ _780478) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1195886), _1195888) = hAPP(c_SetInterval_Oord__class_OlessThan(_1195886), _1195890), -(_1195888 = _1195890)]]], (38440 ^ _780478) ^ [_1519353, _1519355] : [c_Wellfounded_Owf(_1519353, _1519355), -(c_Wellfounded_Owf(tc_List_Olist(_1519353), c_List_Olenlex(_1519353, _1519355)))], (15397 ^ _780478) ^ [_1057865, _1057867, _1057869, _1057871] : [class_Groups_Omonoid__mult(_1057865), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1057865), _1057867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1057869), _1057871)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1057865), hAPP(hAPP(c_Power_Opower__class_Opower(_1057865), _1057867), _1057869)), _1057871))], (40678 ^ _780478) ^ [_1576848, _1576850, _1576852, _1576854] : [-(hBOOL(hAPP(hAPP(c_member(_1576848), _1576850), hAPP(c_Relation_ODomain(_1576848, _1576848), _1576852)))), 40681 ^ _780478 : [(40688 ^ _780478) ^ [] : [_1576850 = _1576854, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576848, _1576848)), hAPP(hAPP(c_Product__Type_OPair(_1576848, _1576848), _1576850), _1576854)), c_Transitive__Closure_Ortrancl(_1576848, _1576852))))], (40682 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576848, _1576848)), hAPP(hAPP(c_Product__Type_OPair(_1576848, _1576848), _1576850), _1576854)), c_Transitive__Closure_Ortrancl(_1576848, _1576852))), -(_1576850 = _1576854)]]], (39640 ^ _780478) ^ [_1552180, _1552182, _1552184, _1552186, _1552188, _1552190] : [-(hAPP(c_Set_Ovimage(_1552180, _1552182, hAPP(c_Fun_Ocomp(_1552184, _1552182, _1552180, _1552186), _1552188)), _1552190) = hAPP(c_Set_Ovimage(_1552180, _1552184, _1552188), hAPP(c_Set_Ovimage(_1552184, _1552182, _1552186), _1552190)))], (9008 ^ _780478) ^ [_935478, _935480, _935482, _935484] : [class_Orderings_Oorder(_935478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935478), _935480), _935482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935478), _935484), _935480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935478), _935484), _935482)))], (47568 ^ _780478) ^ [_1737814, _1737816, _1737818] : [hBOOL(hAPP(hAPP(c_member(_1737814), _1737816), hAPP(c_List_Oset(_1737814), _1737818))), -(c_List_Oinsert(_1737814, _1737816, _1737818) = _1737818)], (48889 ^ _780478) ^ [_1766854] : [-(c_List_Omember(_1766854) = c_List_Oset(_1766854))], (39833 ^ _780478) ^ [_1556354, _1556356, _1556358, _1556360] : [-(c_Hilbert__Choice_OEps(tc_prod(_1556354, _1556356), hAPP(c_Product__Type_Oprod_Oprod__case(_1556354, _1556356, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1556354, tc_fun(_1556356, tc_HOL_Obool), tc_fun(_1556356, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1556356, tc_HOL_Obool), tc_fun(_1556356, tc_HOL_Obool)), _1556354), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1556356)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1556354), c_fconj), hAPP(c_fequal, _1556358)))), hAPP(c_fequal, _1556360)))) = hAPP(hAPP(c_Product__Type_OPair(_1556354, _1556356), _1556358), _1556360))], (5819 ^ _780478) ^ [_872629, _872631, _872633] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_872629), _872631)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_872629), hAPP(hAPP(c_Set_Oinsert(_872629), _872633), _872631))))], (11323 ^ _780478) ^ [_978608, _978610, _978612] : [class_Groups_Ogroup__add(_978608), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_978608), _978610), _978612) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978608), _978610), hAPP(c_Groups_Ouminus__class_Ouminus(_978608), _978612)))], (19448 ^ _780478) ^ [_1144401, _1144403, _1144405] : [class_Rings_Oring__1__no__zero__divisors(_1144401), -(_1144403 = c_Groups_Ozero__class_Ozero(_1144401)), hAPP(hAPP(c_Power_Opower__class_Opower(_1144401), _1144403), _1144405) = c_Groups_Ozero__class_Ozero(_1144401)], (43075 ^ _780478) ^ [_1639484] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639484)), c_List_Olist_ONil(_1639484)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38652 ^ _780478) ^ [_1524661, _1524663, _1524665, _1524667] : [-(hAPP(c_Relation_ODomain(_1524661, _1524663), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1524661, _1524663), tc_HOL_Obool)), _1524665), _1524667)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1524661, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524661, _1524663), _1524665)), hAPP(c_Relation_ODomain(_1524661, _1524663), _1524667)))], (45817 ^ _780478) ^ [_1700314, _1700316, _1700318] : [hBOOL(hAPP(c_List_Odistinct(_1700314), _1700316)), -(c_List_Oremove1(_1700314, _1700318, _1700316) = hAPP(c_List_OremoveAll(_1700314, _1700318), _1700316))], (7784 ^ _780478) ^ [_912232, _912234, _912236, _912238] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912232, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_912232), _912234), _912236)), _912238)), 7787 ^ _780478 : [(7790 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912232, tc_HOL_Obool)), _912236), _912238)))], (7788 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912232), _912234), _912238)))]]], (40355 ^ _780478) ^ [_1568827, _1568829, _1568831, _1568833] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1568827, _1568829, _1568831, tc_prod(_1568829, _1568831)), _1568833), c_Product__Type_OPair(_1568829, _1568831)) = _1568833)], (6162 ^ _780478) ^ [_878959, _878961, _878963] : [hAPP(hAPP(c_Set_Oinsert(_878959), _878961), _878963) = c_Orderings_Obot__class_Obot(tc_fun(_878959, tc_HOL_Obool))], (3310 ^ _780478) ^ [_829792, _829794] : [_829794 = _829792, -(c_Int_OBit1(_829794) = c_Int_OBit1(_829792))], (13300 ^ _780478) ^ [_1016939, _1016941, _1016943] : [-(hAPP(hAPP(c_Set_Oinsert(_1016939), _1016941), _1016943) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016939, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1016939), _1016941), c_Orderings_Obot__class_Obot(tc_fun(_1016939, tc_HOL_Obool)))), _1016943))], (16116 ^ _780478) ^ [_1072285, _1072287, _1072289, _1072291] : [hBOOL(hAPP(hAPP(c_member(_1072285), _1072287), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072285, tc_HOL_Obool)), _1072289), _1072291))), -(hBOOL(hAPP(hAPP(c_member(_1072285), _1072287), _1072289)))], (6798 ^ _780478) ^ [_892950, _892952, _892954, _892956, _892958, _892960] : [_892950 = _892952, -(hAPP(c_Fun_Ofun__upd(_892954, _892956, _892958, _892952, _892960), _892950) = _892960)], (47248 ^ _780478) ^ [_1731123, _1731125] : [-(c_List_OtakeWhile(_1731123, _1731125, c_List_Olist_ONil(_1731123)) = c_List_Olist_ONil(_1731123))], (48947 ^ _780478) ^ [_1768188, _1768190, _1768192, _1768194, _1768196, _1768198] : [c_Nitpick_Opair__box_OPairBox(_1768188, _1768190, _1768192, _1768194) = c_Nitpick_Opair__box_OPairBox(_1768188, _1768190, _1768196, _1768198), 48950 ^ _780478 : [(48953 ^ _780478) ^ [] : [-(_1768194 = _1768198)], (48951 ^ _780478) ^ [] : [-(_1768192 = _1768196)]]], (2384 ^ _780478) ^ [_815399, _815401] : [_815401 = _815399, -(c_Int_OBit0(_815401) = c_Int_OBit0(_815399))], (43987 ^ _780478) ^ [_1660605, _1660607, _1660609, _1660611, _1660613] : [-(hAPP(hAPP(c_List_Oappend(_1660605), _1660607), _1660609) = hAPP(hAPP(c_List_Oappend(_1660605), _1660611), _1660613)), 43990 ^ _780478 : [(43993 ^ _780478) ^ [] : [_1660607 = hAPP(hAPP(c_List_Otake(_1660605), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660605)), _1660607)), _1660611), _1660609 = hAPP(hAPP(c_List_Oappend(_1660605), hAPP(hAPP(c_List_Odrop(_1660605), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660605)), _1660607)), _1660611)), _1660613)], (43991 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660605)), _1660607)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660605)), _1660611))))]], 43998 ^ _780478 : [(44001 ^ _780478) ^ [] : [hAPP(hAPP(c_List_Otake(_1660605), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660605)), _1660611)), _1660607) = _1660611, hAPP(hAPP(c_List_Oappend(_1660605), hAPP(hAPP(c_List_Odrop(_1660605), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660605)), _1660611)), _1660607)), _1660609) = _1660613], (43999 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660605)), _1660607)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660605)), _1660611)))]]], (49436 ^ _780478) ^ [_1780768, _1780770] : [c_Relation_Otrans(_1780768, hAPP(c_Set_OCollect(tc_prod(_1780768, _1780768)), hAPP(c_Product__Type_Oprod_Oprod__case(_1780768, _1780768, tc_HOL_Obool), _1780770))), -(c_Predicate_Otransp(_1780768, _1780770))], (38603 ^ _780478) ^ [_1523599, _1523601, _1523603, _1523605] : [hBOOL(hAPP(hAPP(c_member(_1523599), _1523601), hAPP(c_Relation_ORange(_1523603, _1523599), _1523605))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523603, _1523599)), hAPP(hAPP(c_Product__Type_OPair(_1523603, _1523599), 38606 ^ [_1523599, _1523601, _1523603, _1523605]), _1523601)), _1523605)))], (43568 ^ _780478) ^ [_1650318, _1650320, _1650322] : [_1650322 = c_List_Olist_ONil(_1650320), -(_1650318 = hAPP(hAPP(c_List_Oappend(_1650320), _1650322), _1650318))], (36492 ^ _780478) ^ [_1474817, _1474819] : [36493 ^ _780478 : [(36496 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1474819), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36494 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1474817), _1474819))]], -(c_Divides_OposDivAlg(_1474817, _1474819) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474817))], (23817 ^ _780478) ^ [] : [-(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))))], (18562 ^ _780478) ^ [_1128611, _1128613, _1128615, _1128617, _1128619] : [class_Complete__Lattice_Ocomplete__lattice(_1128611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1128613, tc_HOL_Obool)), _1128615), _1128617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128611), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1128613, _1128611), _1128617), _1128619)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1128613, _1128611), _1128615), _1128619))))], (10007 ^ _780478) ^ [_954474, _954476, _954478] : [class_Groups_Oab__semigroup__mult(_954474), -(_954476 = c_Orderings_Obot__class_Obot(tc_fun(_954474, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_954474), _954476)), -(hBOOL(hAPP(hAPP(c_member(_954474), _954478), _954476))), -(hAPP(c_Finite__Set_Ofold1(_954474, c_Groups_Otimes__class_Otimes(_954474)), hAPP(hAPP(c_Set_Oinsert(_954474), _954478), _954476)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954474), _954478), hAPP(c_Finite__Set_Ofold1(_954474, c_Groups_Otimes__class_Otimes(_954474)), _954476)))], (10771 ^ _780478) ^ [_968360, _968362, _968364] : [class_Orderings_Olinorder(_968360), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968360), hAPP(hAPP(c_Orderings_Oord__class_Omin(_968360), _968362), _968364)), _968364)))], (37610 ^ _780478) ^ [_1498257, _1498259, _1498261] : [-(c_Wellfounded_Omlex__prod(_1498257, _1498259, _1498261) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1498257), _1498257), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1498257, c_Wellfounded_Oless__than, _1498261)), hAPP(hAPP(c_COMBS(_1498257, _1498257, tc_prod(tc_Nat_Onat, _1498257)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1498257, tc_prod(tc_Nat_Onat, _1498257)), _1498257), c_Product__Type_OPair(tc_Nat_Onat, _1498257)), _1498259)), c_COMBI(_1498257))))], (37891 ^ _780478) ^ [_1504975, _1504977, _1504979, _1504981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504975), _1504981)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504979), _1504977))), -(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), _1504975), _1504977)), 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), _1504979), _1504981)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (35321 ^ _780478) ^ [_1446266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446266), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1446266)), c_Int_OMin)))], (40863 ^ _780478) ^ [_1580745, _1580747, _1580749] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580745, _1580747)), hAPP(c_Relation_Oconverse(_1580747, _1580745), _1580749))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580747, _1580745)), _1580749)))], (37601 ^ _780478) ^ [_1498033, _1498035, _1498037, _1498039, _1498041] : [hBOOL(hAPP(hAPP(c_member(_1498033), _1498035), hAPP(c_Relation_OImage(_1498037, _1498033, _1498039), _1498041))), 37605 ^ _780478 : [(37608 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1498037), 37604 ^ [_1498033, _1498035, _1498037, _1498039, _1498041]), _1498041)))], (37606 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1498037, _1498033)), hAPP(hAPP(c_Product__Type_OPair(_1498037, _1498033), 37604 ^ [_1498033, _1498035, _1498037, _1498039, _1498041]), _1498035)), _1498039)))]]], (51939 ^ _780478) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (19494 ^ _780478) ^ [_1145074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145074)), _1145074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42430 ^ _780478) ^ [_1623756, _1623758] : [-(hAPP(c_List_Oset(_1623756), _1623758) = hAPP(c_Set_OCollect(_1623756), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1623756), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1623756, 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)), _1623756), 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)), _1623756), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1623756, tc_fun(tc_Nat_Onat, _1623756), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1623756, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1623756), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1623756), c_COMBB(_1623756, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1623756), _1623758))))), 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(_1623756)), _1623758))))))], (49586 ^ _780478) ^ [_1783266, _1783268, _1783270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1783266, _1783266), tc_HOL_Obool)), _1783268), _1783270)), c_Relation_Oantisym(_1783266, _1783270), -(c_Relation_Oantisym(_1783266, _1783268))], (37507 ^ _780478) ^ [_1496136, _1496138, _1496140, _1496142, _1496144, _1496146] : [hAPP(c_Product__Type_Oapfst(_1496136, _1496138, _1496140, _1496142), _1496144) = hAPP(c_Product__Type_Oapfst(_1496136, _1496138, _1496140, _1496146), _1496144), -(hAPP(_1496142, hAPP(c_Product__Type_Ofst(_1496136, _1496140), _1496144)) = hAPP(_1496146, hAPP(c_Product__Type_Ofst(_1496136, _1496140), _1496144)))], (17393 ^ _780478) ^ [_1101978, _1101980, _1101982, _1101984, _1101986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101978, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1101980, tc_fun(_1101978, tc_HOL_Obool)), _1101982), _1101984)), _1101986)), 17396 ^ _780478 : [(17397 ^ _780478) ^ [_1102111] : [hBOOL(hAPP(hAPP(c_member(_1101980), _1102111), _1101982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1101978, tc_HOL_Obool)), hAPP(_1101984, _1102111)), _1101986)))]]], (10703 ^ _780478) ^ [_967205, _967207, _967209] : [class_Orderings_Olinorder(_967205), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967205), _967207), _967209)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_967205), _967207), _967209) = _967207)], (23673 ^ _780478) ^ [_1220482, _1220484, _1220486, _1220488] : [class_Orderings_Olinorder(_1220482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220482), _1220484), _1220486)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1220482, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220482, _1220484), _1220488)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220482, _1220484), _1220486)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1220482, _1220486), _1220488))], (2 ^ _780478) ^ [_780505] : [-(_780505 = _780505)], (44440 ^ _780478) ^ [_1670370, _1670372, _1670374, _1670376, _1670378] : [class_Orderings_Olinorder(_1670370), 44443 ^ _780478 : [(44452 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1670372), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1670372, _1670370, _1670374), _1670376), _1670378)))), -(hBOOL(hAPP(hAPP(c_member(_1670372), _1670376), hAPP(c_List_Oset(_1670372), _1670378)))), hBOOL(hAPP(c_List_Odistinct(_1670372), _1670378))], (44444 ^ _780478) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1670372), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1670372, _1670370, _1670374), _1670376), _1670378))), 44447 ^ _780478 : [(44450 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1670372), _1670378)))], (44448 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1670372), _1670376), hAPP(c_List_Oset(_1670372), _1670378)))]]]]], (21868 ^ _780478) ^ [_1186456, _1186458, _1186460] : [21869 ^ _780478 : [(21872 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186458), _1186460))], (21870 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186456)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186456), _1186458)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186456), _1186460))))], (33168 ^ _780478) ^ [_1407157, _1407159, _1407161] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407157))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407157)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407159)), _1407161)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407159)), _1407161))], (20772 ^ _780478) ^ [_1167508, _1167510] : [class_Groups_Ogroup__add(_1167508), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167508), hAPP(c_Groups_Ouminus__class_Ouminus(_1167508), _1167510)), _1167510) = c_Groups_Ozero__class_Ozero(_1167508))], (47666 ^ _780478) ^ [_1740557, _1740559, _1740561, _1740563] : [class_Orderings_Oorder(_1740557), class_Enum_Oenum(_1740559), 47673 ^ _780478 : [(47682 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1740559, _1740557)), _1740561), _1740563))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1740559, _1740557)), _1740561), _1740563)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1740559), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1740559), c_fNot), hAPP(hAPP(c_COMBS(_1740559, _1740557, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1740557, tc_fun(_1740557, tc_HOL_Obool), _1740559), c_fequal), _1740561)), _1740563))))], (47674 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1740559, _1740557)), _1740561), _1740563)), 47677 ^ _780478 : [(47680 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1740559), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1740559), c_fNot), hAPP(hAPP(c_COMBS(_1740559, _1740557, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1740557, tc_fun(_1740557, tc_HOL_Obool), _1740559), c_fequal), _1740561)), _1740563)))))], (47678 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1740559, _1740557)), _1740561), _1740563)))]]]]], (20756 ^ _780478) ^ [_1167242, _1167244, _1167246] : [class_Groups_Ogroup__add(_1167242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167242), _1167244), _1167246) = c_Groups_Ozero__class_Ozero(_1167242), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1167242), _1167244) = _1167246)], (5638 ^ _780478) ^ [_866786, _866788, _866790, _866792, _866794, _866796] : [-(c_COMBC(_866796, _866792, _866788) = c_COMBC(_866794, _866790, _866786)), _866796 = _866794, _866792 = _866790, _866788 = _866786], (44989 ^ _780478) ^ [_1682348, _1682350] : [hAPP(c_Code__Numeral_Oof__nat, _1682348) = hAPP(c_Code__Numeral_Oof__nat, _1682350), -(_1682348 = _1682350)], (3316 ^ _780478) ^ [_829877, _829879, _829881, _829883] : [-(c_List_Olistsp(_829883, _829879) = c_List_Olistsp(_829881, _829877)), _829883 = _829881, _829879 = _829877], (29381 ^ _780478) ^ [_1326137, _1326139] : [-(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, _1326137, _1326139)), _1326139) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1326137), _1326139))], (14887 ^ _780478) ^ [_1047811, _1047813] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047811), _1047813) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047813), _1047811))], (21858 ^ _780478) ^ [_1186279, _1186281, _1186283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186279), _1186281)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186279), _1186283))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186281), _1186283)))], (13996 ^ _780478) ^ [_1030727, _1030729, _1030731] : [_1030727 = _1030731, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030727), _1030729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030731), _1030729))], (16490 ^ _780478) ^ [_1081488, _1081490, _1081492, _1081494] : [c_Fun_Oinj__on(_1081488, _1081490, _1081492, c_Orderings_Otop__class_Otop(tc_fun(_1081488, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1081488, _1081490, _1081492), hAPP(c_Set_Oimage(_1081488, _1081490, _1081492), _1081494)) = _1081494)], (45201 ^ _780478) ^ [_1686421] : [-(c_Code__Numeral_OSuc__code__numeral(_1686421) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1686421))))], (27541 ^ _780478) ^ [_1289707] : [class_Rings_Oring__1(_1289707), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289707), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1289707))], (52431 ^ _780478) ^ [_1834833] : [c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P_H, _1834833)), hAPP(v_c0, _1834833)), hAPP(v_Q_H, _1834833))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, _1834833)), hAPP(v_c0, _1834833)), hAPP(v_Q, _1834833))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool)))))], (28094 ^ _780478) ^ [_1300164, _1300166, _1300168, _1300170] : [class_Orderings_Oorder(_1300164), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300164, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300164, _1300166, _1300168)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1300164, _1300168, _1300170)) = c_Orderings_Obot__class_Obot(tc_fun(_1300164, tc_HOL_Obool)))], (2642 ^ _780478) ^ [_819404, _819406, _819408, _819410, _819412, _819414] : [-(c_FunDef_Oin__rel(_819414, _819410, _819406) = c_FunDef_Oin__rel(_819412, _819408, _819404)), _819414 = _819412, _819410 = _819408, _819406 = _819404], (48237 ^ _780478) ^ [_1752817, _1752819, _1752821] : [c_List_Olist__all(_1752817, _1752819, hAPP(c_List_Orev(_1752817), _1752821)), -(c_List_Olist__all(_1752817, _1752819, _1752821))], (51879 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (51955 ^ _780478) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (16955 ^ _780478) ^ [_1092212, _1092214, _1092216] : [class_Lattices_Olattice(_1092212), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092212), _1092214)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092212), _1092216)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1092212, tc_HOL_Obool)), _1092214), _1092216) = c_Orderings_Obot__class_Obot(tc_fun(_1092212, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1092212), c_Big__Operators_Olattice__class_OSup__fin(_1092212, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1092212, tc_HOL_Obool)), _1092214), _1092216))), c_Big__Operators_Olattice__class_OSup__fin(_1092212, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1092212, tc_HOL_Obool)), _1092214), _1092216))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1092212), c_Big__Operators_Olattice__class_OSup__fin(_1092212, _1092214)), c_Big__Operators_Olattice__class_OSup__fin(_1092212, _1092216)))], (25325 ^ _780478) ^ [_1251189, _1251191, _1251193, _1251195] : [class_Rings_Odivision__ring(_1251189), -(_1251191 = c_Groups_Ozero__class_Ozero(_1251189)), 25332 ^ _780478 : [(25339 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251189), _1251193), _1251191) = _1251195, -(_1251193 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251189), _1251195), _1251191))], (25333 ^ _780478) ^ [] : [_1251193 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251189), _1251195), _1251191), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251189), _1251193), _1251191) = _1251195)]]], (33076 ^ _780478) ^ [_1405576] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1405576) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405576)))], (35115 ^ _780478) ^ [_1442253] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1442253, 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, _1442253, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (41558 ^ _780478) ^ [_1599037, _1599039, _1599041, _1599043, _1599045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1599037, tc_HOL_Obool)), _1599039), _1599041)), 41564 ^ _780478 : [(41569 ^ _780478) ^ [] : [hBOOL(hAPP(_1599045, 41563 ^ [_1599037, _1599039, _1599041, _1599043, _1599045]))], (41567 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1599043, 41563 ^ [_1599037, _1599039, _1599041, _1599043, _1599045])))], (41565 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1599037), 41563 ^ [_1599037, _1599039, _1599041, _1599043, _1599045]), _1599039)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1599037, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599037, tc_HOL_Obool)), _1599039), hAPP(c_Set_OCollect(_1599037), _1599043))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1599037, tc_HOL_Obool)), _1599041), hAPP(c_Set_OCollect(_1599037), _1599045)))))], (48969 ^ _780478) ^ [_1768594, _1768596, _1768598] : [-(c_FunDef_OTHE__default(_1768596, _1768598, _1768594) = c_HOL_OThe(_1768596, _1768594)), 48970 ^ _780478 : [(48971 ^ _780478) ^ [_1768658] : [hBOOL(hAPP(_1768594, _1768658)), 48975 ^ _780478 : [(48978 ^ _780478) ^ [] : [48974 ^ [_1768594, _1768596, _1768598, _1768658] = _1768658], (48976 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1768594, 48974 ^ [_1768594, _1768596, _1768598, _1768658])))]]]]], (42475 ^ _780478) ^ [_1626345, _1626347, _1626349, _1626351, _1626353, _1626355] : [-(hAPP(hAPP(c_List_Ozip(_1626345, _1626347), hAPP(hAPP(c_List_Olist_OCons(_1626345), _1626349), _1626351)), hAPP(hAPP(c_List_Olist_OCons(_1626347), _1626353), _1626355)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1626345, _1626347)), hAPP(hAPP(c_Product__Type_OPair(_1626345, _1626347), _1626349), _1626353)), hAPP(hAPP(c_List_Ozip(_1626345, _1626347), _1626351), _1626355)))], (18175 ^ _780478) ^ [_1119926, _1119928, _1119930, _1119932, _1119934] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119926, tc_HOL_Obool)), _1119928), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119930, tc_fun(_1119926, tc_HOL_Obool)), _1119932), _1119934)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119930, tc_fun(_1119926, tc_HOL_Obool)), _1119932), hAPP(hAPP(c_COMBB(tc_fun(_1119926, tc_HOL_Obool), tc_fun(_1119926, tc_HOL_Obool), _1119930), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119926, tc_HOL_Obool)), _1119928)), _1119934)))], (7623 ^ _780478) ^ [_908811, _908813, _908815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908811, tc_HOL_Obool)), _908813), _908815)), hBOOL(hAPP(c_Finite__Set_Ofinite(_908811), _908815)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_908811), _908813)))], (8794 ^ _780478) ^ [_932469, _932471, _932473, _932475] : [class_Orderings_Oord(_932469), _932471 = _932473, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932469), _932473), _932475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932469), _932471), _932475)))], (19200 ^ _780478) ^ [_1140753, _1140755, _1140757] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1140753), 19203 ^ _780478 : [(19210 ^ _780478) ^ [] : [_1140757 = c_Groups_Ozero__class_Ozero(_1140753), -(_1140755 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140753), _1140755), _1140757))], (19204 ^ _780478) ^ [] : [_1140755 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140753), _1140755), _1140757), -(_1140757 = c_Groups_Ozero__class_Ozero(_1140753))]]], (38455 ^ _780478) ^ [_1519833, _1519835, _1519837, _1519839] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1519833), _1519835)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1519833), _1519837)), -(_1519837 = c_Orderings_Obot__class_Obot(tc_fun(_1519833, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1519833, tc_HOL_Obool), tc_fun(_1519833, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1519833, tc_HOL_Obool), tc_fun(_1519833, tc_HOL_Obool)), _1519835), _1519837)), c_Wellfounded_Omax__ext(_1519833, _1519839)))), 38469 ^ _780478 : [(38472 ^ _780478) ^ [_1520238] : [hBOOL(hAPP(hAPP(c_member(_1519833), _1520238), _1519837)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519833, _1519833)), hAPP(hAPP(c_Product__Type_OPair(_1519833, _1519833), 38468 ^ [_1519833, _1519835, _1519837, _1519839]), _1520238)), _1519839))], (38470 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1519833), 38468 ^ [_1519833, _1519835, _1519837, _1519839]), _1519835)))]]], (7904 ^ _780478) ^ [_914672, _914674, _914676, _914678, _914680] : [c_Finite__Set_Ofolding__one__idem(_914672, _914674, _914676), hBOOL(hAPP(c_Finite__Set_Ofinite(_914672), _914678)), -(hAPP(_914676, hAPP(hAPP(c_Set_Oinsert(_914672), _914680), _914678)) = hAPP(hAPP(c_Finite__Set_Ofold(_914672, _914672, _914674), _914680), _914678))], (42746 ^ _780478) ^ [_1632596, _1632598] : [-(c_List_Obutlast(_1632596, _1632598) = hAPP(hAPP(c_List_Otake(_1632596), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632596)), _1632598)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1632598))], (15281 ^ _780478) ^ [_1055545, _1055547, _1055549, _1055551] : [class_Rings_Olinordered__semidom(_1055545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055545), c_Groups_Oone__class_Oone(_1055545)), _1055547)), 15288 ^ _780478 : [(15295 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055549), _1055551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055545), hAPP(hAPP(c_Power_Opower__class_Opower(_1055545), _1055547), _1055549)), hAPP(hAPP(c_Power_Opower__class_Opower(_1055545), _1055547), _1055551))))], (15289 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055545), hAPP(hAPP(c_Power_Opower__class_Opower(_1055545), _1055547), _1055549)), hAPP(hAPP(c_Power_Opower__class_Opower(_1055545), _1055547), _1055551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1055549), _1055551)))]]], (7840 ^ _780478) ^ [_913482, _913484, _913486, _913488] : [-(hBOOL(hAPP(hAPP(c_member(_913482), _913484), _913486))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_913482, tc_Nat_Onat), _913488), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913482, tc_HOL_Obool)), _913486), hAPP(hAPP(c_Set_Oinsert(_913482), _913484), c_Orderings_Obot__class_Obot(tc_fun(_913482, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_913482, tc_Nat_Onat), _913488), _913486))], (35824 ^ _780478) ^ [_1460604, _1460606, _1460608, _1460610] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1460604, _1460606), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1460608), _1460610))), -(_1460606 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1460604), _1460606) = _1460608)], (44502 ^ _780478) ^ [_1671438, _1671440, _1671442] : [class_Orderings_Olinorder(_1671438), -(hAPP(c_List_Oset(_1671438), c_List_Olinorder__class_Oinsort__insert__key(_1671438, _1671438, c_COMBI(_1671438), _1671440, _1671442)) = hAPP(hAPP(c_Set_Oinsert(_1671438), _1671440), hAPP(c_List_Oset(_1671438), _1671442)))], (9126 ^ _780478) ^ [_937186, _937188, _937190] : [class_Orderings_Opreorder(_937186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937186), _937188), _937190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937186), _937188), _937190)))], (20258 ^ _780478) ^ [_1158321, _1158323, _1158325, _1158327] : [class_Rings_Olinordered__semidom(_1158321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158321), c_Groups_Ozero__class_Ozero(_1158321)), _1158323)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158321), _1158325), _1158327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158321), _1158325), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1158321), _1158323), _1158327))))], (17839 ^ _780478) ^ [_1112947, _1112949, _1112951, _1112953, _1112955, _1112957] : [class_Complete__Lattice_Ocomplete__lattice(_1112947), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112949, _1112947), _1112951), hAPP(hAPP(c_COMBB(tc_fun(_1112953, _1112947), _1112947, _1112949), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112953, _1112947), _1112955)), _1112957)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112953, _1112947), _1112955), hAPP(hAPP(c_COMBB(tc_fun(_1112949, _1112947), _1112947, _1112953), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112949, _1112947), _1112951)), hAPP(c_COMBC(_1112949, _1112953, _1112947), _1112957))))], (27134 ^ _780478) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (9748 ^ _780478) ^ [_948843, _948845, _948847, _948849] : [class_Rings_Ocomm__semiring__1(_948843), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948843), _948845), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948843), _948847), _948849)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948843), _948845), _948847)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948843), _948845), _948849)))], (5628 ^ _780478) ^ [_866637, _866639, _866641, _866643] : [-(c_COMBK(_866643, _866639) = c_COMBK(_866641, _866637)), _866643 = _866641, _866639 = _866637], (35377 ^ _780478) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (28398 ^ _780478) ^ [_1305983, _1305985] : [class_Orderings_Olinorder(_1305983), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1305983, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1305983), _1305985)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1305983), _1305985))], (16052 ^ _780478) ^ [_1071021, _1071023, _1071025] : [class_Lattices_Obounded__lattice__top(_1071021), 16055 ^ _780478 : [(16064 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1071021), _1071023), _1071025) = c_Orderings_Otop__class_Otop(_1071021)), _1071023 = c_Orderings_Otop__class_Otop(_1071021), _1071025 = c_Orderings_Otop__class_Otop(_1071021)], (16056 ^ _780478) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1071021), _1071023), _1071025) = c_Orderings_Otop__class_Otop(_1071021), 16059 ^ _780478 : [(16062 ^ _780478) ^ [] : [-(_1071025 = c_Orderings_Otop__class_Otop(_1071021))], (16060 ^ _780478) ^ [] : [-(_1071023 = c_Orderings_Otop__class_Otop(_1071021))]]]]], (7297 ^ _780478) ^ [_902371, _902373, _902375] : [_902371 = _902373, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902375, tc_HOL_Obool)), _902373), _902371)))], (50113 ^ _780478) ^ [_1793715, _1793717, _1793719] : [c_Fun_Oinj__on(_1793715, _1793717, _1793719, c_Orderings_Otop__class_Otop(tc_fun(_1793715, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1793717, _1793715, c_Hilbert__Choice_Oinv__into(_1793715, _1793717, c_Orderings_Otop__class_Otop(tc_fun(_1793715, tc_HOL_Obool)), _1793719)), c_Orderings_Otop__class_Otop(tc_fun(_1793717, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1793715, tc_HOL_Obool)))], (16596 ^ _780478) ^ [_1083718, _1083720, _1083722] : [class_Lattices_Osemilattice__inf(_1083718), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083718), _1083720)), -(_1083720 = c_Orderings_Obot__class_Obot(tc_fun(_1083718, tc_HOL_Obool))), 16607 ^ _780478 : [(16608 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083718), _1083722), hAPP(c_Finite__Set_Ofold1(_1083718, c_Lattices_Osemilattice__inf__class_Oinf(_1083718)), _1083720))), 16611 ^ _780478 : [(16612 ^ _780478) ^ [_1084011] : [hBOOL(hAPP(hAPP(c_member(_1083718), _1084011), _1083720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083718), _1083722), _1084011)))]]], (16618 ^ _780478) ^ [] : [16620 ^ _780478 : [(16623 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083718), _1083722), 16619 ^ [_1083718, _1083720, _1083722]))], (16621 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1083718), 16619 ^ [_1083718, _1083720, _1083722]), _1083720)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083718), _1083722), hAPP(c_Finite__Set_Ofold1(_1083718, c_Lattices_Osemilattice__inf__class_Oinf(_1083718)), _1083720))))]]], (29227 ^ _780478) ^ [_1323006, _1323008, _1323010] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1323006), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1323008, _1323010)), _1323010) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1323006), _1323008), _1323010))], (39244 ^ _780478) ^ [_1542478, _1542480] : [c_Wellfounded_OwfP(_1542478, _1542480), 39247 ^ _780478 : [(39248 ^ _780478) ^ [_1542542] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1542478, _1542480), _1542542)))]]], (7914 ^ _780478) ^ [_914865, _914867, _914869, _914871, _914873] : [c_Finite__Set_Ofolding__one__idem(_914865, _914867, _914869), hBOOL(hAPP(c_Finite__Set_Ofinite(_914865), _914871)), -(_914873 = c_Orderings_Obot__class_Obot(tc_fun(_914865, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_914865, tc_HOL_Obool)), _914873), _914871)), -(hAPP(hAPP(_914867, hAPP(_914869, _914873)), hAPP(_914869, _914871)) = hAPP(_914869, _914871))], (9782 ^ _780478) ^ [_949579, _949581, _949583, _949585] : [class_Rings_Ocomm__semiring__1(_949579), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949579), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949579), _949581), _949583)), _949585) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_949579), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949579), _949581), _949585)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_949579), _949583), _949585)))], (21169 ^ _780478) ^ [_1173932, _1173934, _1173936] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173932), _1173934)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173936), _1173934)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173934)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173932), _1173936))], (40476 ^ _780478) ^ [_1571710, _1571712] : [-(c_Transitive__Closure_Otrancl(_1571710, _1571712) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1571710, _1571710), tc_HOL_Obool)), _1571712), hAPP(hAPP(c_Relation_Orel__comp(_1571710, _1571710, _1571710), c_Transitive__Closure_Otrancl(_1571710, _1571712)), _1571712)))], (32756 ^ _780478) ^ [_1399237, _1399239, _1399241, _1399243] : [class_Fields_Olinordered__field__inverse__zero(_1399237), class_Int_Onumber(_1399237), 32763 ^ _780478 : [(32764 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399237), _1399239), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1399237), _1399241), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243)))), 32767 ^ _780478 : [(32774 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399237), c_Groups_Ozero__class_Ozero(_1399237)), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243)))), 32777 ^ _780478 : [(32784 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399237), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243)), c_Groups_Ozero__class_Ozero(_1399237)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399237), _1399239), c_Groups_Ozero__class_Ozero(_1399237))))], (32778 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399237), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243)), c_Groups_Ozero__class_Ozero(_1399237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399237), _1399241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399237), _1399239), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243)))))]]], (32768 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399237), c_Groups_Ozero__class_Ozero(_1399237)), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399237), _1399239), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243))), _1399241)))]]], (32790 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399237), _1399239), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1399237), _1399241), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243))))), 32793 ^ _780478 : [(32796 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399237), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399237), _1399239), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243))), _1399241))], (32794 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399237), c_Groups_Ozero__class_Ozero(_1399237)), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243))))]], 32797 ^ _780478 : [(32800 ^ _780478) ^ [] : [32801 ^ _780478 : [(32804 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399237), _1399241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1399237), _1399239), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243))))], (32802 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399237), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243)), c_Groups_Ozero__class_Ozero(_1399237))))]], 32805 ^ _780478 : [(32808 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1399237), _1399239), c_Groups_Ozero__class_Ozero(_1399237)))], (32806 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399237), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243)), c_Groups_Ozero__class_Ozero(_1399237)))]]], (32798 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1399237), c_Groups_Ozero__class_Ozero(_1399237)), hAPP(c_Int_Onumber__class_Onumber__of(_1399237), _1399243)))]]]]], (29041 ^ _780478) ^ [_1318823, _1318825, _1318827] : [-(hAPP(c_Set_OPow(_1318823), hAPP(hAPP(c_Set_Oinsert(_1318823), _1318825), _1318827)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1318823, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1318823), _1318827)), hAPP(c_Set_Oimage(tc_fun(_1318823, tc_HOL_Obool), tc_fun(_1318823, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1318823), _1318825)), hAPP(c_Set_OPow(_1318823), _1318827))))], (44378 ^ _780478) ^ [_1669045, _1669047, _1669049, _1669051, _1669053, _1669055] : [class_Orderings_Olinorder(_1669045), 44381 ^ _780478 : [(44388 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1669045), hAPP(_1669047, _1669049)), hAPP(_1669047, _1669051)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669053, _1669045, _1669047), _1669049), hAPP(hAPP(c_List_Olist_OCons(_1669053), _1669051), _1669055)) = hAPP(hAPP(c_List_Olist_OCons(_1669053), _1669051), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669053, _1669045, _1669047), _1669049), _1669055)))], (44382 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1669045), hAPP(_1669047, _1669049)), hAPP(_1669047, _1669051))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1669053, _1669045, _1669047), _1669049), hAPP(hAPP(c_List_Olist_OCons(_1669053), _1669051), _1669055)) = hAPP(hAPP(c_List_Olist_OCons(_1669053), _1669049), hAPP(hAPP(c_List_Olist_OCons(_1669053), _1669051), _1669055)))]]], (5813 ^ _780478) ^ [_872518, _872520, _872522, _872524] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_872518), _872520)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_872522), hAPP(c_Set_Oimage(_872518, _872522, _872524), _872520))))], (41233 ^ _780478) ^ [_1590283, _1590285, _1590287, _1590289] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590283, _1590283), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1590285), _1590287)), _1590289) = hAPP(hAPP(c_Relation_Orel__comp(_1590283, _1590283, _1590283), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590283, _1590283), tc_HOL_Obool), _1590285), _1590289)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590283, _1590283), tc_HOL_Obool), _1590287), _1590289)))], (16534 ^ _780478) ^ [_1082579, _1082581, _1082583, _1082585] : [-(hBOOL(hAPP(hAPP(c_member(_1082579), _1082581), _1082583))), -(hAPP(c_Set_Ovimage(_1082585, _1082579, hAPP(c_COMBK(_1082579, _1082585), _1082581)), _1082583) = c_Orderings_Obot__class_Obot(tc_fun(_1082585, tc_HOL_Obool)))], (31688 ^ _780478) ^ [_1378543, _1378545, _1378547] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378543), _1378545), _1378547) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1378543, tc_fun(tc_fun(_1378543, tc_HOL_Obool), tc_HOL_Obool)), _1378545), hAPP(hAPP(c_COMBC(_1378543, tc_fun(tc_fun(_1378543, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1378543, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1378543, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1378543, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1378543, tc_HOL_Obool), tc_HOL_Obool)), _1378543), c_Set_Oinsert(tc_fun(_1378543, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1378543, tc_HOL_Obool), tc_fun(_1378543, tc_HOL_Obool), _1378543), c_Relation_OImage(_1378543, _1378543, _1378547)), hAPP(hAPP(c_COMBC(_1378543, tc_fun(_1378543, tc_HOL_Obool), tc_fun(_1378543, tc_HOL_Obool)), c_Set_Oinsert(_1378543)), c_Orderings_Obot__class_Obot(tc_fun(_1378543, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1378543, tc_HOL_Obool), tc_HOL_Obool)))))], (52025 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (45651 ^ _780478) ^ [_1697105, _1697107, _1697109] : [hBOOL(hAPP(c_List_Odistinct(_1697105), _1697107)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1697105)), c_Enum_On__lists(_1697105, _1697109, _1697107))))], (14191 ^ _780478) ^ [_1034097, _1034099, _1034101] : [class_Rings_Ocomm__semiring__1(_1034097), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034097), _1034099), _1034101)), _1034101) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034097), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034097), _1034099), c_Groups_Oone__class_Oone(_1034097))), _1034101))], (30296 ^ _780478) ^ [_1342542, _1342544] : [class_Rings_Olinordered__idom(_1342542), -(hAPP(c_Groups_Oabs__class_Oabs(_1342542), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1342542), _1342544)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1342542), _1342544))], (3438 ^ _780478) ^ [_831748, _831750, _831752, _831754, _831756, _831758] : [-(c_List_Opartition(_831758, _831754, _831750) = c_List_Opartition(_831756, _831752, _831748)), _831758 = _831756, _831754 = _831752, _831750 = _831748], (52335 ^ _780478) ^ [_1833600, _1833602, _1833604, _1833606, _1833608, _1833610] : [-(hAPP(hAPP(hAPP(c_COMBS(_1833600, _1833602, _1833604), _1833606), _1833608), _1833610) = hAPP(hAPP(_1833606, _1833610), hAPP(_1833608, _1833610)))], (47981 ^ _780478) ^ [_1747616, _1747618, _1747620, _1747622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747616), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747618)), _1747620))), 47987 ^ _780478 : [(47990 ^ _780478) ^ [] : [hBOOL(hAPP(_1747622, 47986 ^ [_1747616, _1747618, _1747620, _1747622]))], (47988 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1747618), 47986 ^ [_1747616, _1747618, _1747620, _1747622]), hAPP(c_List_Oset(_1747618), _1747620))))]], -(hBOOL(hAPP(_1747622, hAPP(hAPP(c_List_Onth(_1747618), _1747620), _1747616))))], (24019 ^ _780478) ^ [_1227120, _1227122] : [24021 ^ _780478 : [(24024 ^ _780478) ^ [] : [hBOOL(hAPP(_1227122, 24020 ^ [_1227120, _1227122]))], (24022 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24020 ^ [_1227120, _1227122]), _1227120)))]], 24025 ^ _780478 : [(24026 ^ _780478) ^ [_1227270] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1227270), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227120))), -(hBOOL(hAPP(_1227122, _1227270)))]]], (45003 ^ _780478) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (17877 ^ _780478) ^ [_1113655, _1113657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113655), _1113657)), -(hAPP(c_Nat_OSuc, _1113655) = _1113657), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113655)), _1113657)))], (37750 ^ _780478) ^ [] : [-(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)))))], (51999 ^ _780478) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (10217 ^ _780478) ^ [_958284, _958286, _958288, _958290] : [class_Orderings_Olinorder(_958284), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_958284), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958284), _958286), _958288)), _958290) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_958284), _958286), hAPP(hAPP(c_Orderings_Oord__class_Omin(_958284), _958288), _958290)))], (39240 ^ _780478) ^ [_1542396] : [-(c_Wellfounded_OwfP(_1542396, hAPP(c_COMBK(tc_fun(_1542396, tc_HOL_Obool), _1542396), hAPP(c_COMBK(tc_HOL_Obool, _1542396), c_fFalse))))], (8571 ^ _780478) ^ [_928657, _928659, _928661, _928663] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928657, tc_HOL_Obool)), _928659), hAPP(hAPP(c_Set_Oinsert(_928657), _928661), _928663))), 8574 ^ _780478 : [(8581 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928657), _928661), _928663))), 8584 ^ _780478 : [(8591 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928657), _928661), _928659))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928657, tc_HOL_Obool)), _928659), _928663)))], (8585 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_928657), _928661), _928659)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928657, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_928657, tc_HOL_Obool)), _928659), hAPP(hAPP(c_Set_Oinsert(_928657), _928661), c_Orderings_Obot__class_Obot(tc_fun(_928657, tc_HOL_Obool))))), _928663)))]]], (8575 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_928657), _928661), _928663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_928657, tc_HOL_Obool)), _928659), _928663)))]]], (49770 ^ _780478) ^ [_1786979, _1786981] : [-(c_Relation_Osym(_1786979, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1786979, _1786979), tc_HOL_Obool)), _1786981), hAPP(c_Relation_Oconverse(_1786979, _1786979), _1786981))))], (39149 ^ _780478) ^ [_1540022, _1540024, _1540026, _1540028, _1540030, _1540032, _1540034] : [-(hAPP(c_Product__Type_Osnd(_1540022, _1540024), hAPP(c_Product__Type_Omap__pair(_1540026, _1540022, _1540028, _1540024, _1540030, _1540032), _1540034)) = hAPP(_1540032, hAPP(c_Product__Type_Osnd(_1540026, _1540028), _1540034)))], (21584 ^ _780478) ^ [_1181358, _1181360, _1181362, _1181364] : [class_Rings_Olinordered__semiring__strict(_1181358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181358), _1181360), _1181362)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181358), _1181364), _1181362))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181358), c_Groups_Ozero__class_Ozero(_1181358)), _1181362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181358), _1181360), _1181364)))], (39337 ^ _780478) ^ [_1544357, _1544359] : [c_Wellfounded_Owf(_1544357, _1544359), -(c_Wellfounded_OwfP(_1544357, hAPP(hAPP(c_COMBC(_1544357, tc_fun(tc_prod(_1544357, _1544357), tc_HOL_Obool), tc_fun(_1544357, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544357, tc_fun(tc_fun(tc_prod(_1544357, _1544357), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1544357, _1544357), tc_HOL_Obool), tc_fun(_1544357, tc_HOL_Obool)), _1544357), c_COMBC(_1544357, tc_fun(tc_prod(_1544357, _1544357), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1544357, tc_prod(_1544357, _1544357)), tc_fun(_1544357, tc_fun(tc_fun(tc_prod(_1544357, _1544357), tc_HOL_Obool), tc_HOL_Obool)), _1544357), hAPP(c_COMBB(tc_prod(_1544357, _1544357), tc_fun(tc_fun(tc_prod(_1544357, _1544357), tc_HOL_Obool), tc_HOL_Obool), _1544357), c_member(tc_prod(_1544357, _1544357)))), c_Product__Type_OPair(_1544357, _1544357)))), _1544359)))], (52089 ^ _780478) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (7164 ^ _780478) ^ [_900001, _900003, _900005, _900007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900001, tc_HOL_Obool)), _900003), _900005)), hBOOL(hAPP(_900003, _900007)), -(hBOOL(hAPP(_900005, _900007)))], (46358 ^ _780478) ^ [_1713491, _1713493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713491), _1713493)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1713491, _1713493)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1713493), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (50967 ^ _780478) ^ [_1813467, _1813469, _1813471] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1813467), _1813469)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1813467), _1813471))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1813467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1813469), _1813471)))], (33110 ^ _780478) ^ [_1406179, _1406181] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1406179) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406181)), _1406179 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406181)), 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), _1406181)))], (4276 ^ _780478) ^ [_845159, _845161, _845163, _845165] : [-(c_List_Oconcat(_845165, _845161) = c_List_Oconcat(_845163, _845159)), _845165 = _845163, _845161 = _845159], (37385 ^ _780478) ^ [_1492087] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1492087)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1492087)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (16867 ^ _780478) ^ [_1090120, _1090122, _1090124, _1090126, _1090128] : [class_Complete__Lattice_Ocomplete__lattice(_1090120), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090122), _1090124)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1090120), _1090126), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1090122, _1090120), _1090124), _1090128)) = hAPP(hAPP(c_Finite__Set_Ofold(_1090122, _1090120, hAPP(hAPP(c_COMBB(_1090120, tc_fun(_1090120, _1090120), _1090122), c_Lattices_Osemilattice__sup__class_Osup(_1090120)), _1090128)), _1090126), _1090124))], (15723 ^ _780478) ^ [_1064631, _1064633, _1064635] : [class_Lattices_Osemilattice__inf(_1064631), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064631), _1064633), _1064635) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064631), _1064635), _1064633))], (45049 ^ _780478) ^ [] : [-(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))], (34405 ^ _780478) ^ [_1429392, _1429394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1429392)), c_Int_OBit0(_1429394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429392), _1429394)))], (34621 ^ _780478) ^ [_1433150] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1433150)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433150)), 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))))], (43331 ^ _780478) ^ [_1645108, _1645110, _1645112, _1645114, _1645116] : [hAPP(hAPP(c_List_Oappend(_1645108), _1645110), _1645112) = hAPP(hAPP(c_List_Olist_OCons(_1645108), _1645114), _1645116), 43336 ^ _780478 : [(43339 ^ _780478) ^ [] : [-(_1645112 = hAPP(hAPP(c_List_Olist_OCons(_1645108), _1645114), _1645116))], (43337 ^ _780478) ^ [] : [-(_1645110 = c_List_Olist_ONil(_1645108))]], 43341 ^ _780478 : [(43344 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1645108), 43340 ^ [_1645108, _1645110, _1645112, _1645114, _1645116]), _1645112) = _1645116)], (43342 ^ _780478) ^ [] : [-(_1645110 = hAPP(hAPP(c_List_Olist_OCons(_1645108), _1645114), 43340 ^ [_1645108, _1645110, _1645112, _1645114, _1645116]))]]], (39023 ^ _780478) ^ [_1536903, _1536905] : [-(hAPP(c_Fun_Oid(_1536903), _1536905) = _1536905)], (28760 ^ _780478) ^ [_1313041, _1313043, _1313045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1313041)), 28763 ^ _780478 : [(28764 ^ _780478) ^ [_1313175] : [28766 ^ _780478 : [(28772 ^ _780478) ^ [] : [-(_1313175 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28768 ^ [_1313041, _1313043, _1313045, _1313175]), 28765 ^ [_1313041, _1313043, _1313045, _1313175]))], (28770 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28768 ^ [_1313041, _1313043, _1313045, _1313175]), _1313043)))], (28767 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28765 ^ [_1313041, _1313043, _1313045, _1313175]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1313041))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1313175), _1313045)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1313175), _1313041)), _1313045)))]]], (21840 ^ _780478) ^ [_1185983, _1185985] : [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), _1185983), _1185985))), 21843 ^ _780478 : [(21846 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1185985)))], (21844 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1185983)))]]], (14080 ^ _780478) ^ [_1032117, _1032119, _1032121, _1032123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032117), _1032119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1032121), _1032123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032117), _1032121)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032119), _1032123))))], (35375 ^ _780478) ^ [_1447081] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1447081) = c_Int_Opred(_1447081))], (12047 ^ _780478) ^ [_992139, _992141, _992143] : [class_Orderings_Olinorder(_992139), hBOOL(hAPP(c_Finite__Set_Ofinite(_992139), _992141)), -(c_Big__Operators_Olattice_OSup__fin(_992139, c_Orderings_Oord__class_Omax(_992139), hAPP(hAPP(c_Set_Oinsert(_992139), _992143), _992141)) = hAPP(hAPP(c_Finite__Set_Ofold(_992139, _992139, c_Orderings_Oord__class_Omax(_992139)), _992143), _992141))], (52049 ^ _780478) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (52421 ^ _780478) ^ [_1834694, _1834696] : [hBOOL(hAPP(hAPP(c_fimplies, _1834694), _1834696)), hBOOL(_1834694), -(hBOOL(_1834696))], (7563 ^ _780478) ^ [_907677, _907679, _907681, _907683] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_907677, _907679, _907681), _907683), c_Orderings_Obot__class_Obot(tc_fun(_907677, tc_HOL_Obool))) = _907683)], (42630 ^ _780478) ^ [_1630054, _1630056, _1630058, _1630060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630054)), _1630056)), _1630058)), -(hAPP(hAPP(c_List_Olist__update(_1630054, _1630056), _1630058), _1630060) = _1630056)], (34845 ^ _780478) ^ [_1437320, _1437322] : [class_Fields_Olinordered__field__inverse__zero(_1437320), class_Int_Onumber__ring(_1437320), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437320), c_Groups_Ozero__class_Ozero(_1437320)), _1437322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437320), c_Groups_Ozero__class_Ozero(_1437320)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1437320), _1437322), hAPP(c_Int_Onumber__class_Onumber__of(_1437320), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (31216 ^ _780478) ^ [_1361445, _1361447, _1361449] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1361445), hAPP(c_Set_OCollect(_1361445), hAPP(hAPP(c_COMBS(_1361445, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361445), c_fdisj), _1361447)), _1361449))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361445), hAPP(c_Set_OCollect(_1361445), _1361447))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361445), hAPP(c_Set_OCollect(_1361445), _1361449)))], (46064 ^ _780478) ^ [_1706428, _1706430] : [-(hAPP(c_List_Ofilter(_1706428, _1706430), c_List_Olist_ONil(_1706428)) = c_List_Olist_ONil(_1706428))], (13466 ^ _780478) ^ [_1020499, _1020501, _1020503] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1020499), _1020501)), -(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(_1020499), _1020503)), hAPP(c_Finite__Set_Ocard(_1020499), _1020501))), hAPP(c_Finite__Set_Ocard(_1020499), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020499, tc_HOL_Obool)), _1020503), _1020501)))))], (30019 ^ _780478) ^ [_1337432, _1337434, _1337436] : [-(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), _1337432), _1337434)), _1337436)), _1337434) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1337436), _1337434))], (29558 ^ _780478) ^ [_1329385, _1329387] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329385)), 29561 ^ _780478 : [(29564 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329387, _1329385)), _1329385)))], (29562 ^ _780478) ^ [] : [-(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, _1329387, _1329385))))]]], (36932 ^ _780478) ^ [_1482976, _1482978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1482976), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1482978), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1482976, _1482978) = 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), _1482976), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1482978)))))], (40857 ^ _780478) ^ [_1580554, _1580556, _1580558, _1580560] : [-(hAPP(c_Relation_Oconverse(_1580554, _1580554), hAPP(hAPP(c_Relation_Oinv__image(_1580556, _1580554), _1580558), _1580560)) = hAPP(hAPP(c_Relation_Oinv__image(_1580556, _1580554), hAPP(c_Relation_Oconverse(_1580556, _1580556), _1580558)), _1580560))], (48545 ^ _780478) ^ [_1760027, _1760029, _1760031, _1760033] : [-(hAPP(hAPP(c_List_Odrop(_1760027), _1760029), c_List_Oreplicate(_1760027, _1760031, _1760033)) = c_List_Oreplicate(_1760027, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1760031), _1760029), _1760033))], (45303 ^ _780478) ^ [_1688615, _1688617, _1688619, _1688621] : [hBOOL(hAPP(c_List_Olistsp(_1688615, _1688617), _1688619)), hBOOL(hAPP(c_List_Olistsp(_1688615, _1688621), _1688619)), -(hBOOL(hAPP(c_List_Olistsp(_1688615, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1688615, tc_HOL_Obool)), _1688617), _1688621)), _1688619)))], (21556 ^ _780478) ^ [_1180820, _1180822, _1180824, _1180826] : [class_Rings_Olinordered__semiring(_1180820), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180820), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180820), _1180822), _1180824)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180820), _1180822), _1180826))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180820), c_Groups_Ozero__class_Ozero(_1180820)), _1180822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180820), _1180824), _1180826)))], (45341 ^ _780478) ^ [_1689377, _1689379, _1689381, _1689383] : [-(hBOOL(hAPP(c_List_Olistsp(_1689377, _1689379), hAPP(hAPP(c_List_Oappend(_1689377), _1689381), _1689383)))), hBOOL(hAPP(c_List_Olistsp(_1689377, _1689379), _1689381)), hBOOL(hAPP(c_List_Olistsp(_1689377, _1689379), _1689383))], (31326 ^ _780478) ^ [_1364566, _1364568, _1364570, _1364572, _1364574, _1364576] : [-(hAPP(c_Set_Oimage(_1364566, _1364568, hAPP(hAPP(c_COMBS(_1364566, _1364568, _1364568), hAPP(hAPP(c_COMBS(_1364566, _1364568, tc_fun(_1364568, _1364568)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1364568, tc_fun(_1364568, _1364568)), _1364566), c_If(_1364568)), _1364570)), _1364572)), _1364574)), _1364576) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1364568, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1364566, _1364568, _1364572), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364566, tc_HOL_Obool)), _1364576), hAPP(c_Set_OCollect(_1364566), _1364570)))), hAPP(c_Set_Oimage(_1364566, _1364568, _1364574), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1364566, tc_HOL_Obool)), _1364576), hAPP(c_Set_OCollect(_1364566), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1364566), c_fNot), _1364570))))))], (23425 ^ _780478) ^ [_1216027] : [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)), _1216027)), _1216027) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36758 ^ _780478) ^ [_1479663, _1479665, _1479667, _1479669, _1479671] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479663, _1479665), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1479667), _1479669))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1479665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1479671)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479663, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479665), _1479671)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1479667), _1479671)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479665), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1479667, _1479671))), _1479669)))))], (14889 ^ _780478) ^ [_1047848, _1047850, _1047852, _1047854] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047848), _1047850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047852), _1047850)), _1047854)) = 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), _1047848), _1047852)), _1047850)), _1047854))], (35665 ^ _780478) ^ [_1454636, _1454638, _1454640, _1454642] : [_1454640 = _1454642, -(hAPP(hAPP(c_COMBC(_1454636, tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_fun(_1454638, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454638, tc_fun(tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_fun(_1454638, tc_HOL_Obool)), _1454636), c_COMBC(_1454638, tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454638, tc_prod(_1454636, _1454638)), tc_fun(_1454638, tc_fun(tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_HOL_Obool)), _1454636), hAPP(c_COMBB(tc_prod(_1454636, _1454638), tc_fun(tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_HOL_Obool), _1454638), c_member(tc_prod(_1454636, _1454638)))), c_Product__Type_OPair(_1454636, _1454638)))), _1454640) = hAPP(hAPP(c_COMBC(_1454636, tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_fun(_1454638, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454638, tc_fun(tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_fun(_1454638, tc_HOL_Obool)), _1454636), c_COMBC(_1454638, tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454638, tc_prod(_1454636, _1454638)), tc_fun(_1454638, tc_fun(tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_HOL_Obool)), _1454636), hAPP(c_COMBB(tc_prod(_1454636, _1454638), tc_fun(tc_fun(tc_prod(_1454636, _1454638), tc_HOL_Obool), tc_HOL_Obool), _1454638), c_member(tc_prod(_1454636, _1454638)))), c_Product__Type_OPair(_1454636, _1454638)))), _1454642))], (25156 ^ _780478) ^ [_1247820, _1247822, _1247824, _1247826] : [-(c_Sum__Type_OPlus(_1247820, _1247822, _1247824, _1247826) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1247820, _1247822), tc_HOL_Obool))), _1247824 = c_Orderings_Obot__class_Obot(tc_fun(_1247820, tc_HOL_Obool)), _1247826 = c_Orderings_Obot__class_Obot(tc_fun(_1247822, tc_HOL_Obool))], (20995 ^ _780478) ^ [_1171197, _1171199] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1171197), _1171199)), 20996 ^ _780478 : [(21003 ^ _780478) ^ [] : [_1171197 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1171199 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20997 ^ _780478) ^ [] : [_1171197 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171199 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (41692 ^ _780478) ^ [_1602194, _1602196] : [-(c_List_Olenlex(_1602194, _1602196) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1602194)), tc_List_Olist(_1602194)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1602194), c_Wellfounded_Oless__than, c_List_Olex(_1602194, _1602196))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1602194), tc_List_Olist(_1602194), tc_prod(tc_Nat_Onat, tc_List_Olist(_1602194))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1602194), tc_prod(tc_Nat_Onat, tc_List_Olist(_1602194))), tc_List_Olist(_1602194)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1602194))), c_Nat_Osize__class_Osize(tc_List_Olist(_1602194)))), c_COMBI(tc_List_Olist(_1602194)))))], (9460 ^ _780478) ^ [_942658, _942660, _942662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942658, tc_HOL_Obool)), _942660), _942662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942658, tc_HOL_Obool)), _942660), _942662)))], (49405 ^ _780478) ^ [_1780139, _1780141, _1780143, _1780145] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1780139), _1780141)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1780139), _1780143)), -(_1780143 = c_Orderings_Obot__class_Obot(tc_fun(_1780139, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1780139, _1780145, _1780141, _1780143)), 49419 ^ _780478 : [(49422 ^ _780478) ^ [_1780484] : [hBOOL(hAPP(hAPP(c_member(_1780139), _1780484), _1780143)), hBOOL(hAPP(hAPP(_1780145, 49418 ^ [_1780139, _1780141, _1780143, _1780145]), _1780484))], (49420 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1780139), 49418 ^ [_1780139, _1780141, _1780143, _1780145]), _1780141)))]]], (7884 ^ _780478) ^ [_914226, _914228, _914230, _914232, _914234, _914236] : [c_Finite__Set_Ofun__left__comm__idem(_914226, _914228, _914230), hBOOL(hAPP(c_Finite__Set_Ofinite(_914226), _914232)), -(hAPP(hAPP(c_Finite__Set_Ofold(_914226, _914228, _914230), _914234), hAPP(hAPP(c_Set_Oinsert(_914226), _914236), _914232)) = hAPP(hAPP(c_Finite__Set_Ofold(_914226, _914228, _914230), hAPP(hAPP(_914230, _914236), _914234)), _914232))], (44712 ^ _780478) ^ [_1675681, _1675683, _1675685] : [-(hAPP(hAPP(c_List_Omap(_1675681, _1675683), _1675685), c_List_Olist_ONil(_1675681)) = c_List_Olist_ONil(_1675683))], (34209 ^ _780478) ^ [_1425757, _1425759] : [class_Int_Onumber__ring(_1425757), class_Rings_Olinordered__idom(_1425757), 34216 ^ _780478 : [(34223 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425759), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425757), hAPP(c_Int_Onumber__class_Onumber__of(_1425757), _1425759)), c_Groups_Oone__class_Oone(_1425757))))], (34217 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1425757), hAPP(c_Int_Onumber__class_Onumber__of(_1425757), _1425759)), c_Groups_Oone__class_Oone(_1425757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425759), c_Int_OBit1(c_Int_OPls))))]]], (10555 ^ _780478) ^ [_964562, _964564, _964566] : [class_Lattices_Oboolean__algebra(_964562), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964562), _964564), _964566)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_964562), hAPP(c_Groups_Ouminus__class_Ouminus(_964562), _964566)), hAPP(c_Groups_Ouminus__class_Ouminus(_964562), _964564))))], (25892 ^ _780478) ^ [_1260448, _1260450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260450)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1260448)), hAPP(c_Int_Onat, _1260450)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1260448), _1260450)))], (14585 ^ _780478) ^ [_1041171, _1041173, _1041175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041171), _1041173)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041173), _1041175)), _1041171) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041173), _1041171)), _1041175))], (27120 ^ _780478) ^ [_1283015, _1283017, _1283019] : [class_Groups_Ocomm__monoid__add(_1283015), class_Groups_Ocomm__monoid__mult(_1283015), c_Nat__Transfer_Onat__set(_1283017), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1283015), _1283019), _1283017) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1283015), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1283015, tc_Nat_Onat), _1283019), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1283017)))], (50044 ^ _780478) ^ [_1792004, _1792006, _1792008, _1792010, _1792012] : [hBOOL(hAPP(hAPP(c_member(_1792004), _1792006), hAPP(c_Set_Oimage(_1792008, _1792004, _1792010), _1792012))), -(hAPP(_1792010, hAPP(c_Hilbert__Choice_Oinv__into(_1792008, _1792004, _1792012, _1792010), _1792006)) = _1792006)], (8214 ^ _780478) ^ [_920997, _920999, _921001, _921003] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_920997), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920997), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920997), _920999), _921001)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920997), _921003), _921001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920997), _920999), _921003)))], (16416 ^ _780478) ^ [_1079832, _1079834, _1079836] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079832, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1079832, tc_HOL_Obool)), _1079834), _1079836)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079832, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079832, tc_HOL_Obool)), _1079834)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079832, tc_HOL_Obool)), _1079836)))], (37477 ^ _780478) ^ [_1494957] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1494957) = _1494957)], (50640 ^ _780478) ^ [_1804914, _1804916, _1804918, _1804920] : [c_Fun_Obij__betw(_1804914, _1804916, _1804918, c_Orderings_Otop__class_Otop(tc_fun(_1804914, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1804916, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1804914, _1804916, _1804918), _1804920) = hAPP(c_Set_Oimage(_1804916, _1804914, c_Hilbert__Choice_Oinv__into(_1804914, _1804916, c_Orderings_Otop__class_Otop(tc_fun(_1804914, tc_HOL_Obool)), _1804918)), _1804920))], (40087 ^ _780478) ^ [_1562164, _1562166, _1562168, _1562170, _1562172, _1562174, _1562176] : [c_Hoare__Mirabelle_Ohoare__derivs(_1562164, _1562166, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1562164)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1562164), c_Hoare__Mirabelle_Opeek__and(_1562164, _1562168, _1562170)), _1562172), _1562174)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1562164), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1562164, _1562166, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1562164)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1562164), c_Hoare__Mirabelle_Opeek__and(_1562164, _1562168, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1562170))), _1562176), _1562174)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1562164), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1562164, _1562166, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1562164)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1562164), _1562168), c_Com_Ocom_OCond(_1562170, _1562172, _1562176)), _1562174)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1562164), tc_HOL_Obool)))))], (45381 ^ _780478) ^ [_1690284, _1690286, _1690288] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1690284)), _1690288), c_List_Olists(_1690284, _1690286))), -(hBOOL(hAPP(c_List_Olistsp(_1690284, hAPP(hAPP(c_COMBC(_1690284, tc_fun(_1690284, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690284)), _1690286)), _1690288)))], (6302 ^ _780478) ^ [_882029, _882031, _882033] : [hBOOL(hAPP(hAPP(c_member(_882029), _882031), hAPP(c_fequal, _882033))), -(_882031 = _882033)], (10959 ^ _780478) ^ [_971566, _971568, _971570, _971572] : [class_Orderings_Olinorder(_971566), 10962 ^ _780478 : [(10971 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971566), _971568), hAPP(hAPP(c_Orderings_Oord__class_Omin(_971566), _971570), _971572)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971566), _971568), _971570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971566), _971568), _971572))], (10963 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971566), _971568), hAPP(hAPP(c_Orderings_Oord__class_Omin(_971566), _971570), _971572))), 10966 ^ _780478 : [(10969 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971566), _971568), _971572)))], (10967 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971566), _971568), _971570)))]]]]], (50489 ^ _780478) ^ [_1801979, _1801981, _1801983, _1801985, _1801987] : [c_Fun_Obij__betw(_1801979, _1801981, _1801983, _1801985, _1801987), -(c_Fun_Obij__betw(_1801981, _1801979, c_Fun_Othe__inv__into(_1801979, _1801981, _1801985, _1801983), _1801987, _1801985))], (39865 ^ _780478) ^ [_1557088, _1557090, _1557092, _1557094, _1557096, _1557098, _1557100] : [c_Fun_Oinj__on(_1557088, _1557090, _1557092, hAPP(c_Set_Oimage(_1557094, _1557088, _1557096), _1557098)), c_Fun_Oinj__on(_1557094, _1557088, _1557096, _1557098), hBOOL(hAPP(hAPP(c_member(_1557090), _1557100), hAPP(c_Set_Oimage(_1557088, _1557090, _1557092), hAPP(c_Set_Oimage(_1557094, _1557088, _1557096), _1557098)))), -(hAPP(c_Fun_Othe__inv__into(_1557094, _1557090, _1557098, hAPP(c_Fun_Ocomp(_1557088, _1557090, _1557094, _1557092), _1557096)), _1557100) = hAPP(hAPP(c_Fun_Ocomp(_1557088, _1557094, _1557090, c_Fun_Othe__inv__into(_1557094, _1557088, _1557098, _1557096)), c_Fun_Othe__inv__into(_1557088, _1557090, hAPP(c_Set_Oimage(_1557094, _1557088, _1557096), _1557098), _1557092)), _1557100))], (5750 ^ _780478) ^ [_871355, _871357] : [hAPP(_871355, 5751 ^ [_871355, _871357]) = hAPP(_871357, 5751 ^ [_871355, _871357]), -(_871355 = _871357)], (32318 ^ _780478) ^ [_1391156, _1391158] : [class_Int_Onumber__ring(_1391156), -(hAPP(c_Int_Onumber__class_Onumber__of(_1391156), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1391158)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1391156), hAPP(c_Int_Onumber__class_Onumber__of(_1391156), _1391158)))], (3882 ^ _780478) ^ [_838700, _838702] : [_838702 = _838700, -(c_Lazy__Sequence_Ohit__bound(_838702) = c_Lazy__Sequence_Ohit__bound(_838700))], (44696 ^ _780478) ^ [_1675213, _1675215, _1675217, _1675219, _1675221, _1675223, _1675225, _1675227] : [-(hAPP(hAPP(c_List_Ozip(_1675213, _1675215), hAPP(hAPP(c_List_Omap(_1675217, _1675213), _1675219), _1675221)), hAPP(hAPP(c_List_Omap(_1675223, _1675215), _1675225), _1675227)) = hAPP(hAPP(c_List_Omap(tc_prod(_1675217, _1675223), tc_prod(_1675213, _1675215)), hAPP(c_Product__Type_Oprod_Oprod__case(_1675217, _1675223, tc_prod(_1675213, _1675215)), hAPP(hAPP(c_COMBC(_1675217, tc_fun(_1675223, _1675215), tc_fun(_1675223, tc_prod(_1675213, _1675215))), hAPP(hAPP(c_COMBB(tc_fun(_1675215, tc_prod(_1675213, _1675215)), tc_fun(tc_fun(_1675223, _1675215), tc_fun(_1675223, tc_prod(_1675213, _1675215))), _1675217), c_COMBB(_1675215, tc_prod(_1675213, _1675215), _1675223)), hAPP(hAPP(c_COMBB(_1675213, tc_fun(_1675215, tc_prod(_1675213, _1675215)), _1675217), c_Product__Type_OPair(_1675213, _1675215)), _1675219))), _1675225))), hAPP(hAPP(c_List_Ozip(_1675217, _1675223), _1675221), _1675227)))], (41304 ^ _780478) ^ [_1592113, _1592115, _1592117] : [c_Relation_Ototal__on(_1592113, _1592115, _1592117), 41307 ^ _780478 : [(41308 ^ _780478) ^ [_1592257] : [hBOOL(hAPP(hAPP(c_member(_1592113), _1592257), _1592115)), 41311 ^ _780478 : [(41312 ^ _780478) ^ [_1592397] : [hBOOL(hAPP(hAPP(c_member(_1592113), _1592397), _1592115)), -(_1592257 = _1592397), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592113, _1592113)), hAPP(hAPP(c_Product__Type_OPair(_1592113, _1592113), _1592257), _1592397)), _1592117))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592113, _1592113)), hAPP(hAPP(c_Product__Type_OPair(_1592113, _1592113), _1592397), _1592257)), _1592117)))]]]]], (27649 ^ _780478) ^ [_1291598, _1291600] : [class_Rings_Olinordered__idom(_1291598), 27652 ^ _780478 : [(27659 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291598), c_Groups_Ozero__class_Ozero(_1291598)), hAPP(c_Int_Oring__1__class_Oof__int(_1291598), _1291600))))], (27653 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291598), c_Groups_Ozero__class_Ozero(_1291598)), hAPP(c_Int_Oring__1__class_Oof__int(_1291598), _1291600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291600)))]]], (34161 ^ _780478) ^ [] : [-(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))))))], (46194 ^ _780478) ^ [_1710050, _1710052] : [-(c_List_Ofoldr(tc_List_Olist(_1710050), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1710050)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1710050))), c_List_Otranspose(_1710050, _1710052), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1710050))), hAPP(c_List_Ofilter(tc_List_Olist(_1710050), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1710050)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1710050), tc_List_Olist(_1710050), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1710050)))), _1710052)))], (39037 ^ _780478) ^ [_1537140, _1537142, _1537144, _1537146] : [class_Groups_Ocomm__monoid__add(_1537140), c_Fun_Oinj__on(_1537142, _1537140, _1537144, _1537146), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537142, _1537140), _1537144), _1537146) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1537140, _1537140), c_Fun_Oid(_1537140)), hAPP(c_Set_Oimage(_1537142, _1537140, _1537144), _1537146)))], (13801 ^ _780478) ^ [_1027274, _1027276, _1027278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027274), _1027276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1027274), _1027278)), 13808 ^ _780478 : [(13815 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027276), _1027278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027276), _1027274)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027278), _1027274))))], (13809 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027276), _1027274)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027278), _1027274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027276), _1027278)))]]], (50267 ^ _780478) ^ [_1797296] : [-(c_Quickcheck_Obeyond(_1797296, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (18414 ^ _780478) ^ [_1124929, _1124931, _1124933, _1124935, _1124937, _1124939] : [hBOOL(hAPP(hAPP(c_member(_1124929), _1124931), _1124933)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1124929, tc_fun(_1124935, tc_HOL_Obool)), _1124933), hAPP(hAPP(c_COMBB(tc_fun(_1124935, tc_HOL_Obool), tc_fun(_1124935, tc_HOL_Obool), _1124929), hAPP(c_Set_Oinsert(_1124935), _1124937)), _1124939)) = hAPP(hAPP(c_Set_Oinsert(_1124935), _1124937), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1124929, tc_fun(_1124935, tc_HOL_Obool)), _1124933), _1124939)))], (22612 ^ _780478) ^ [_1201549, _1201551, _1201553] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201549), _1201551)), _1201553) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201551), _1201553)))], (45823 ^ _780478) ^ [_1700433, _1700435, _1700437] : [hBOOL(hAPP(hAPP(c_member(_1700433), _1700435), hAPP(c_List_Oset(_1700433), _1700437))), -(c_List_Oremdups(_1700433, hAPP(hAPP(c_List_Olist_OCons(_1700433), _1700435), _1700437)) = c_List_Oremdups(_1700433, _1700437))], (50930 ^ _780478) ^ [_1812745, _1812747, _1812749] : [c_List_Olist__ex(tc_Nat_Onat, _1812745, c_List_Oupt(_1812747, _1812749)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1812745), _1812747, _1812749)], (2390 ^ _780478) ^ [_815484, _815486, _815488, _815490] : [-(c_Nitpick_Onat__gcd(_815490, _815486) = c_Nitpick_Onat__gcd(_815488, _815484)), _815490 = _815488, _815486 = _815484], (43401 ^ _780478) ^ [_1646613, _1646615, _1646617, _1646619, _1646621] : [-(hAPP(hAPP(c_List_Oappend(_1646613), _1646615), hAPP(hAPP(c_List_Olist_OCons(_1646613), _1646617), c_List_Olist_ONil(_1646613))) = hAPP(hAPP(c_List_Oappend(_1646613), _1646619), hAPP(hAPP(c_List_Olist_OCons(_1646613), _1646621), c_List_Olist_ONil(_1646613)))), _1646615 = _1646619, _1646617 = _1646621], (28780 ^ _780478) ^ [_1313449, _1313451, _1313453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1313449)), 28783 ^ _780478 : [(28784 ^ _780478) ^ [_1313583] : [28786 ^ _780478 : [(28792 ^ _780478) ^ [] : [-(_1313583 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28788 ^ [_1313449, _1313451, _1313453, _1313583]), 28785 ^ [_1313449, _1313451, _1313453, _1313583]))], (28790 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28788 ^ [_1313449, _1313451, _1313453, _1313583]), _1313451)))], (28787 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28785 ^ [_1313449, _1313451, _1313453, _1313583]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1313449))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1313453), _1313583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1313453), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1313583), _1313449))))]]], (27289 ^ _780478) ^ [_1285551, _1285553, _1285555, _1285557, _1285559] : [class_Fields_Ofield(_1285551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285553), _1285555)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1285553), _1285557)), 27303 ^ _780478 : [(27306 ^ _780478) ^ [] : [-(hAPP(_1285559, 27302 ^ [_1285551, _1285553, _1285555, _1285557, _1285559]) = c_Groups_Ozero__class_Ozero(_1285551))], (27304 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1285553), 27302 ^ [_1285551, _1285553, _1285555, _1285557, _1285559]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285553, tc_HOL_Obool)), _1285555), _1285557))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1285553, _1285551), _1285559), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285553, tc_HOL_Obool)), _1285555), _1285557)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285551), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1285553, _1285551), _1285559), _1285555)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1285553, _1285551), _1285559), _1285557))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1285553, _1285551), _1285559), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1285553, tc_HOL_Obool)), _1285555), _1285557))))], (14707 ^ _780478) ^ [_1043719, _1043721, _1043723] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1043719), _1043721)), -(hBOOL(hAPP(hAPP(c_member(_1043719), _1043723), _1043721))), -(hAPP(c_Finite__Set_Ocard(_1043719), hAPP(hAPP(c_Set_Oinsert(_1043719), _1043723), _1043721)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1043719), _1043721)))], (19458 ^ _780478) ^ [_1144575, _1144577] : [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), _1144575), _1144577))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144575))), -(_1144577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11377 ^ _780478) ^ [_979775, _979777, _979779, _979781] : [c_Finite__Set_Ofolding__one(_979775, _979777, _979779), hBOOL(hAPP(c_Finite__Set_Ofinite(_979775), _979781)), -(hAPP(_979779, _979781) = hAPP(c_Finite__Set_Ofold1(_979775, _979777), _979781))], (14859 ^ _780478) ^ [_1047156, _1047158, _1047160, _1047162, _1047164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047156), _1047158)), -(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), _1047156), _1047160)), _1047162)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047158), _1047160)), _1047164)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1047162), 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), _1047158), _1047156)), _1047160)), _1047164)))], (46212 ^ _780478) ^ [_1710651, _1710653] : [class_Groups_Omonoid__add(_1710651), -(hAPP(c_List_Ofoldl(_1710651, _1710651, c_Groups_Oplus__class_Oplus(_1710651), c_Groups_Ozero__class_Ozero(_1710651)), _1710653) = c_List_Ofoldr(_1710651, _1710651, c_Groups_Oplus__class_Oplus(_1710651), _1710653, c_Groups_Ozero__class_Ozero(_1710651)))], (22195 ^ _780478) ^ [_1193036, _1193038, _1193040, _1193042] : [class_Groups_Ocomm__monoid__add(_1193036), 22198 ^ _780478 : [(22205 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1193038), _1193040))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193038, _1193036), _1193042), _1193040) = c_Groups_Ozero__class_Ozero(_1193036))], (22199 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1193038), _1193040)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193038, _1193036), _1193042), _1193040) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1193036, _1193038, c_Groups_Oplus__class_Oplus(_1193036)), _1193042), c_Groups_Ozero__class_Ozero(_1193036)), _1193040))]]], (40784 ^ _780478) ^ [_1579119, _1579121] : [-(c_Random_Olog(_1579119, _1579121) = 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(_1579119, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1579121), _1579119)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1579119), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1579121), _1579119)))], (43762 ^ _780478) ^ [_1654861, _1654863, _1654865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1654861), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654863)), _1654865))), -(hAPP(hAPP(c_List_Otake(_1654863), hAPP(c_Nat_OSuc, _1654861)), _1654865) = hAPP(hAPP(c_List_Oappend(_1654863), hAPP(hAPP(c_List_Otake(_1654863), _1654861), _1654865)), hAPP(hAPP(c_List_Olist_OCons(_1654863), hAPP(hAPP(c_List_Onth(_1654863), _1654865), _1654861)), c_List_Olist_ONil(_1654863))))], (22169 ^ _780478) ^ [_1192558, _1192560] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1192558), _1192560)))), -(_1192560 = c_Orderings_Obot__class_Obot(tc_fun(_1192558, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192558), _1192560))], (41208 ^ _780478) ^ [_1589619, _1589621] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589619, _1589619), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1589621) = _1589621)], (46228 ^ _780478) ^ [_1711067, _1711069, _1711071, _1711073] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1711067, tc_Nat_Onat), _1711067), c_Product__Type_Ofst(_1711067, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1711067, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1711067, 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(_1711067, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1711067, tc_Nat_Onat))), _1711069)), hAPP(hAPP(c_List_Ozip(_1711067, tc_Nat_Onat), _1711071), c_List_Oupt(_1711073, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1711073), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711067)), _1711071)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1711067, tc_Nat_Onat), _1711067), c_Product__Type_Ofst(_1711067, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1711067, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1711067, 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(_1711067, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1711067, 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(_1711067, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1711067, tc_Nat_Onat))), _1711073))), _1711069)), hAPP(hAPP(c_List_Ozip(_1711067, tc_Nat_Onat), _1711071), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711067)), _1711071))))))], (44558 ^ _780478) ^ [_1672326, _1672328, _1672330] : [_1672326 = c_List_Olist_ONil(_1672328), -(c_List_Olast(_1672328, hAPP(hAPP(c_List_Olist_OCons(_1672328), _1672330), _1672326)) = _1672330)], (11341 ^ _780478) ^ [_978965, _978967, _978969] : [class_Rings_Ocomm__ring__1(_978965), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_978965), _978967), _978969) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_978965), _978967), hAPP(c_Groups_Ouminus__class_Ouminus(_978965), _978969)))], (42660 ^ _780478) ^ [_1630653, _1630655, _1630657, _1630659, _1630661, _1630663] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1630653, _1630655), hAPP(hAPP(c_List_Ozip(_1630653, _1630655), _1630657), _1630659)), _1630661), _1630663) = hAPP(hAPP(c_List_Ozip(_1630653, _1630655), hAPP(hAPP(c_List_Olist__update(_1630653, _1630657), _1630661), hAPP(c_Product__Type_Ofst(_1630653, _1630655), _1630663))), hAPP(hAPP(c_List_Olist__update(_1630655, _1630659), _1630661), hAPP(c_Product__Type_Osnd(_1630653, _1630655), _1630663))))], (19748 ^ _780478) ^ [_1149023, _1149025, _1149027] : [class_Rings_Olinordered__ring(_1149023), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1149023), c_Groups_Ozero__class_Ozero(_1149023)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149023), _1149025), _1149025)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149023), _1149027), _1149027)))))], (18083 ^ _780478) ^ [_1117112, _1117114, _1117116] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1117112, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1117112, tc_HOL_Obool), tc_HOL_Obool)), _1117114), _1117116)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1117112, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1117112, tc_HOL_Obool), _1117114)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1117112, tc_HOL_Obool), _1117116)))], (7052 ^ _780478) ^ [_898233, _898235, _898237, _898239] : [class_Orderings_Oorder(_898233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898233), _898235), _898237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898233), _898239), _898235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898233), _898239), _898237)))], (24104 ^ _780478) ^ [_1229095, _1229097, _1229099] : [class_Orderings_Olinorder(_1229095), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229095), _1229097), _1229099)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1229095, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1229095), _1229097), c_Orderings_Obot__class_Obot(tc_fun(_1229095, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1229095, _1229097, _1229099)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1229095, _1229097), _1229099))], (12349 ^ _780478) ^ [_998286, _998288, _998290] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_998286), _998288)), hBOOL(hAPP(hAPP(c_member(_998286), _998290), _998288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_998286), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_998286, tc_HOL_Obool)), _998288), hAPP(hAPP(c_Set_Oinsert(_998286), _998290), c_Orderings_Obot__class_Obot(tc_fun(_998286, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_998286), _998288))))], (39151 ^ _780478) ^ [_1540082, _1540084, _1540086, _1540088, _1540090, _1540092, _1540094] : [-(hAPP(c_Product__Type_Ofst(_1540082, _1540084), hAPP(c_Product__Type_Omap__pair(_1540086, _1540082, _1540088, _1540084, _1540090, _1540092), _1540094)) = hAPP(_1540090, hAPP(c_Product__Type_Ofst(_1540086, _1540088), _1540094)))], (36335 ^ _780478) ^ [_1471596, _1471598, _1471600, _1471602, _1471604, _1471606] : [_1471596 = _1471598, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471600, _1471602, _1471604), _1471606), _1471596) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471600, _1471602, _1471604), _1471606), _1471598))], (45389 ^ _780478) ^ [_1690848, _1690850, _1690852] : [-(c_List_Olistsp(_1690848, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1690848, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1690848, tc_fun(_1690848, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690848)), _1690850)), hAPP(hAPP(c_COMBC(_1690848, tc_fun(_1690848, tc_HOL_Obool), tc_HOL_Obool), c_member(_1690848)), _1690852))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1690848), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690848), tc_fun(tc_List_Olist(_1690848), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1690848))), c_List_Olists(_1690848, _1690850))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690848), tc_fun(tc_List_Olist(_1690848), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1690848))), c_List_Olists(_1690848, _1690852))))], (15037 ^ _780478) ^ [_1051088, _1051090, _1051092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051088), _1051090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051088), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051092), _1051090))))], (24543 ^ _780478) ^ [_1236456, _1236458, _1236460] : [class_Divides_Osemiring__div(_1236456), -(_1236458 = c_Groups_Ozero__class_Ozero(_1236456)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236456), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236456), _1236460), _1236458)), _1236458) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236456), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236456), _1236460), _1236458)), c_Groups_Oone__class_Oone(_1236456)))], (16302 ^ _780478) ^ [_1076820, _1076822, _1076824] : [class_Lattices_Oboolean__algebra(_1076820), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1076820), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076820), _1076822), _1076824)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076820), hAPP(c_Groups_Ouminus__class_Ouminus(_1076820), _1076822)), hAPP(c_Groups_Ouminus__class_Ouminus(_1076820), _1076824)))], (6198 ^ _780478) ^ [_879717, _879719, _879721, _879723] : [_879723 = c_Orderings_Obot__class_Obot(tc_fun(_879719, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_879717, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_879719, _879717, _879721), _879723))], (25851 ^ _780478) ^ [_1259704, _1259706] : [-(hBOOL(hAPP(_1259704, hAPP(c_Int_Onat, _1259706)))), 25855 ^ _780478 : [(25858 ^ _780478) ^ [] : [hBOOL(hAPP(_1259704, 25854 ^ [_1259704, _1259706]))], (25856 ^ _780478) ^ [] : [-(_1259706 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 25854 ^ [_1259704, _1259706]))]], 25859 ^ _780478 : [(25862 ^ _780478) ^ [] : [hBOOL(hAPP(_1259704, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25860 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1259706), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (18868 ^ _780478) ^ [_1134647, _1134649, _1134651] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1134647), _1134649)), -(hAPP(c_Finite__Set_Ocard(_1134647), hAPP(hAPP(c_Set_Oinsert(_1134647), _1134651), _1134649)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1134647), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1134647, tc_HOL_Obool)), _1134649), hAPP(hAPP(c_Set_Oinsert(_1134647), _1134651), c_Orderings_Obot__class_Obot(tc_fun(_1134647, tc_HOL_Obool)))))))], (23825 ^ _780478) ^ [_1223607, _1223609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1223607), _1223609)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1223607), hAPP(c_Nat_OSuc, _1223609)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1223609), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1223607), _1223609)))], (38498 ^ _780478) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (32064 ^ _780478) ^ [_1386070, _1386072, _1386074, _1386076, _1386078, _1386080] : [-(c_Com_Ocom_OLocal(_1386070, _1386072, _1386074) = c_Com_Ocom_OLocal(_1386076, _1386078, _1386080)), _1386070 = _1386076, _1386072 = _1386078, _1386074 = _1386080], (39715 ^ _780478) ^ [_1553775, _1553777, _1553779] : [39716 ^ _780478 : [(39717 ^ _780478) ^ [_1553829] : [hBOOL(hAPP(_1553775, _1553829))]], _1553777 = c_Hilbert__Choice_OEps(_1553779, _1553775), -(hBOOL(hAPP(_1553775, _1553777)))], (33048 ^ _780478) ^ [_1405052, _1405054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1405052), _1405054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405052)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405054))))], (14056 ^ _780478) ^ [_1031723, _1031725] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031723), _1031725), 14059 ^ _780478 : [(14062 ^ _780478) ^ [] : [-(_1031725 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (14060 ^ _780478) ^ [] : [-(_1031723 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (24445 ^ _780478) ^ [_1234702, _1234704] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234702), 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)), _1234704)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234702), _1234704)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (10025 ^ _780478) ^ [_954773, _954775, _954777, _954779, _954781] : [class_Groups_Ocomm__monoid__mult(_954773), hBOOL(hAPP(c_Finite__Set_Ofinite(_954775), _954777)), hBOOL(hAPP(hAPP(c_member(_954775), _954779), _954777)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_954775, _954773), _954781), _954777) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954773), hAPP(_954781, _954779)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_954775, _954773), _954781), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_954775, tc_HOL_Obool)), _954777), hAPP(hAPP(c_Set_Oinsert(_954775), _954779), c_Orderings_Obot__class_Obot(tc_fun(_954775, tc_HOL_Obool)))))))], (46232 ^ _780478) ^ [_1711309, _1711311] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1711309), _1711311) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1711309, _1711311)))], (25365 ^ _780478) ^ [_1251819, _1251821] : [class_Rings_Odivision__ring(_1251819), -(_1251821 = c_Groups_Ozero__class_Ozero(_1251819)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1251819), _1251821), _1251821) = c_Groups_Oone__class_Oone(_1251819))], (40357 ^ _780478) ^ [_1568873, _1568875, _1568877, _1568879, _1568881, _1568883, _1568885, _1568887, _1568889] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1568873, _1568875, _1568877, _1568879), hAPP(hAPP(c_Product__Type_Oscomp(_1568873, _1568881, _1568883, tc_prod(_1568875, _1568877)), _1568885), _1568887)), _1568889) = hAPP(hAPP(c_Product__Type_Oscomp(_1568873, _1568881, _1568883, _1568879), _1568885), hAPP(hAPP(c_COMBC(_1568881, tc_fun(_1568875, tc_fun(_1568877, _1568879)), tc_fun(_1568883, _1568879)), hAPP(hAPP(c_COMBB(tc_fun(_1568883, tc_prod(_1568875, _1568877)), tc_fun(tc_fun(_1568875, tc_fun(_1568877, _1568879)), tc_fun(_1568883, _1568879)), _1568881), c_Product__Type_Oscomp(_1568883, _1568875, _1568877, _1568879)), _1568887)), _1568889)))], (39957 ^ _780478) ^ [_1559226, _1559228, _1559230, _1559232, _1559234, _1559236] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1559226, tc_fun(_1559228, tc_HOL_Obool)), _1559230), hAPP(c_Fun_Ocomp(_1559232, tc_fun(_1559228, tc_HOL_Obool), _1559226, _1559234), _1559236)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1559232, tc_fun(_1559228, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1559226, _1559232, _1559236), _1559230)), _1559234))], (22644 ^ _780478) ^ [_1202176, _1202178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202176)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202178)))), 22647 ^ _780478 : [(22650 ^ _780478) ^ [] : [-(_1202178 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22648 ^ _780478) ^ [] : [-(_1202176 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (49744 ^ _780478) ^ [_1786553, _1786555] : [hAPP(c_Relation_Oconverse(_1786553, _1786553), _1786555) = _1786555, -(c_Relation_Osym(_1786553, _1786555))], (37881 ^ _780478) ^ [_1504671, _1504673] : [-(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), _1504671), _1504673)), 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), _1504671), _1504673))], (48431 ^ _780478) ^ [_1756979, _1756981, _1756983] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756979)), c_List_Osplice(_1756979, _1756981, _1756983)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756979)), _1756981)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1756979)), _1756983)))], (16182 ^ _780478) ^ [_1073649, _1073651, _1073653] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073649, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073649, tc_HOL_Obool)), _1073651), _1073653)), _1073651)))], (4768 ^ _780478) ^ [_853119, _853121, _853123, _853125, _853127, _853129, _853131, _853133] : [-(c_Random__Sequence_Omap(_853133, _853129, _853125, _853121) = c_Random__Sequence_Omap(_853131, _853127, _853123, _853119)), _853133 = _853131, _853129 = _853127, _853125 = _853123, _853121 = _853119], (12301 ^ _780478) ^ [_997203, _997205, _997207, _997209] : [class_Orderings_Olinorder(_997203), hBOOL(hAPP(c_Finite__Set_Ofinite(_997203), _997205)), 12311 ^ _780478 : [(12314 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997203), 12310 ^ [_997203, _997205, _997207, _997209]), _997207))], (12312 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_997203), 12310 ^ [_997203, _997205, _997207, _997209]), _997205)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997203), hAPP(hAPP(c_Finite__Set_Ofold(_997203, _997203, c_Orderings_Oord__class_Omax(_997203)), _997209), _997205)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_997203), _997207), _997209))))], (35716 ^ _780478) ^ [_1457314, _1457316, _1457318, _1457320, _1457322] : [-(hBOOL(hAPP(hAPP(c_member(_1457314), _1457316), hAPP(c_Relation_OImage(_1457318, _1457314, _1457320), _1457322)))), 35717 ^ _780478 : [(35718 ^ _780478) ^ [_1457400] : [hBOOL(hAPP(hAPP(c_member(_1457318), _1457400), _1457322)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1457318, _1457314)), hAPP(hAPP(c_Product__Type_OPair(_1457318, _1457314), _1457400), _1457316)), _1457320))]]], (44995 ^ _780478) ^ [_1682433, _1682435] : [_1682433 = _1682435, -(hAPP(c_Code__Numeral_Oof__nat, _1682433) = hAPP(c_Code__Numeral_Oof__nat, _1682435))], (11611 ^ _780478) ^ [_984078, _984080, _984082] : [class_Orderings_Olinorder(_984078), hBOOL(hAPP(c_Finite__Set_Ofinite(_984078), _984080)), -(hBOOL(hAPP(hAPP(c_member(_984078), _984082), _984080))), -(_984080 = c_Orderings_Obot__class_Obot(tc_fun(_984078, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_984078, hAPP(hAPP(c_Set_Oinsert(_984078), _984082), _984080)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_984078), _984082), c_Big__Operators_Olinorder__class_OMax(_984078, _984080)))], (21059 ^ _780478) ^ [_1172114, _1172116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1172114)), -(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), _1172114), _1172116))))], (9106 ^ _780478) ^ [_936930, _936932, _936934] : [class_Orderings_Olinorder(_936930), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936930), _936932), _936934)), 9113 ^ _780478 : [(9120 ^ _780478) ^ [] : [_936932 = _936934, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936930), _936932), _936934))], (9114 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936930), _936932), _936934))), -(_936932 = _936934)]]], (22227 ^ _780478) ^ [_1193735, _1193737] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1193735), _1193737)), -(hAPP(c_Finite__Set_Ocard(_1193735), _1193737) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1193735, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1193735), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193737))], (23407 ^ _780478) ^ [_1215719] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215719) = _1215719)], (49772 ^ _780478) ^ [_1787042, _1787044, _1787046] : [c_Equiv__Relations_Oequiv(_1787042, _1787044, _1787046), 49775 ^ _780478 : [(49780 ^ _780478) ^ [] : [-(c_Relation_Otrans(_1787042, _1787046))], (49778 ^ _780478) ^ [] : [-(c_Relation_Osym(_1787042, _1787046))], (49776 ^ _780478) ^ [] : [-(c_Relation_Orefl__on(_1787042, _1787044, _1787046))]]], (10 ^ _780478) ^ [_780601, _780603, _780605] : [-(_780605 = _780601), _780605 = _780603, _780603 = _780601], (30526 ^ _780478) ^ [_1347070, _1347072, _1347074] : [class_Groups_Oordered__ab__group__add__abs(_1347070), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347070), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1347070), hAPP(c_Groups_Oabs__class_Oabs(_1347070), _1347072)), hAPP(c_Groups_Oabs__class_Oabs(_1347070), _1347074))), hAPP(c_Groups_Oabs__class_Oabs(_1347070), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1347070), _1347072), _1347074)))))], (7575 ^ _780478) ^ [_907916, _907918, _907920, _907922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_907916, tc_HOL_Obool)), _907918), _907920)), hBOOL(hAPP(hAPP(c_member(_907916), _907922), _907918)), -(hBOOL(hAPP(hAPP(c_member(_907916), _907922), _907920)))], (1794 ^ _780478) ^ [_805767, _805769] : [-(class_Rings_Osemiring__0(_805767)), _805769 = _805767, class_Rings_Osemiring__0(_805769)], (9484 ^ _780478) ^ [_943100, _943102, _943104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943100, tc_HOL_Obool)), _943102), _943104)), 9487 ^ _780478 : [(9490 ^ _780478) ^ [] : [_943102 = _943104], (9488 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943100, tc_HOL_Obool)), _943102), _943104)))]]], (27745 ^ _780478) ^ [_1293226, _1293228, _1293230] : [class_Orderings_Oorder(_1293226), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293226, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1293226, _1293228, _1293230)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1293226), _1293230)) = c_Orderings_Obot__class_Obot(tc_fun(_1293226, tc_HOL_Obool)))], (50107 ^ _780478) ^ [_1793566, _1793568, _1793570, _1793572, _1793574] : [c_Fun_Oinj__on(_1793566, _1793568, _1793570, c_Orderings_Otop__class_Otop(tc_fun(_1793566, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1793568, _1793572, _1793566, hAPP(c_Fun_Ocomp(_1793566, _1793572, _1793568, _1793574), c_Hilbert__Choice_Oinv__into(_1793566, _1793568, c_Orderings_Otop__class_Otop(tc_fun(_1793566, tc_HOL_Obool)), _1793570))), _1793570) = _1793574)], (23239 ^ _780478) ^ [_1212983, _1212985] : [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)), _1212983)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1212983), _1212985)))], (43843 ^ _780478) ^ [_1657251, _1657253, _1657255] : [hBOOL(hAPP(c_List_Odistinct(_1657251), _1657253)), -(hBOOL(hAPP(c_List_Odistinct(_1657251), hAPP(hAPP(c_List_Odrop(_1657251), _1657255), _1657253))))], (28460 ^ _780478) ^ [_1307095, _1307097, _1307099] : [class_Orderings_Oorder(_1307095), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307095, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1307095, _1307097), _1307099)), hAPP(c_SetInterval_Oord__class_OatLeast(_1307095), _1307099)) = c_Orderings_Obot__class_Obot(tc_fun(_1307095, tc_HOL_Obool)))], (20230 ^ _780478) ^ [_1157811, _1157813, _1157815] : [class_Groups_Oordered__comm__monoid__add(_1157811), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157811), c_Groups_Ozero__class_Ozero(_1157811)), _1157813)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157811), c_Groups_Ozero__class_Ozero(_1157811)), _1157815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157811), c_Groups_Ozero__class_Ozero(_1157811)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157811), _1157813), _1157815))))], (48407 ^ _780478) ^ [_1756178, _1756180, _1756182, _1756184, _1756186, _1756188, _1756190] : [-(c_New__Random__Sequence_Opos__decr__bind(_1756178, _1756180, _1756182, _1756184, _1756186, _1756188, _1756190) = c_New__DSequence_Opos__decr__bind(_1756178, _1756180, hAPP(hAPP(hAPP(_1756182, _1756186), _1756188), _1756190), hAPP(hAPP(c_COMBC(_1756178, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1756180))), hAPP(hAPP(c_COMBC(_1756178, 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(_1756180)))), hAPP(hAPP(c_COMBC(_1756178, 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(_1756180))))), _1756184), _1756186)), _1756188)), _1756190)))], (33857 ^ _780478) ^ [_1420163, _1420165] : [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), _1420163))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1420165), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1420163))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1420165), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1420163))), 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), _1420165))), c_COMBI(tc_Int_Oint))))], (13382 ^ _780478) ^ [_1018824] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1018824, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1018824, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1018824, tc_HOL_Obool)))], (43241 ^ _780478) ^ [_1642767, _1642769, _1642771] : [-(hBOOL(hAPP(hAPP(c_member(_1642767), _1642769), hAPP(c_List_Oset(_1642767), _1642771)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642767)), c_List_Oremove1(_1642767, _1642769, _1642771)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642767)), _1642771))], (7956 ^ _780478) ^ [_915652, _915654, _915656, _915658, _915660, _915662] : [c_Finite__Set_Ofun__left__comm(_915652, _915654, _915656), hBOOL(hAPP(c_Finite__Set_Ofinite(_915652), _915658)), hBOOL(hAPP(hAPP(c_member(_915652), _915660), _915658)), -(hAPP(hAPP(c_Finite__Set_Ofold(_915652, _915654, _915656), _915662), _915658) = hAPP(hAPP(_915656, _915660), hAPP(hAPP(c_Finite__Set_Ofold(_915652, _915654, _915656), _915662), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915652, tc_HOL_Obool)), _915658), hAPP(hAPP(c_Set_Oinsert(_915652), _915660), c_Orderings_Obot__class_Obot(tc_fun(_915652, tc_HOL_Obool)))))))], (19906 ^ _780478) ^ [_1151847, _1151849, _1151851] : [class_Rings_Olinordered__ring__strict(_1151847), 19909 ^ _780478 : [(19924 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151847), c_Groups_Ozero__class_Ozero(_1151847)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151847), _1151849), _1151851)))), 19925 ^ _780478 : [(19932 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151847), _1151849), c_Groups_Ozero__class_Ozero(_1151847))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151847), _1151851), c_Groups_Ozero__class_Ozero(_1151847)))], (19926 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151847), c_Groups_Ozero__class_Ozero(_1151847)), _1151849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151847), c_Groups_Ozero__class_Ozero(_1151847)), _1151851))]]], (19910 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151847), c_Groups_Ozero__class_Ozero(_1151847)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151847), _1151849), _1151851))), 19915 ^ _780478 : [(19918 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151847), c_Groups_Ozero__class_Ozero(_1151847)), _1151851)))], (19916 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151847), c_Groups_Ozero__class_Ozero(_1151847)), _1151849)))]], 19919 ^ _780478 : [(19922 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151847), _1151851), c_Groups_Ozero__class_Ozero(_1151847))))], (19920 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151847), _1151849), c_Groups_Ozero__class_Ozero(_1151847))))]]]]], (52135 ^ _780478) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (16080 ^ _780478) ^ [_1071499, _1071501, _1071503, _1071505, _1071507] : [hBOOL(hAPP(hAPP(c_member(_1071503), hAPP(_1071505, _1071501)), _1071507)), -(hBOOL(hAPP(hAPP(c_member(_1071499), _1071501), hAPP(c_Set_Ovimage(_1071499, _1071503, _1071505), _1071507))))], (46188 ^ _780478) ^ [_1709923] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1709923)), c_List_Otranspose__rel(_1709923)), c_List_Olist_ONil(tc_List_Olist(_1709923)))), -(c_List_Otranspose(_1709923, c_List_Olist_ONil(tc_List_Olist(_1709923))) = c_List_Olist_ONil(tc_List_Olist(_1709923)))], (22439 ^ _780478) ^ [_1197781, _1197783, _1197785, _1197787] : [class_Rings_Ocomm__semiring__1(_1197781), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197781), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197781), c_Groups_Oone__class_Oone(_1197781)), c_Groups_Oone__class_Oone(_1197781))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1197781), hAPP(hAPP(c_COMBB(_1197781, _1197781, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1197781), _1197783)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1197781, _1197781), hAPP(hAPP(c_COMBB(_1197781, tc_fun(_1197781, _1197781), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1197781)), c_Nat_Osemiring__1__class_Oof__nat(_1197781))), _1197785))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1197787))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197781), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1197781), _1197787)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197781), _1197783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1197781), _1197783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197781), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1197781), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1197787), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1197785)))))], (35505 ^ _780478) ^ [_1449012] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1449012)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1449012)))], (37189 ^ _780478) ^ [_1487954, _1487956, _1487958, _1487960, _1487962] : [hAPP(c_Product__Type_Ofst(_1487954, _1487956), hAPP(hAPP(c_Product__Type_OPair(_1487954, _1487956), _1487958), _1487960)) = _1487962, -(_1487958 = _1487962)], (742 ^ _780478) ^ [_791669, _791671, _791673, _791675] : [-(c_Wellfounded_Oacyclic(_791673, _791669)), c_Wellfounded_Oacyclic(_791675, _791671), _791675 = _791673, _791671 = _791669], (38521 ^ _780478) ^ [_1521244, _1521246, _1521248, _1521250] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521244, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1521244, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521246, _1521244), _1521248)), hAPP(c_Relation_ORange(_1521246, _1521244), _1521250))), hAPP(c_Relation_ORange(_1521246, _1521244), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1521246, _1521244), tc_HOL_Obool)), _1521248), _1521250)))))], (33700 ^ _780478) ^ [_1416232, _1416234] : [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(_1416232))), 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)), _1416234)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416232)), hAPP(c_Nat_OSuc, _1416234))))], (9732 ^ _780478) ^ [_948446, _948448, _948450, _948452, _948454, _948456] : [class_Rings_Oring(_948446), 9735 ^ _780478 : [(9742 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948446), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_948446), _948448), _948454)), _948450)), _948452) = _948456, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948446), _948448), _948450)), _948452) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948446), _948454), _948450)), _948456))], (9736 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948446), _948448), _948450)), _948452) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948446), _948454), _948450)), _948456), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948446), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948446), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_948446), _948448), _948454)), _948450)), _948452) = _948456)]]], (22097 ^ _780478) ^ [_1191222, _1191224, _1191226] : [class_Rings_Olinordered__semidom(_1191222), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191222), c_Groups_Ozero__class_Ozero(_1191222)), _1191224)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191222), _1191224), c_Groups_Oone__class_Oone(_1191222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1191222), hAPP(hAPP(c_Power_Opower__class_Opower(_1191222), _1191224), hAPP(c_Nat_OSuc, _1191226))), c_Groups_Oone__class_Oone(_1191222))))], (28254 ^ _780478) ^ [_1303535, _1303537] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1303535, _1303537))))], (25691 ^ _780478) ^ [_1257142] : [-(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)), _1257142)) = hAPP(c_Int_Onat, _1257142))], (50578 ^ _780478) ^ [_1803553, _1803555, _1803557, _1803559, _1803561, _1803563, _1803565] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803553, tc_HOL_Obool)), _1803555), _1803557) = c_Orderings_Obot__class_Obot(tc_fun(_1803553, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803559, tc_HOL_Obool)), _1803561), _1803563) = c_Orderings_Obot__class_Obot(tc_fun(_1803559, tc_HOL_Obool)), c_Fun_Obij__betw(_1803553, _1803559, _1803565, _1803555, _1803561), c_Fun_Obij__betw(_1803553, _1803559, _1803565, _1803557, _1803563), -(c_Fun_Obij__betw(_1803553, _1803559, _1803565, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1803553, tc_HOL_Obool)), _1803555), _1803557), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1803559, tc_HOL_Obool)), _1803561), _1803563)))], (11769 ^ _780478) ^ [_986905, _986907] : [class_Orderings_Olinorder(_986905), hBOOL(hAPP(c_Finite__Set_Ofinite(_986905), _986907)), -(_986907 = c_Orderings_Obot__class_Obot(tc_fun(_986905, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_986905), hAPP(hAPP(c_Orderings_Oord__class_Omin(_986905), 11782 ^ [_986905, _986907]), 11783 ^ [_986905, _986907])), hAPP(hAPP(c_Set_Oinsert(_986905), 11782 ^ [_986905, _986907]), hAPP(hAPP(c_Set_Oinsert(_986905), 11783 ^ [_986905, _986907]), c_Orderings_Obot__class_Obot(tc_fun(_986905, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_986905), c_Big__Operators_Olinorder__class_OMin(_986905, _986907)), _986907)))], (26986 ^ _780478) ^ [_1280447, _1280449, _1280451] : [class_Fields_Olinordered__field(_1280447), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280447), _1280449), _1280451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280447), _1280449), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280447), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280447), _1280449), _1280451)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1280447), c_Groups_Oone__class_Oone(_1280447)), c_Groups_Oone__class_Oone(_1280447))))))], (43728 ^ _780478) ^ [_1653882, _1653884, _1653886, _1653888, _1653890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653882), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653884)), _1653886))), -(hAPP(hAPP(c_List_Olist__update(_1653884, hAPP(hAPP(c_List_Oappend(_1653884), _1653886), _1653888)), _1653882), _1653890) = hAPP(hAPP(c_List_Oappend(_1653884), hAPP(hAPP(c_List_Olist__update(_1653884, _1653886), _1653882), _1653890)), _1653888))], (48907 ^ _780478) ^ [_1767257, _1767259, _1767261] : [c_List_Olist__ex1(_1767257, _1767259, _1767261), 48911 ^ _780478 : [(48916 ^ _780478) ^ [_1767503] : [-(_1767503 = 48910 ^ [_1767257, _1767259, _1767261]), hBOOL(hAPP(hAPP(c_member(_1767257), _1767503), hAPP(c_List_Oset(_1767257), _1767261))), hBOOL(hAPP(_1767259, _1767503))], (48914 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1767259, 48910 ^ [_1767257, _1767259, _1767261])))], (48912 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767257), 48910 ^ [_1767257, _1767259, _1767261]), hAPP(c_List_Oset(_1767257), _1767261))))]]], (31705 ^ _780478) ^ [_1379073, _1379075] : [31707 ^ _780478 : [(31710 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1379075), 31706 ^ [_1379073, _1379075]))], (31708 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 31706 ^ [_1379073, _1379075]), _1379073)))]], -(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)), _1379075), _1379073))], (15105 ^ _780478) ^ [_1052450, _1052452, _1052454, _1052456] : [class_Rings_Ocomm__semiring__1(_1052450), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1052450), hAPP(hAPP(c_Power_Opower__class_Opower(_1052450), _1052452), _1052454)), hAPP(hAPP(c_Power_Opower__class_Opower(_1052450), _1052452), _1052456)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1052450), _1052452), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1052454), _1052456)))], (7565 ^ _780478) ^ [_907721, _907723, _907725, _907727, _907729] : [c_Fun_Oinj__on(_907721, _907723, _907725, _907727), hBOOL(hAPP(hAPP(c_member(_907723), _907729), hAPP(c_Set_Oimage(_907721, _907723, _907725), _907727))), -(hAPP(_907725, hAPP(c_Fun_Othe__inv__into(_907721, _907723, _907727, _907725), _907729)) = _907729)], (27346 ^ _780478) ^ [_1286612, _1286614, _1286616, _1286618, _1286620, _1286622] : [class_Groups_Oordered__ab__group__add(_1286612), hBOOL(hAPP(c_Finite__Set_Ofinite(_1286614), _1286616)), 27356 ^ _780478 : [(27359 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286612), c_Groups_Ozero__class_Ozero(_1286612)), hAPP(_1286618, 27355 ^ [_1286612, _1286614, _1286616, _1286618, _1286620, _1286622])))], (27357 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1286614), 27355 ^ [_1286612, _1286614, _1286616, _1286618, _1286620, _1286622]), _1286616)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1286614, _1286612), _1286618), _1286616) = _1286620, hBOOL(hAPP(hAPP(c_member(_1286614), _1286622), _1286616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286612), hAPP(_1286618, _1286622)), _1286620)))], (52057 ^ _780478) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (11521 ^ _780478) ^ [_982346, _982348, _982350] : [class_Orderings_Olinorder(_982346), hBOOL(hAPP(c_Finite__Set_Ofinite(_982346), _982348)), -(_982350 = c_Orderings_Obot__class_Obot(tc_fun(_982346, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_982346, tc_HOL_Obool)), _982350), _982348)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_982346), c_Big__Operators_Olinorder__class_OMax(_982346, _982350)), c_Big__Operators_Olinorder__class_OMax(_982346, _982348)) = c_Big__Operators_Olinorder__class_OMax(_982346, _982348))], (5064 ^ _780478) ^ [_857793, _857795, _857797, _857799, _857801, _857803, _857805, _857807] : [-(c_Product__Type_Ocurry(_857807, _857803, _857799, _857795) = c_Product__Type_Ocurry(_857805, _857801, _857797, _857793)), _857807 = _857805, _857803 = _857801, _857799 = _857797, _857795 = _857793], (30693 ^ _780478) ^ [_1350493, _1350495, _1350497] : [class_Rings_Oordered__ring__abs(_1350493), -(hAPP(c_Groups_Oabs__class_Oabs(_1350493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350493), _1350495), _1350497)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1350493), hAPP(c_Groups_Oabs__class_Oabs(_1350493), _1350495)), hAPP(c_Groups_Oabs__class_Oabs(_1350493), _1350497))), 30700 ^ _780478 : [(30703 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350493), _1350495), c_Groups_Ozero__class_Ozero(_1350493)))], (30701 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350493), c_Groups_Ozero__class_Ozero(_1350493)), _1350495))]], 30704 ^ _780478 : [(30707 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350493), _1350497), c_Groups_Ozero__class_Ozero(_1350493)))], (30705 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1350493), c_Groups_Ozero__class_Ozero(_1350493)), _1350497))]]], (39117 ^ _780478) ^ [_1539104, _1539106, _1539108, _1539110, _1539112] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1539104, _1539106)), _1539108), hAPP(hAPP(c_Product__Type_OSigma(_1539104, _1539106), _1539110), _1539112))), 39121 ^ _780478 : [(39127 ^ _780478) ^ [] : [-(_1539108 = hAPP(hAPP(c_Product__Type_OPair(_1539104, _1539106), 39120 ^ [_1539104, _1539106, _1539108, _1539110, _1539112]), 39123 ^ [_1539104, _1539106, _1539108, _1539110, _1539112]))], (39125 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539106), 39123 ^ [_1539104, _1539106, _1539108, _1539110, _1539112]), hAPP(_1539112, 39120 ^ [_1539104, _1539106, _1539108, _1539110, _1539112]))))], (39122 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539104), 39120 ^ [_1539104, _1539106, _1539108, _1539110, _1539112]), _1539110)))]]], (43101 ^ _780478) ^ [_1639946] : [-(hAPP(c_List_Oset(_1639946), c_List_Olist_ONil(_1639946)) = c_Orderings_Obot__class_Obot(tc_fun(_1639946, tc_HOL_Obool)))], (17719 ^ _780478) ^ [_1110388, _1110390] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1110388), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1110388, tc_HOL_Obool), _1110390)))), 17720 ^ _780478 : [(17721 ^ _780478) ^ [_1110452] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1110388, tc_HOL_Obool)), _1110452), _1110390)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110388), _1110452))]]], (3210 ^ _780478) ^ [_828192, _828194, _828196, _828198, _828200, _828202] : [-(c_Big__Operators_Olattice_OSup__fin(_828202, _828198, _828194) = c_Big__Operators_Olattice_OSup__fin(_828200, _828196, _828192)), _828202 = _828200, _828198 = _828196, _828194 = _828192], (31256 ^ _780478) ^ [_1362530, _1362532] : [-(hAPP(c_Set_OCollect(_1362530), hAPP(c_fequal, _1362532)) = hAPP(hAPP(c_Set_Oinsert(_1362530), _1362532), c_Orderings_Obot__class_Obot(tc_fun(_1362530, tc_HOL_Obool))))], (33312 ^ _780478) ^ [_1409700] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1409700), c_Int_OPls) = _1409700)], (44045 ^ _780478) ^ [_1662119, _1662121, _1662123, _1662125, _1662127] : [-(hAPP(hAPP(c_List_Ozip(_1662119, _1662121), hAPP(hAPP(c_List_Oappend(_1662119), _1662123), _1662125)), _1662127) = hAPP(hAPP(c_List_Oappend(tc_prod(_1662119, _1662121)), hAPP(hAPP(c_List_Ozip(_1662119, _1662121), _1662123), hAPP(hAPP(c_List_Otake(_1662121), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662119)), _1662123)), _1662127))), hAPP(hAPP(c_List_Ozip(_1662119, _1662121), _1662125), hAPP(hAPP(c_List_Odrop(_1662121), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662119)), _1662123)), _1662127))))], (30332 ^ _780478) ^ [_1343306, _1343308] : [class_Groups_Oordered__ab__group__add__abs(_1343306), 30335 ^ _780478 : [(30342 ^ _780478) ^ [] : [_1343308 = c_Groups_Ozero__class_Ozero(_1343306), -(hAPP(c_Groups_Oabs__class_Oabs(_1343306), _1343308) = c_Groups_Ozero__class_Ozero(_1343306))], (30336 ^ _780478) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1343306), _1343308) = c_Groups_Ozero__class_Ozero(_1343306), -(_1343308 = c_Groups_Ozero__class_Ozero(_1343306))]]], (25144 ^ _780478) ^ [_1247562, _1247564] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1247562, _1247564)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1247564)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23411 ^ _780478) ^ [_1215778, _1215780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215778), _1215780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1215778), _1215780)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52399 ^ _780478) ^ [_1834473, _1834475] : [hBOOL(hAPP(hAPP(c_fdisj, _1834473), _1834475)), -(hBOOL(_1834473)), -(hBOOL(_1834475))], (2656 ^ _780478) ^ [_819625, _819627] : [_819627 = _819625, -(c_Set_OBall(_819627) = c_Set_OBall(_819625))], (1634 ^ _780478) ^ [_803767, _803769] : [-(class_Groups_Ocomm__monoid__mult(_803767)), _803769 = _803767, class_Groups_Ocomm__monoid__mult(_803769)], (52131 ^ _780478) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (46015 ^ _780478) ^ [_1705405, _1705407, _1705409] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1705405, tc_HOL_Obool)), hAPP(c_List_Oset(_1705405), hAPP(c_List_Ofilter(_1705405, _1705407), _1705409))), hAPP(c_List_Oset(_1705405), _1705409))))], (22179 ^ _780478) ^ [_1192724] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1192724), c_Orderings_Otop__class_Otop(tc_fun(_1192724, 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(_1192724), c_Orderings_Otop__class_Otop(tc_fun(_1192724, tc_HOL_Obool))))))], (43873 ^ _780478) ^ [_1657905, _1657907, _1657909, _1657911, _1657913] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1657905, _1657907)), _1657909), hAPP(hAPP(c_List_Ozip(_1657905, _1657907), _1657911), _1657913)) = hAPP(hAPP(c_List_Ozip(_1657905, _1657907), hAPP(hAPP(c_List_Odrop(_1657905), _1657909), _1657911)), hAPP(hAPP(c_List_Odrop(_1657907), _1657909), _1657913)))], (48871 ^ _780478) ^ [_1766555, _1766557, _1766559, _1766561] : [hBOOL(hAPP(hAPP(c_List_Omember(_1766555), hAPP(hAPP(c_List_Olist_OCons(_1766555), _1766557), _1766559)), _1766561)), -(_1766557 = _1766561), -(hBOOL(hAPP(hAPP(c_List_Omember(_1766555), _1766559), _1766561)))], (48415 ^ _780478) ^ [_1756418, _1756420, _1756422, _1756424, _1756426, _1756428, _1756430] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1756418, _1756420, _1756422, _1756424), _1756426), _1756428), _1756430) = c_New__DSequence_Oneg__bind(_1756418, _1756420, hAPP(hAPP(hAPP(_1756422, _1756426), _1756428), _1756430), hAPP(hAPP(c_COMBC(_1756418, 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(_1756420)))), hAPP(hAPP(c_COMBC(_1756418, 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(_1756420))))), hAPP(hAPP(c_COMBC(_1756418, 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(_1756420)))))), _1756424), _1756426)), _1756428)), _1756430)))], (15998 ^ _780478) ^ [_1069878, _1069880] : [class_Lattices_Obounded__lattice__bot(_1069878), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069878), _1069880), c_Orderings_Obot__class_Obot(_1069878)) = c_Orderings_Obot__class_Obot(_1069878))], (44235 ^ _780478) ^ [_1665874, _1665876, _1665878] : [class_Groups_Omonoid__add(_1665874), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1665874), _1665876), hAPP(c_List_Ofoldl(_1665874, _1665874, c_Groups_Oplus__class_Oplus(_1665874), c_Groups_Ozero__class_Ozero(_1665874)), _1665878)) = hAPP(c_List_Ofoldl(_1665874, _1665874, c_Groups_Oplus__class_Oplus(_1665874), _1665876), _1665878))], (37612 ^ _780478) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (706 ^ _780478) ^ [_791123, _791125, _791127, _791129] : [-(c_Predicate_Oreflp(_791127, _791123)), c_Predicate_Oreflp(_791129, _791125), _791129 = _791127, _791125 = _791123], (39263 ^ _780478) ^ [_1542777, _1542779, _1542781] : [c_Wellfounded_OwfP(_1542777, _1542779), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1542777, tc_fun(_1542777, tc_HOL_Obool))), _1542781), _1542779)), -(c_Wellfounded_OwfP(_1542777, _1542781))], (29233 ^ _780478) ^ [_1323135] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1323135) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (41075 ^ _780478) ^ [_1586317, _1586319] : [-(c_Transitive__Closure_Ortrancl(_1586317, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586317, _1586317), tc_HOL_Obool)), _1586319), c_Relation_OId(_1586317))) = c_Transitive__Closure_Ortrancl(_1586317, _1586319))], (30520 ^ _780478) ^ [_1346917, _1346919, _1346921] : [class_Groups_Oordered__ab__group__add__abs(_1346917), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346917), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346917), hAPP(c_Groups_Oabs__class_Oabs(_1346917), _1346919)), hAPP(c_Groups_Oabs__class_Oabs(_1346917), _1346921))), hAPP(c_Groups_Oabs__class_Oabs(_1346917), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346917), _1346921), _1346919)))))], (23775 ^ _780478) ^ [_1222560, _1222562, _1222564, _1222566, _1222568] : [class_Orderings_Olinorder(_1222560), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222560, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222560, _1222562), _1222564)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222560, _1222566), _1222568)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222560, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1222560), _1222562), _1222566)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1222560), _1222564), _1222568)))], (35613 ^ _780478) ^ [_1450990, _1450992] : [class_Int_Onumber__ring(_1450990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1450992)), -(hBOOL(hAPP(hAPP(c_member(_1450990), hAPP(c_Int_Onumber__class_Onumber__of(_1450990), _1450992)), c_Nat_Osemiring__1__class_ONats(_1450990))))], (2050 ^ _780478) ^ [_810260, _810262, _810264, _810266] : [-(c_Orderings_Oord_Omax(_810266, _810262) = c_Orderings_Oord_Omax(_810264, _810260)), _810266 = _810264, _810262 = _810260], (25259 ^ _780478) ^ [_1249916, _1249918, _1249920, _1249922] : [class_Rings_Odivision__ring(_1249916), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249916), _1249918), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249916), _1249920), _1249922)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249916), _1249918), _1249920)), _1249922))], (33746 ^ _780478) ^ [_1417238, _1417240, _1417242, _1417244, _1417246] : [-(c_Nat_Onat_Onat__case(_1417238, _1417240, _1417242, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417244)), _1417246)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1417238), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417244))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417238, _1417238), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1417238, tc_fun(_1417238, _1417238)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417238, tc_fun(_1417238, _1417238)), tc_Int_Oint), c_If(_1417238)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1417238, _1417240, _1417242, _1417246))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1417238, tc_Int_Oint), _1417242), 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)), _1417246)))))], (28454 ^ _780478) ^ [_1307032, _1307034] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1307032), _1307034))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1307034, _1307032) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1307034), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1307034), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1307032)))], (23667 ^ _780478) ^ [_1220291, _1220293, _1220295, _1220297, _1220299] : [class_Groups_Ocomm__monoid__add(_1220291), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220291), _1220293), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220295), _1220297)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1220299), _1220297))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220291), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1220291, tc_Nat_Onat), _1220293), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1220297))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220295), _1220299)))], (35103 ^ _780478) ^ [_1442073, _1442075] : [-(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), _1442073)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1442075))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1442073))) = 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), _1442075)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1442073)))], (43362 ^ _780478) ^ [_1645772, _1645774, _1645776, _1645778, _1645780] : [hAPP(hAPP(c_List_Olist_OCons(_1645772), _1645774), _1645776) = hAPP(hAPP(c_List_Oappend(_1645772), _1645778), _1645780), 43367 ^ _780478 : [(43370 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1645772), _1645774), _1645776) = _1645780)], (43368 ^ _780478) ^ [] : [-(_1645778 = c_List_Olist_ONil(_1645772))]], 43372 ^ _780478 : [(43375 ^ _780478) ^ [] : [-(_1645776 = hAPP(hAPP(c_List_Oappend(_1645772), 43371 ^ [_1645772, _1645774, _1645776, _1645778, _1645780]), _1645780))], (43373 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1645772), _1645774), 43371 ^ [_1645772, _1645774, _1645776, _1645778, _1645780]) = _1645778)]]], (28436 ^ _780478) ^ [] : [-(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))))], (4244 ^ _780478) ^ [_844691, _844693, _844695, _844697] : [-(c_List_Ozip(_844697, _844693) = c_List_Ozip(_844695, _844691)), _844697 = _844695, _844693 = _844691], (14421 ^ _780478) ^ [_1037826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037826), _1037826))], (42089 ^ _780478) ^ [_1615144, _1615146, _1615148] : [c_Relation_Orefl__on(_1615144, _1615146, _1615148), -(c_Relation_Orefl__on(tc_List_Olist(_1615144), c_List_Olists(_1615144, _1615146), c_List_Olistrel(_1615144, _1615148)))], (49654 ^ _780478) ^ [_1784669, _1784671, _1784673, _1784675, _1784677, _1784679] : [-(c_Partial__Function_Ofun__lub(_1784669, _1784671, _1784673, _1784675, _1784677, _1784679) = hAPP(_1784675, hAPP(c_Set_OCollect(_1784669), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1784673, _1784669), tc_HOL_Obool), tc_HOL_Obool, _1784669), c_HOL_OEx(tc_fun(_1784673, _1784669))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1784673, _1784669), tc_HOL_Obool), tc_fun(tc_fun(_1784673, _1784669), tc_HOL_Obool), _1784669), hAPP(c_COMBS(tc_fun(_1784673, _1784669), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1784673, _1784669)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1784673, _1784669), tc_fun(tc_fun(_1784673, _1784669), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1784673, _1784669))), _1784677)))), hAPP(hAPP(c_COMBC(_1784669, tc_fun(tc_fun(_1784673, _1784669), _1784669), tc_fun(tc_fun(_1784673, _1784669), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1784669, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1784673, _1784669), _1784669), tc_fun(tc_fun(_1784673, _1784669), tc_HOL_Obool)), _1784669), c_COMBB(_1784669, tc_HOL_Obool, tc_fun(_1784673, _1784669))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1784673, _1784669), _1784673, _1784669), c_COMBI(tc_fun(_1784673, _1784669))), _1784679)))))))], (7692 ^ _780478) ^ [_910329, _910331, _910333, _910335, _910337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910329, tc_HOL_Obool)), _910331), _910333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910329, tc_HOL_Obool)), _910335), _910337)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_910329, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910329, tc_HOL_Obool)), _910331), _910337)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910329, tc_HOL_Obool)), _910333), _910335))))], (29910 ^ _780478) ^ [_1335653, _1335655, _1335657] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1335653), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335655, _1335657)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1335653), _1335655), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1335653), _1335657)))], (28154 ^ _780478) ^ [_1301452, _1301454, _1301456, _1301458, _1301460] : [class_Groups_Ocomm__monoid__add(_1301452), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1301454), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301456), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1301452), _1301458), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1301454, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301456), _1301460))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1301452), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1301452), _1301458), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1301454, _1301456))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1301452), _1301458), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301456), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1301456), _1301460)))))], (25721 ^ _780478) ^ [_1257689, _1257691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257689)), 25724 ^ _780478 : [(25731 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257689), _1257691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1257689)), hAPP(c_Int_Onat, _1257691))))], (25725 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1257689)), hAPP(c_Int_Onat, _1257691))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257689), _1257691)))]]], (17645 ^ _780478) ^ [_1108875, _1108877, _1108879] : [class_Lattices_Olattice(_1108875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108875), _1108877)), hBOOL(hAPP(hAPP(c_member(_1108875), _1108879), _1108877)), 17656 ^ _780478 : [(17663 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108875, tc_HOL_Obool)), _1108877), hAPP(hAPP(c_Set_Oinsert(_1108875), _1108879), c_Orderings_Obot__class_Obot(tc_fun(_1108875, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1108875, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1108875, _1108877) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1108875), _1108879), c_Big__Operators_Olattice__class_OInf__fin(_1108875, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108875, tc_HOL_Obool)), _1108877), hAPP(hAPP(c_Set_Oinsert(_1108875), _1108879), c_Orderings_Obot__class_Obot(tc_fun(_1108875, tc_HOL_Obool)))))))], (17657 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1108875, tc_HOL_Obool)), _1108877), hAPP(hAPP(c_Set_Oinsert(_1108875), _1108879), c_Orderings_Obot__class_Obot(tc_fun(_1108875, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1108875, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1108875, _1108877) = _1108879)]]], (46322 ^ _780478) ^ [_1712845, _1712847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712845)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712847))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712845), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712847)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712845)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712845)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712847))))], (52249 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (36652 ^ _780478) ^ [_1477455, _1477457] : [-(c_Divides_Odivmod__nat(_1477455, _1477457) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1477455), _1477457)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1477455, _1477457)))], (36357 ^ _780478) ^ [_1472246, _1472248, _1472250] : [-(c_HOL_OThe(tc_prod(_1472246, _1472248), _1472250) = c_HOL_OThe(tc_prod(_1472246, _1472248), hAPP(c_Product__Type_Oprod_Oprod__case(_1472246, _1472248, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1472248, tc_prod(_1472246, _1472248)), tc_fun(_1472248, tc_HOL_Obool), _1472246), hAPP(c_COMBB(tc_prod(_1472246, _1472248), tc_HOL_Obool, _1472248), _1472250)), c_Product__Type_OPair(_1472246, _1472248)))))], (40384 ^ _780478) ^ [_1569442, _1569444, _1569446, _1569448] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569442, _1569442)), hAPP(hAPP(c_Product__Type_OPair(_1569442, _1569442), _1569444), _1569446)), _1569448)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569442, _1569442)), hAPP(hAPP(c_Product__Type_OPair(_1569442, _1569442), _1569444), _1569446)), c_Transitive__Closure_Otrancl(_1569442, _1569448))))], (2626 ^ _780478) ^ [_819170, _819172, _819174, _819176] : [-(c_Nitpick_Onorm__frac(_819176, _819172) = c_Nitpick_Onorm__frac(_819174, _819170)), _819176 = _819174, _819172 = _819170], (23257 ^ _780478) ^ [_1213340, _1213342] : [_1213340 = _1213342, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213340) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213342))], (40654 ^ _780478) ^ [_1576325, _1576327, _1576329, _1576331] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576325, _1576325)), hAPP(hAPP(c_Product__Type_OPair(_1576325, _1576325), _1576327), _1576329)), c_Transitive__Closure_Ortrancl(_1576325, _1576331))), -(_1576327 = _1576329), 40661 ^ _780478 : [(40664 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576325, _1576325)), hAPP(hAPP(c_Product__Type_OPair(_1576325, _1576325), _1576327), _1576329)), c_Transitive__Closure_Otrancl(_1576325, _1576331))))], (40662 ^ _780478) ^ [] : [_1576327 = _1576329]]], (23329 ^ _780478) ^ [_1214495, _1214497, _1214499, _1214501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214495), _1214497)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214499), _1214501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214495), _1214499)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214497), _1214501))))], (31856 ^ _780478) ^ [_1382110, _1382112] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1382110), _1382112)), 31862 ^ _780478 : [(31865 ^ _780478) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31863 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382110), 31861 ^ [_1382110, _1382112]), _1382112)))]], -(hAPP(c_Finite__Set_Ocard(_1382110), _1382112) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30562 ^ _780478) ^ [_1347812, _1347814, _1347816] : [class_Groups_Oordered__ab__group__add__abs(_1347812), 30565 ^ _780478 : [(30574 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347812), hAPP(c_Groups_Oabs__class_Oabs(_1347812), _1347814)), _1347816))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347812), _1347814), _1347816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347812), hAPP(c_Groups_Ouminus__class_Ouminus(_1347812), _1347814)), _1347816))], (30566 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347812), hAPP(c_Groups_Oabs__class_Oabs(_1347812), _1347814)), _1347816)), 30569 ^ _780478 : [(30572 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347812), hAPP(c_Groups_Ouminus__class_Ouminus(_1347812), _1347814)), _1347816)))], (30570 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347812), _1347814), _1347816)))]]]]], (16973 ^ _780478) ^ [_1092560, _1092562, _1092564] : [class_Lattices_Olattice(_1092560), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092560), _1092562)), -(_1092562 = c_Orderings_Obot__class_Obot(tc_fun(_1092560, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092560), _1092564)), -(_1092564 = c_Orderings_Obot__class_Obot(tc_fun(_1092560, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1092560, tc_HOL_Obool)), _1092562), _1092564) = c_Orderings_Obot__class_Obot(tc_fun(_1092560, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1092560, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1092560, tc_HOL_Obool)), _1092562), _1092564)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1092560), c_Big__Operators_Olattice__class_OSup__fin(_1092560, _1092562)), c_Big__Operators_Olattice__class_OSup__fin(_1092560, _1092564)))], (44947 ^ _780478) ^ [_1681300, _1681302, _1681304, _1681306] : [class_Rings_Osemiring__1(_1681300), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1681300), hAPP(hAPP(c_List_Omap(_1681302, _1681300), hAPP(c_COMBK(_1681300, _1681302), _1681304)), _1681306)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1681300), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1681300), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681302)), _1681306))), _1681304))], (21778 ^ _780478) ^ [_1184796, _1184798, _1184800] : [hBOOL(hAPP(_1184796, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1184798), _1184800))), 21781 ^ _780478 : [(21788 ^ _780478) ^ [_1184987] : [_1184798 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1184800), _1184987), -(hBOOL(hAPP(_1184796, _1184987)))], (21782 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184798), _1184800)), -(hBOOL(hAPP(_1184796, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (51605 ^ _780478) ^ [_1824970, _1824972, _1824974, _1824976] : [class_Divides_Osemiring__div(_1824970), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824970), _1824972), _1824974)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824970), _1824972), _1824976)), 51616 ^ _780478 : [(51623 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824970), _1824974), _1824976)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824970), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824970), _1824974), _1824972)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824970), _1824976), _1824972))))], (51617 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824970), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824970), _1824974), _1824972)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824970), _1824976), _1824972))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824970), _1824974), _1824976)))]]], (41405 ^ _780478) ^ [_1594794, _1594796, _1594798, _1594800, _1594802] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594794, _1594794)), hAPP(hAPP(c_Product__Type_OPair(_1594794, _1594794), _1594796), _1594798)), c_Transitive__Closure_Ortrancl(_1594794, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1594794, _1594794), tc_HOL_Obool)), _1594800), _1594802)))), 41411 ^ _780478 : [(41417 ^ _780478) ^ [] : [41410 ^ [_1594794, _1594796, _1594798, _1594800, _1594802] = 41413 ^ [_1594794, _1594796, _1594798, _1594800, _1594802]], (41415 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594794, _1594794)), hAPP(hAPP(c_Product__Type_OPair(_1594794, _1594794), 41410 ^ [_1594794, _1594796, _1594798, _1594800, _1594802]), 41413 ^ [_1594794, _1594796, _1594798, _1594800, _1594802])), _1594802)))], (41412 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594794, _1594794)), hAPP(hAPP(c_Product__Type_OPair(_1594794, _1594794), _1594796), 41410 ^ [_1594794, _1594796, _1594798, _1594800, _1594802])), c_Transitive__Closure_Ortrancl(_1594794, _1594800))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594794, _1594794)), hAPP(hAPP(c_Product__Type_OPair(_1594794, _1594794), _1594796), _1594798)), c_Transitive__Closure_Ortrancl(_1594794, _1594800))))], (40009 ^ _780478) ^ [_1560528, _1560530, _1560532, _1560534, _1560536, _1560538, _1560540, _1560542] : [c_Finite__Set_Ofolding(_1560528, _1560530, _1560532, _1560534), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560528), _1560536)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560528), _1560538)), -(hAPP(c_Fun_Ocomp(_1560530, _1560530, _1560540, hAPP(_1560534, _1560538)), hAPP(c_Fun_Ocomp(_1560530, _1560530, _1560540, hAPP(_1560534, _1560536)), _1560542)) = hAPP(c_Fun_Ocomp(_1560530, _1560530, _1560540, hAPP(_1560534, _1560536)), hAPP(c_Fun_Ocomp(_1560530, _1560530, _1560540, hAPP(_1560534, _1560538)), _1560542)))], (43089 ^ _780478) ^ [_1639746, _1639748] : [c_Orderings_Obot__class_Obot(tc_fun(_1639746, tc_HOL_Obool)) = hAPP(c_List_Oset(_1639746), _1639748), -(_1639748 = c_List_Olist_ONil(_1639746))], (51967 ^ _780478) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (2126 ^ _780478) ^ [_811442, _811444, _811446, _811448, _811450, _811452] : [-(c_Power_Opower_Opower(_811452, _811448, _811444) = c_Power_Opower_Opower(_811450, _811446, _811442)), _811452 = _811450, _811448 = _811446, _811444 = _811442], (14165 ^ _780478) ^ [_1033618, _1033620, _1033622] : [class_Groups_Ocomm__monoid__mult(_1033618), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1033620, _1033618), hAPP(c_COMBK(_1033618, _1033620), c_Groups_Oone__class_Oone(_1033618))), _1033622) = c_Groups_Oone__class_Oone(_1033618))], (21115 ^ _780478) ^ [_1172963, _1172965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172965)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1172965), _1172963)), _1172965)))], (18522 ^ _780478) ^ [_1127577, _1127579, _1127581, _1127583, _1127585] : [-(_1127577 = c_Orderings_Obot__class_Obot(tc_fun(_1127579, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127581, tc_HOL_Obool)), _1127583), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127579, tc_fun(_1127581, tc_HOL_Obool)), _1127577), _1127585)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127579, tc_fun(_1127581, tc_HOL_Obool)), _1127577), hAPP(hAPP(c_COMBB(tc_fun(_1127581, tc_HOL_Obool), tc_fun(_1127581, tc_HOL_Obool), _1127579), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127581, tc_HOL_Obool)), _1127583)), _1127585)))], (35577 ^ _780478) ^ [_1450381, _1450383] : [_1450381 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1450381, _1450383) = _1450383)], (9820 ^ _780478) ^ [_950336, _950338, _950340, _950342] : [class_Rings_Ocomm__semiring__1(_950336), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950336), _950338), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950336), _950340), _950342)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950336), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950336), _950338), _950340)), _950342))], (51211 ^ _780478) ^ [_1818276, _1818278, _1818280, _1818282] : [class_Rings_Ocomm__semiring__1(_1818276), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818276), _1818278), _1818280)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818276), _1818278), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1818276), _1818280), _1818282))))], (22417 ^ _780478) ^ [_1197381, _1197383] : [class_Orderings_Oorder(_1197381), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1197381, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1197381), _1197383), c_Orderings_Obot__class_Obot(tc_fun(_1197381, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1197381), _1197383)) = hAPP(hAPP(c_Set_Oinsert(_1197381), _1197383), c_Orderings_Obot__class_Obot(tc_fun(_1197381, tc_HOL_Obool))))], (40353 ^ _780478) ^ [_1568776, _1568778, _1568780, _1568782, _1568784] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1568776, _1568778, _1568776, _1568780), hAPP(c_Product__Type_OPair(_1568778, _1568776), _1568782)), _1568784) = hAPP(_1568784, _1568782))], (6694 ^ _780478) ^ [_890849, _890851] : [c_Com_Ocom_OWhile(_890849, _890851) = c_Com_Ocom_OSKIP], (17351 ^ _780478) ^ [_1100966, _1100968, _1100970, _1100972] : [17353 ^ _780478 : [(17356 ^ _780478) ^ [] : [hAPP(_1100972, 17352 ^ [_1100966, _1100968, _1100970, _1100972]) = c_Orderings_Obot__class_Obot(tc_fun(_1100968, tc_HOL_Obool))], (17354 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1100966), 17352 ^ [_1100966, _1100968, _1100970, _1100972]), _1100970)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1100966, tc_fun(_1100968, tc_HOL_Obool)), _1100970), _1100972) = c_Orderings_Obot__class_Obot(tc_fun(_1100968, tc_HOL_Obool)))], (50653 ^ _780478) ^ [_1805190, _1805192, _1805194, _1805196, _1805198, _1805200] : [c_Fun_Oinj__on(_1805190, _1805192, _1805194, _1805196), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1805192, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1805190, _1805192, _1805194), _1805196)), _1805198)), c_Fun_Oinj__on(_1805192, _1805190, _1805200, _1805198), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1805190, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1805192, _1805190, _1805200), _1805198)), _1805196)), -(c_Fun_Obij__betw(_1805190, _1805192, 50668 ^ [_1805190, _1805192, _1805194, _1805196, _1805198, _1805200], _1805196, _1805198))], (21910 ^ _780478) ^ [_1187258, _1187260, _1187262] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1187258), _1187260)), 21913 ^ _780478 : [(21933 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187258, tc_Nat_Onat), _1187262), _1187260) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 21934 ^ _780478 : [(21935 ^ _780478) ^ [_1187739] : [hBOOL(hAPP(hAPP(c_member(_1187258), _1187739), _1187260)), hAPP(_1187262, _1187739) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21943 ^ _780478 : [(21948 ^ _780478) ^ [] : [hAPP(_1187262, 21942 ^ [_1187258, _1187260, _1187262, _1187739]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21946 ^ _780478) ^ [] : [_1187739 = 21942 ^ [_1187258, _1187260, _1187262, _1187739]], (21944 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1187258), 21942 ^ [_1187258, _1187260, _1187262, _1187739]), _1187260)))]]]]], (21914 ^ _780478) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187258, tc_Nat_Onat), _1187262), _1187260) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21918 ^ _780478 : [(21923 ^ _780478) ^ [_1187578] : [hBOOL(hAPP(hAPP(c_member(_1187258), _1187578), _1187260)), -(21917 ^ [_1187258, _1187260, _1187262] = _1187578), -(hAPP(_1187262, _1187578) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21921 ^ _780478) ^ [] : [-(hAPP(_1187262, 21917 ^ [_1187258, _1187260, _1187262]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21919 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1187258), 21917 ^ [_1187258, _1187260, _1187262]), _1187260)))]]]]], (6636 ^ _780478) ^ [_889543, _889545, _889547, _889549, _889551, _889553, _889555, _889557] : [c_Finite__Set_Ofolding__image__simple(_889543, _889545, _889547, _889549, _889551, _889553), hBOOL(hAPP(c_Finite__Set_Ofinite(_889545), _889555)), hBOOL(hAPP(hAPP(c_member(_889545), _889557), _889555)), -(hAPP(_889553, _889555) = hAPP(hAPP(_889547, hAPP(_889551, _889557)), hAPP(_889553, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889545, tc_HOL_Obool)), _889555), hAPP(hAPP(c_Set_Oinsert(_889545), _889557), c_Orderings_Obot__class_Obot(tc_fun(_889545, tc_HOL_Obool)))))))], (34671 ^ _780478) ^ [_1434117, _1434119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434117), _1434119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1434117)), c_Int_OBit1(_1434119))))], (44241 ^ _780478) ^ [_1666011, _1666013, _1666015, _1666017, _1666019, _1666021] : [-(hAPP(c_List_Ofoldl(_1666011, _1666013, _1666015, _1666017), hAPP(hAPP(c_List_Olist_OCons(_1666013), _1666019), _1666021)) = hAPP(c_List_Ofoldl(_1666011, _1666013, _1666015, hAPP(hAPP(_1666015, _1666017), _1666019)), _1666021))], (41842 ^ _780478) ^ [_1607498, _1607500, _1607502, _1607504] : [-(c_List_Olist_Olist__size(_1607498, _1607500, hAPP(hAPP(c_List_Olist_OCons(_1607498), _1607502), _1607504)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1607500, _1607502)), c_List_Olist_Olist__size(_1607498, _1607500, _1607504))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6706 ^ _780478) ^ [_891141, _891143, _891145, _891147, _891149, _891151] : [hBOOL(hAPP(hAPP(c_member(_891141), _891143), _891145)), -(hAPP(c_Set_Oimage(_891141, _891147, c_Fun_Ofun__upd(_891141, _891147, _891149, _891143, _891151)), _891145) = hAPP(hAPP(c_Set_Oinsert(_891147), _891151), hAPP(c_Set_Oimage(_891141, _891147, _891149), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891141, tc_HOL_Obool)), _891145), hAPP(hAPP(c_Set_Oinsert(_891141), _891143), c_Orderings_Obot__class_Obot(tc_fun(_891141, tc_HOL_Obool)))))))], (2226 ^ _780478) ^ [_813018, _813020] : [_813020 = _813018, -(c_SetInterval_Oord__class_OatLeast(_813020) = c_SetInterval_Oord__class_OatLeast(_813018))], (30268 ^ _780478) ^ [_1342078, _1342080, _1342082] : [class_Groups_Oordered__ab__group__add__abs(_1342078), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342078), hAPP(c_Groups_Oabs__class_Oabs(_1342078), _1342080)), _1342082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1342078), _1342080), _1342082)))], (22965 ^ _780478) ^ [_1207894, _1207896] : [class_Rings_Oring__1(_1207894), hBOOL(hAPP(hAPP(c_member(_1207894), _1207896), c_Int_Oring__1__class_OInts(_1207894))), -(hBOOL(hAPP(hAPP(c_member(_1207894), hAPP(c_Groups_Ouminus__class_Ouminus(_1207894), _1207896)), c_Int_Oring__1__class_OInts(_1207894))))], (43622 ^ _780478) ^ [_1651268, _1651270, _1651272] : [_1651268 = c_List_Olist_ONil(_1651270), -(c_List_Obutlast(_1651270, hAPP(hAPP(c_List_Oappend(_1651270), _1651272), _1651268)) = c_List_Obutlast(_1651270, _1651272))], (41938 ^ _780478) ^ [_1610536, _1610538, _1610540] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1610536, _1610536)), hAPP(hAPP(c_Product__Type_OPair(_1610536, _1610536), 41939 ^ [_1610536, _1610538, _1610540]), 41939 ^ [_1610536, _1610538, _1610540])), _1610538))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610536), tc_List_Olist(_1610536))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610536), tc_List_Olist(_1610536)), _1610540), _1610540)), c_List_Olexord(_1610536, _1610538)))], (40312 ^ _780478) ^ [_1567843, _1567845, _1567847, _1567849, _1567851, _1567853, _1567855] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1567843, _1567845, _1567847, _1567849), _1567851), _1567853), _1567855) = hAPP(hAPP(_1567853, hAPP(c_Product__Type_Ofst(_1567845, _1567847), hAPP(_1567851, _1567855))), hAPP(c_Product__Type_Osnd(_1567845, _1567847), hAPP(_1567851, _1567855))))], (43133 ^ _780478) ^ [_1640497, _1640499, _1640501, _1640503] : [-(_1640497 = _1640499), 43136 ^ _780478 : [(43143 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1640501), _1640497), hAPP(c_List_Oset(_1640501), _1640503))), -(hBOOL(hAPP(hAPP(c_member(_1640501), _1640497), hAPP(c_List_Oset(_1640501), c_List_Oremove1(_1640501, _1640499, _1640503)))))], (43137 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1640501), _1640497), hAPP(c_List_Oset(_1640501), c_List_Oremove1(_1640501, _1640499, _1640503)))), -(hBOOL(hAPP(hAPP(c_member(_1640501), _1640497), hAPP(c_List_Oset(_1640501), _1640503))))]]], (50131 ^ _780478) ^ [_1794148, _1794150, _1794152] : [hAPP(c_Set_Oimage(_1794148, _1794150, _1794152), c_Orderings_Otop__class_Otop(tc_fun(_1794148, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1794150, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1794150, _1794148, c_Hilbert__Choice_Oinv__into(_1794148, _1794150, c_Orderings_Otop__class_Otop(tc_fun(_1794148, tc_HOL_Obool)), _1794152), c_Orderings_Otop__class_Otop(tc_fun(_1794150, tc_HOL_Obool))))], (47352 ^ _780478) ^ [_1733354, _1733356, _1733358] : [c_List_OdropWhile(_1733354, _1733356, _1733358) = c_List_Olist_ONil(_1733354), 47355 ^ _780478 : [(47356 ^ _780478) ^ [_1733445] : [hBOOL(hAPP(hAPP(c_member(_1733354), _1733445), hAPP(c_List_Oset(_1733354), _1733358))), -(hBOOL(hAPP(_1733356, _1733445)))]]], (1004 ^ _780478) ^ [_795640, _795642, _795644, _795646, _795648, _795650] : [-(c_List_Olist__all(_795648, _795644, _795640)), c_List_Olist__all(_795650, _795646, _795642), _795650 = _795648, _795646 = _795644, _795642 = _795640], (18167 ^ _780478) ^ [_1119447, _1119449, _1119451, _1119453, _1119455, _1119457] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119447, tc_fun(_1119449, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1119451, _1119447, _1119453), _1119455)), _1119457) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119451, tc_fun(_1119449, tc_HOL_Obool)), _1119455), hAPP(hAPP(c_COMBB(_1119447, tc_fun(_1119449, tc_HOL_Obool), _1119451), _1119457), _1119453)))], (42077 ^ _780478) ^ [_1614910, _1614912, _1614914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1614910, tc_HOL_Obool)), _1614912), _1614914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1614910), tc_HOL_Obool)), c_List_Olists(_1614910, _1614912)), c_List_Olists(_1614910, _1614914))))], (15946 ^ _780478) ^ [_1068927, _1068929, _1068931, _1068933, _1068935] : [class_Lattices_Osemilattice__inf(_1068927), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068927), _1068929), _1068931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068927), _1068933), _1068935)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068927), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068927), _1068929), _1068933)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068927), _1068931), _1068935))))], (52149 ^ _780478) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (16891 ^ _780478) ^ [_1090674, _1090676, _1090678, _1090680, _1090682] : [c_Fun_Oinj__on(_1090674, _1090676, _1090678, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1090674, tc_HOL_Obool)), _1090680), _1090682)), 16894 ^ _780478 : [(16899 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1090676, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1090674, _1090676, _1090678), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090674, tc_HOL_Obool)), _1090680), _1090682))), hAPP(c_Set_Oimage(_1090674, _1090676, _1090678), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090674, tc_HOL_Obool)), _1090682), _1090680))) = c_Orderings_Obot__class_Obot(tc_fun(_1090676, tc_HOL_Obool)))], (16897 ^ _780478) ^ [] : [-(c_Fun_Oinj__on(_1090674, _1090676, _1090678, _1090682))], (16895 ^ _780478) ^ [] : [-(c_Fun_Oinj__on(_1090674, _1090676, _1090678, _1090680))]]], (16254 ^ _780478) ^ [_1075641] : [class_Lattices_Osemilattice__inf(_1075641), -(c_Finite__Set_Ofun__left__comm__idem(_1075641, _1075641, c_Lattices_Osemilattice__inf__class_Oinf(_1075641)))], (33879 ^ _780478) ^ [_1420529, _1420531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1420529)), c_Int_OBit1(_1420531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420529), _1420531)))], (10175 ^ _780478) ^ [_957243, _957245, _957247] : [class_Groups_Olinordered__ab__group__add(_957243), -(hAPP(c_Groups_Ouminus__class_Ouminus(_957243), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957243), _957245), _957247)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_957243), hAPP(c_Groups_Ouminus__class_Ouminus(_957243), _957245)), hAPP(c_Groups_Ouminus__class_Ouminus(_957243), _957247)))], (49568 ^ _780478) ^ [_1783006, _1783008] : [c_Relation_Oantisym(_1783006, hAPP(c_Relation_Oconverse(_1783006, _1783006), _1783008)), -(c_Relation_Oantisym(_1783006, _1783008))], (39153 ^ _780478) ^ [_1540142, _1540144] : [-(c_Product__Type_Omap__pair(_1540142, _1540142, _1540144, _1540144, c_COMBI(_1540142), c_COMBI(_1540144)) = c_Fun_Oid(tc_prod(_1540142, _1540144)))], (6908 ^ _780478) ^ [_895070, _895072, _895074] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_895070), _895072)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895070, tc_HOL_Obool)), _895074), _895072) = hAPP(hAPP(c_Finite__Set_Ofold(_895070, tc_fun(_895070, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_895070, tc_HOL_Obool), tc_fun(tc_fun(_895070, tc_HOL_Obool), tc_fun(_895070, tc_HOL_Obool)), _895070), hAPP(c_COMBC(tc_fun(_895070, tc_HOL_Obool), tc_fun(_895070, tc_HOL_Obool), tc_fun(_895070, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_895070, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_895070, tc_fun(_895070, tc_HOL_Obool), tc_fun(_895070, tc_HOL_Obool)), c_Set_Oinsert(_895070)), c_Orderings_Obot__class_Obot(tc_fun(_895070, tc_HOL_Obool))))), _895074), _895072))], (15385 ^ _780478) ^ [_1057607, _1057609, _1057611, _1057613] : [class_Groups_Ocomm__monoid__mult(_1057607), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1057607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057607), _1057609), _1057611)), _1057613) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1057607), hAPP(hAPP(c_Power_Opower__class_Opower(_1057607), _1057609), _1057613)), hAPP(hAPP(c_Power_Opower__class_Opower(_1057607), _1057611), _1057613)))], (18065 ^ _780478) ^ [_1116655, _1116657, _1116659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1116655, tc_HOL_Obool), tc_HOL_Obool)), _1116657), _1116659)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1116655, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116655, tc_HOL_Obool), _1116659)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1116655, tc_HOL_Obool), _1116657))))], (12804 ^ _780478) ^ [_1007366, _1007368] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1007366, tc_HOL_Obool)), _1007368), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1007366, tc_HOL_Obool)), _1007368)) = c_Orderings_Otop__class_Otop(tc_fun(_1007366, tc_HOL_Obool)))], (14136 ^ _780478) ^ [_1033103, _1033105] : [class_Rings_Ocomm__semiring__1(_1033103), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033103), _1033105), c_Groups_Oone__class_Oone(_1033103)) = _1033105)], (14363 ^ _780478) ^ [_1036955, _1036957, _1036959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036955), _1036957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036959), _1036957))))], (25803 ^ _780478) ^ [_1258901, _1258903] : [-(_1258901 = hAPP(c_Int_Onat, _1258903)), 25806 ^ _780478 : [(25809 ^ _780478) ^ [] : [_1258903 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258901)], (25807 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258903)))]], 25810 ^ _780478 : [(25813 ^ _780478) ^ [] : [_1258901 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25811 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1258903))]]], (52331 ^ _780478) ^ [_1833496, _1833498, _1833500, _1833502, _1833504, _1833506] : [-(hAPP(hAPP(hAPP(c_COMBB(_1833496, _1833498, _1833500), _1833502), _1833504), _1833506) = hAPP(_1833502, hAPP(_1833504, _1833506)))], (46001 ^ _780478) ^ [_1705118, _1705120, _1705122] : [-(hAPP(c_List_Ofilter(_1705118, _1705120), c_List_Oconcat(_1705118, _1705122)) = c_List_Oconcat(_1705118, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1705118), tc_List_Olist(_1705118)), c_List_Ofilter(_1705118, _1705120)), _1705122)))], (47584 ^ _780478) ^ [_1738147, _1738149, _1738151, _1738153, _1738155] : [-(c_List_Omaps(_1738147, _1738149, _1738151, hAPP(hAPP(c_List_Olist_OCons(_1738147), _1738153), _1738155)) = hAPP(hAPP(c_List_Oappend(_1738149), hAPP(_1738151, _1738153)), c_List_Omaps(_1738147, _1738149, _1738151, _1738155)))], (37225 ^ _780478) ^ [_1488659, _1488661, _1488663] : [-(hAPP(hAPP(c_Product__Type_OPair(_1488659, _1488661), hAPP(c_Product__Type_Ofst(_1488659, _1488661), _1488663)), hAPP(c_Product__Type_Osnd(_1488659, _1488661), _1488663)) = _1488663)], (5422 ^ _780478) ^ [_863420, _863422] : [_863422 = _863420, -(c_Orderings_Oord__class_Oless__eq(_863422) = c_Orderings_Oord__class_Oless__eq(_863420))], (28490 ^ _780478) ^ [] : [-(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)))], (34825 ^ _780478) ^ [_1436970, _1436972] : [class_Fields_Olinordered__field__inverse__zero(_1436970), class_Int_Onumber__ring(_1436970), 34832 ^ _780478 : [(34839 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436970), c_Groups_Ozero__class_Ozero(_1436970)), _1436972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436970), c_Groups_Ozero__class_Ozero(_1436970)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436970), _1436972), hAPP(c_Int_Onumber__class_Onumber__of(_1436970), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34833 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436970), c_Groups_Ozero__class_Ozero(_1436970)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1436970), _1436972), hAPP(c_Int_Onumber__class_Onumber__of(_1436970), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436970), c_Groups_Ozero__class_Ozero(_1436970)), _1436972)))]]], (50477 ^ _780478) ^ [_1801767, _1801769, _1801771, _1801773, _1801775] : [c_Fun_Obij__betw(_1801767, _1801769, _1801771, _1801773, _1801775), -(c_Fun_Oinj__on(_1801767, _1801769, _1801771, _1801773))], (29385 ^ _780478) ^ [_1326222, _1326224] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1326222, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1326224)) = 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), _1326222), _1326224)))], (35011 ^ _780478) ^ [_1440100, _1440102, _1440104] : [class_Rings_Olinordered__idom(_1440100), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1440100), c_Groups_Ozero__class_Ozero(_1440100)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440100), hAPP(hAPP(c_Power_Opower__class_Opower(_1440100), _1440102), 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(_1440100), _1440104), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (6214 ^ _780478) ^ [_880051, _880053] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_880051, tc_HOL_Obool)), _880053)), -(hBOOL(hAPP(hAPP(c_member(_880051), _880053), c_Orderings_Obot__class_Obot(tc_fun(_880051, tc_HOL_Obool)))))], (12716 ^ _780478) ^ [_1005466, _1005468, _1005470] : [class_Lattices_Olattice(_1005466), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005466), _1005468), _1005470) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005466), _1005470), _1005468))], (43869 ^ _780478) ^ [_1657813, _1657815] : [-(hAPP(hAPP(c_List_Odrop(_1657813), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1657815) = _1657815)], (1058 ^ _780478) ^ [_796447, _796449, _796451, _796453, _796455, _796457, _796459, _796461, _796463, _796465] : [-(c_Finite__Set_Ofolding__image(_796463, _796459, _796455, _796451, _796447)), c_Finite__Set_Ofolding__image(_796465, _796461, _796457, _796453, _796449), _796465 = _796463, _796461 = _796459, _796457 = _796455, _796453 = _796451, _796449 = _796447], (44576 ^ _780478) ^ [_1672600, _1672602, _1672604] : [-(_1672600 = c_List_Olist_ONil(_1672602)), -(c_List_Olast(_1672602, hAPP(hAPP(c_List_Oappend(_1672602), _1672604), _1672600)) = c_List_Olast(_1672602, _1672600))], (8808 ^ _780478) ^ [_932688, _932690, _932692] : [class_Orderings_Oorder(_932688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932688), _932690), _932692)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932688), _932692), _932690))], (19240 ^ _780478) ^ [_1141390, _1141392, _1141394] : [class_Rings_Oring__no__zero__divisors(_1141390), 19243 ^ _780478 : [(19244 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141390), _1141392), _1141394) = c_Groups_Ozero__class_Ozero(_1141390), -(_1141392 = c_Groups_Ozero__class_Ozero(_1141390)), -(_1141394 = c_Groups_Ozero__class_Ozero(_1141390))], (19254 ^ _780478) ^ [] : [19255 ^ _780478 : [(19258 ^ _780478) ^ [] : [_1141394 = c_Groups_Ozero__class_Ozero(_1141390)], (19256 ^ _780478) ^ [] : [_1141392 = c_Groups_Ozero__class_Ozero(_1141390)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141390), _1141392), _1141394) = c_Groups_Ozero__class_Ozero(_1141390))]]], (18156 ^ _780478) ^ [_1119140, _1119142, _1119144, _1119146] : [18158 ^ _780478 : [(18161 ^ _780478) ^ [] : [hAPP(_1119146, 18157 ^ [_1119140, _1119142, _1119144, _1119146]) = c_Orderings_Otop__class_Otop(tc_fun(_1119140, tc_HOL_Obool))], (18159 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1119142), 18157 ^ [_1119140, _1119142, _1119144, _1119146]), _1119144)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1119140, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119142, tc_fun(_1119140, tc_HOL_Obool)), _1119144), _1119146))], (10505 ^ _780478) ^ [_963743, _963745, _963747] : [class_Orderings_Olinorder(_963743), 10508 ^ _780478 : [(10515 ^ _780478) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_963743), _963745), _963747) = _963747, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963743), _963745), _963747)))], (10509 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963743), _963745), _963747)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_963743), _963745), _963747) = _963747)]]], (27841 ^ _780478) ^ [_1295533, _1295535] : [27849 ^ _780478 : [(27852 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1295535, 27848 ^ [_1295533, _1295535])))], (27850 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 27848 ^ [_1295533, _1295535]), _1295533)))]], 27842 ^ _780478 : [(27843 ^ _780478) ^ [_1295602] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1295602), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1295533))), hBOOL(hAPP(_1295535, _1295602))]]], (16370 ^ _780478) ^ [_1078300, _1078302, _1078304, _1078306, _1078308] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1078300, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1078302, _1078300, _1078304), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078302, tc_HOL_Obool)), _1078306), _1078308))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078300, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1078302, _1078300, _1078304), _1078306)), hAPP(c_Set_Oimage(_1078302, _1078300, _1078304), _1078308)))))], (28316 ^ _780478) ^ [_1304582] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1304582) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304582))], (1514 ^ _780478) ^ [_802267, _802269] : [-(class_Rings_Olinordered__comm__semiring__strict(_802267)), _802269 = _802267, class_Rings_Olinordered__comm__semiring__strict(_802269)], (31470 ^ _780478) ^ [_1370340] : [-(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)))), _1370340))))], (10733 ^ _780478) ^ [_967724, _967726, _967728, _967730] : [class_Orderings_Olinorder(_967724), 10736 ^ _780478 : [(10745 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967724), _967726), hAPP(hAPP(c_Orderings_Oord__class_Omin(_967724), _967728), _967730)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967724), _967726), _967728)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967724), _967726), _967730))], (10737 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967724), _967726), hAPP(hAPP(c_Orderings_Oord__class_Omin(_967724), _967728), _967730))), 10740 ^ _780478 : [(10743 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967724), _967726), _967730)))], (10741 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967724), _967726), _967728)))]]]]], (48717 ^ _780478) ^ [_1763063, _1763065, _1763067] : [_1763063 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1763065), c_List_Oreplicate(_1763065, _1763063, _1763067)) = c_Orderings_Obot__class_Obot(tc_fun(_1763065, tc_HOL_Obool)))], (47403 ^ _780478) ^ [_1734335, _1734337, _1734339, _1734341, _1734343] : [c_List_OdropWhile(_1734335, _1734337, _1734339) = hAPP(hAPP(c_List_Olist_OCons(_1734335), _1734341), _1734343), 47406 ^ _780478 : [(47409 ^ _780478) ^ [] : [hBOOL(hAPP(_1734337, _1734341))], (47407 ^ _780478) ^ [] : [-(_1734339 = hAPP(hAPP(c_List_Oappend(_1734335), c_List_OtakeWhile(_1734335, _1734337, _1734339)), hAPP(hAPP(c_List_Olist_OCons(_1734335), _1734341), _1734343)))]]], (24733 ^ _780478) ^ [_1240039, _1240041] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240039))), -(c_SMT_Oz3div(_1240041, _1240039) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1240041), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1240039))))], (52095 ^ _780478) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (8136 ^ _780478) ^ [_919628, _919630, _919632, _919634] : [class_Groups_Ocancel__semigroup__add(_919628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919628), _919630), _919632) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919628), _919634), _919632), -(_919630 = _919634)], (37867 ^ _780478) ^ [] : [-(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))))))], (37869 ^ _780478) ^ [_1504290, _1504292, _1504294, _1504296] : [-(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), _1504290), _1504292)), 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), _1504294), _1504296)), 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), _1504290), _1504294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1504292), _1504296))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1504290), _1504296)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1504292), _1504294)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (43574 ^ _780478) ^ [_1650437, _1650439, _1650441] : [hAPP(hAPP(c_List_Oappend(_1650437), _1650439), _1650441) = c_List_Olist_ONil(_1650437), 43577 ^ _780478 : [(43580 ^ _780478) ^ [] : [-(_1650441 = c_List_Olist_ONil(_1650437))], (43578 ^ _780478) ^ [] : [-(_1650439 = c_List_Olist_ONil(_1650437))]]], (44101 ^ _780478) ^ [_1663189, _1663191] : [-(_1663189 = c_List_Olist_ONil(_1663191)), -(hAPP(c_List_Orotate1(_1663191), _1663189) = hAPP(hAPP(c_List_Oappend(_1663191), hAPP(c_List_Otl(_1663191), _1663189)), hAPP(hAPP(c_List_Olist_OCons(_1663191), hAPP(c_List_Ohd(_1663191), _1663189)), c_List_Olist_ONil(_1663191))))], (13849 ^ _780478) ^ [_1028111, _1028113, _1028115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028111), _1028115)), _1028113)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1028111), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1028113), _1028115))))], (16178 ^ _780478) ^ [_1073500, _1073502, _1073504, _1073506] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073500, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1073500), _1073502), _1073504)), hAPP(hAPP(c_Set_Oinsert(_1073500), _1073502), _1073506)) = hAPP(hAPP(c_Set_Oinsert(_1073500), _1073502), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073500, tc_HOL_Obool)), _1073504), _1073506)))], (8130 ^ _780478) ^ [_919493, _919495, _919497, _919499, _919501, _919503] : [c_Finite__Set_Ofun__left__comm(_919493, _919495, _919497), -(hAPP(hAPP(_919497, _919499), hAPP(hAPP(_919497, _919501), _919503)) = hAPP(hAPP(_919497, _919501), hAPP(hAPP(_919497, _919499), _919503)))], (39549 ^ _780478) ^ [_1549220, _1549222, _1549224, _1549226] : [39551 ^ _780478 : [(39554 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1549220, _1549220, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1549220, tc_fun(_1549220, _1549222), tc_fun(_1549220, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549222, tc_HOL_Obool), tc_fun(tc_fun(_1549220, _1549222), tc_fun(_1549220, tc_HOL_Obool)), _1549220), c_COMBB(_1549222, tc_HOL_Obool, _1549220)), hAPP(hAPP(c_COMBB(_1549222, tc_fun(_1549222, tc_HOL_Obool), _1549220), c_fequal), _1549226))), _1549226)), 39550 ^ [_1549220, _1549222, _1549224, _1549226]))], (39552 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549220, _1549220)), 39550 ^ [_1549220, _1549222, _1549224, _1549226]), _1549224)))]], -(c_Equiv__Relations_Ocongruent(_1549220, _1549222, _1549224, _1549226))], (10229 ^ _780478) ^ [_958570, _958572, _958574, _958576] : [class_Orderings_Olinorder(_958570), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_958570), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958570), _958572), _958574)), _958576) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_958570), _958572), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958570), _958574), _958576)))], (29662 ^ _780478) ^ [_1331172, _1331174, _1331176, _1331178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331174), _1331176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1331176), 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), _1331174), _1331172)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1331174), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331178, _1331172))), _1331176))))], (42818 ^ _780478) ^ [_1634336, _1634338, _1634340] : [-(hBOOL(hAPP(c_List_Odistinct(_1634336), hAPP(hAPP(c_List_Olist_OCons(_1634336), _1634338), _1634340)))), -(hBOOL(hAPP(hAPP(c_member(_1634336), _1634338), hAPP(c_List_Oset(_1634336), _1634340)))), hBOOL(hAPP(c_List_Odistinct(_1634336), _1634340))], (47310 ^ _780478) ^ [_1732383] : [-(c_List_Oembed__list(_1732383) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1732383))], (36616 ^ _780478) ^ [_1476766, _1476768] : [_1476766 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1476766, _1476768) = 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)))], (23181 ^ _780478) ^ [_1212021] : [-(hBOOL(hAPP(_1212021, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23188 ^ [_1212021])))), 23182 ^ _780478 : [(23183 ^ _780478) ^ [_1212073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1212073)), hBOOL(hAPP(_1212021, _1212073))]]], (37913 ^ _780478) ^ [] : [-(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))], (2818 ^ _780478) ^ [_822178, _822180, _822182, _822184, _822186, _822188] : [-(c_Random_Ominus__shift(_822188, _822184, _822180) = c_Random_Ominus__shift(_822186, _822182, _822178)), _822188 = _822186, _822184 = _822182, _822180 = _822178], (6340 ^ _780478) ^ [_882740, _882742, _882744] : [_882742 = _882744, -(hAPP(hAPP(c_COMBC(_882740, tc_fun(_882740, tc_HOL_Obool), tc_HOL_Obool), c_member(_882740)), _882742) = hAPP(hAPP(c_COMBC(_882740, tc_fun(_882740, tc_HOL_Obool), tc_HOL_Obool), c_member(_882740)), _882744))], (20456 ^ _780478) ^ [_1161933, _1161935, _1161937] : [class_Rings_Olinordered__semiring__strict(_1161933), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161933), _1161935), c_Groups_Ozero__class_Ozero(_1161933))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161933), c_Groups_Ozero__class_Ozero(_1161933)), _1161937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161933), _1161935), _1161937)), c_Groups_Ozero__class_Ozero(_1161933))))], (47250 ^ _780478) ^ [_1731156, _1731158, _1731160] : [-(c_List_OtakeWhile(_1731156, _1731158, _1731160) = hAPP(hAPP(c_List_Otake(_1731156), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731156)), c_List_OtakeWhile(_1731156, _1731158, _1731160))), _1731160))], (8926 ^ _780478) ^ [_934291, _934293, _934295] : [class_Orderings_Olinorder(_934291), 8929 ^ _780478 : [(8930 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934291), _934293), _934295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934291), _934295), _934293))), -(_934293 = _934295)], (8940 ^ _780478) ^ [] : [8941 ^ _780478 : [(8944 ^ _780478) ^ [] : [_934293 = _934295], (8942 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934291), _934295), _934293))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934291), _934293), _934295))]]], (37734 ^ _780478) ^ [_1500711, _1500713, _1500715] : [-(hAPP(c_Relation_OField(_1500711), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1500711, _1500711), tc_HOL_Obool)), _1500713), _1500715)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1500711, tc_HOL_Obool)), hAPP(c_Relation_OField(_1500711), _1500713)), hAPP(c_Relation_OField(_1500711), _1500715)))], (22767 ^ _780478) ^ [_1204340, _1204342, _1204344] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1204340, tc_Nat_Onat), _1204342), _1204344)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1204340, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1204340), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1204342)), _1204344))], (14074 ^ _780478) ^ [_1031977] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1031977) = _1031977)], (40861 ^ _780478) ^ [_1580688, _1580690, _1580692] : [-(hAPP(c_Relation_Oconverse(_1580688, _1580690), hAPP(c_Relation_Oconverse(_1580690, _1580688), _1580692)) = _1580692)], (47574 ^ _780478) ^ [_1737925, _1737927, _1737929] : [-(hAPP(c_List_Oset(_1737925), c_List_Oinsert(_1737925, _1737927, _1737929)) = hAPP(hAPP(c_Set_Oinsert(_1737925), _1737927), hAPP(c_List_Oset(_1737925), _1737929)))], (32990 ^ _780478) ^ [_1403810, _1403812, _1403814] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_1403810, _1403812, _1403814)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1403814)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42244 ^ _780478) ^ [_1619157, _1619159, _1619161, _1619163] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1619157), tc_List_Olist(_1619157))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1619157), tc_List_Olist(_1619157)), _1619159), _1619161)), c_List_Olexord(_1619157, _1619163)))), 42245 ^ _780478 : [(42252 ^ _780478) ^ [_1619464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619464), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619157)), _1619159)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619157)), _1619161)))), hAPP(hAPP(c_List_Otake(_1619157), _1619464), _1619159) = hAPP(hAPP(c_List_Otake(_1619157), _1619464), _1619161), hBOOL(hAPP(hAPP(c_member(tc_prod(_1619157, _1619157)), hAPP(hAPP(c_Product__Type_OPair(_1619157, _1619157), hAPP(hAPP(c_List_Onth(_1619157), _1619159), _1619464)), hAPP(hAPP(c_List_Onth(_1619157), _1619161), _1619464))), _1619163))], (42246 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619157)), _1619159)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619157)), _1619161))), hAPP(hAPP(c_List_Otake(_1619157), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619157)), _1619159)), _1619161) = _1619159]]], (33402 ^ _780478) ^ [_1411014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411014), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411014)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14865 ^ _780478) ^ [_1047357, _1047359, _1047361, _1047363, _1047365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1047357), _1047359)), 14868 ^ _780478 : [(14875 ^ _780478) ^ [] : [_1047363 = 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), _1047359), _1047357)), _1047361)), _1047365), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047357), _1047361)), _1047363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047359), _1047361)), _1047365))], (14869 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047357), _1047361)), _1047363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047359), _1047361)), _1047365), -(_1047363 = 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), _1047359), _1047357)), _1047361)), _1047365))]]], (43877 ^ _780478) ^ [_1658036, _1658038] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658036)), hAPP(c_List_Orotate1(_1658036), _1658038)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658036)), _1658038))], (3876 ^ _780478) ^ [_838615, _838617] : [_838617 = _838615, -(c_Nat_Osemiring__1__class_Oof__nat(_838617) = c_Nat_Osemiring__1__class_Oof__nat(_838615))], (35611 ^ _780478) ^ [] : [-(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))], (45073 ^ _780478) ^ [_1683954, _1683956, _1683958, _1683960, _1683962] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683954)), _1683956) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683958)), _1683960), 45076 ^ _780478 : [(45085 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1683954, _1683958), _1683956), _1683960) = _1683962), hAPP(hAPP(c_List_Omap(tc_prod(_1683954, _1683958), _1683954), c_Product__Type_Ofst(_1683954, _1683958)), _1683962) = _1683956, hAPP(hAPP(c_List_Omap(tc_prod(_1683954, _1683958), _1683958), c_Product__Type_Osnd(_1683954, _1683958)), _1683962) = _1683960], (45077 ^ _780478) ^ [] : [hAPP(hAPP(c_List_Ozip(_1683954, _1683958), _1683956), _1683960) = _1683962, 45080 ^ _780478 : [(45083 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1683954, _1683958), _1683958), c_Product__Type_Osnd(_1683954, _1683958)), _1683962) = _1683960)], (45081 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1683954, _1683958), _1683954), c_Product__Type_Ofst(_1683954, _1683958)), _1683962) = _1683956)]]]]], (48555 ^ _780478) ^ [_1760168, _1760170, _1760172] : [-(_1760168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1760170, c_List_Oreplicate(_1760170, _1760168, _1760172)) = _1760172)], (5837 ^ _780478) ^ [_872965, _872967, _872969, _872971] : [hBOOL(hAPP(hAPP(c_member(_872965), _872967), hAPP(hAPP(c_Set_Oinsert(_872965), _872969), _872971))), -(_872967 = _872969), -(hBOOL(hAPP(hAPP(c_member(_872965), _872967), _872971)))], (19340 ^ _780478) ^ [_1142834] : [class_Rings_Ozero__neq__one(_1142834), c_Groups_Oone__class_Oone(_1142834) = c_Groups_Ozero__class_Ozero(_1142834)], (5258 ^ _780478) ^ [_860830, _860832, _860834, _860836] : [-(c_Product__Type_OPair(_860836, _860832) = c_Product__Type_OPair(_860834, _860830)), _860836 = _860834, _860832 = _860830], (31903 ^ _780478) ^ [_1383004, _1383006, _1383008] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_1383004, _1383006, _1383008)], (48046 ^ _780478) ^ [_1749024, _1749026, _1749028, _1749030] : [c_List_Olist__ex(_1749024, _1749026, hAPP(hAPP(c_List_Oappend(_1749024), _1749028), _1749030)), -(c_List_Olist__ex(_1749024, _1749026, _1749028)), -(c_List_Olist__ex(_1749024, _1749026, _1749030))], (34455 ^ _780478) ^ [_1430280, _1430282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430280), _1430282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430280)), c_Int_OBit0(_1430282))))], (37678 ^ _780478) ^ [_1499562] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1499562)), -(_1499562 = 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))), _1499562)), c_FunDef_Omax__strict)))], (15043 ^ _780478) ^ [_1051199, _1051201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051199), _1051201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1051199), _1051201)))], (44811 ^ _780478) ^ [_1678211, _1678213] : [-(hAPP(hAPP(c_List_Omap(_1678211, _1678211), c_COMBI(_1678211)), _1678213) = _1678213)], (42403 ^ _780478) ^ [_1623093, _1623095, _1623097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623093), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623095)), _1623097))), -(hBOOL(hAPP(hAPP(c_member(_1623095), hAPP(hAPP(c_List_Onth(_1623095), _1623097), _1623093)), hAPP(c_List_Oset(_1623095), _1623097))))], (15828 ^ _780478) ^ [_1066899, _1066901, _1066903] : [class_Lattices_Olattice(_1066899), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066899), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066899), _1066901), _1066903)), _1066903)))], (46449 ^ _780478) ^ [_1715544, _1715546] : [class_Orderings_Olinorder(_1715544), -(c_List_Olinorder__class_Osorted(_1715544, c_List_Olinorder__class_Osort__key(_1715544, _1715544, c_COMBI(_1715544), _1715546)))], (40173 ^ _780478) ^ [_1564369, _1564371, _1564373, _1564375, _1564377, _1564379] : [c_Finite__Set_Ofolding__idem(_1564369, _1564371, _1564373, _1564375), hBOOL(hAPP(c_Finite__Set_Ofinite(_1564369), _1564377)), -(hAPP(_1564375, hAPP(hAPP(c_Set_Oinsert(_1564369), _1564379), _1564377)) = hAPP(c_Fun_Ocomp(_1564371, _1564371, _1564371, hAPP(_1564375, _1564377)), hAPP(_1564373, _1564379)))], (43921 ^ _780478) ^ [_1658985, _1658987, _1658989] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658985)), _1658987)), _1658989)), -(hAPP(hAPP(c_List_Odrop(_1658985), _1658989), _1658987) = c_List_Olist_ONil(_1658985))], (38279 ^ _780478) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (17175 ^ _780478) ^ [_1096421, _1096423, _1096425, _1096427] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1096421), _1096423)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096421), _1096425)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1096421, tc_Nat_Onat), _1096427), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1096421, tc_HOL_Obool)), _1096423), _1096425)) = 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(_1096421, tc_Nat_Onat), _1096427), _1096423)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1096421, tc_Nat_Onat), _1096427), _1096425))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1096421, tc_Nat_Onat), _1096427), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1096421, tc_HOL_Obool)), _1096423), _1096425))))], (36668 ^ _780478) ^ [_1477756, _1477758] : [-(c_Divides_Odivmod__nat(_1477758, _1477756) = 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), _1477758), _1477756), _1477756))), -(_1477756 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1477758), _1477756)))], (18446 ^ _780478) ^ [_1125846, _1125848, _1125850, _1125852] : [hBOOL(hAPP(hAPP(c_member(_1125848), _1125852), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125846, tc_fun(_1125848, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1125846, tc_HOL_Obool))), _1125850))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1125846, tc_fun(_1125848, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1125846, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1125848, tc_HOL_Obool), tc_fun(_1125848, tc_HOL_Obool), _1125846), hAPP(c_COMBC(_1125848, tc_fun(_1125848, tc_HOL_Obool), tc_HOL_Obool), c_member(_1125848))), _1125850)), _1125852)))], (9560 ^ _780478) ^ [_944812, _944814, _944816, _944818, _944820] : [c_Fun_Oinj__on(_944812, _944814, _944816, _944818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944812, tc_HOL_Obool)), _944820), _944818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_944814, tc_HOL_Obool)), hAPP(c_Set_Oimage(_944812, _944814, _944816), _944820)), hAPP(c_Set_Oimage(_944812, _944814, _944816), _944818))))], (35647 ^ _780478) ^ [_1453746, _1453748, _1453750, _1453752] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1453746, tc_fun(_1453748, tc_HOL_Obool))), _1453750), _1453752)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1453746, _1453748)), hAPP(hAPP(c_Product__Type_OPair(_1453746, _1453748), _1453750), _1453752)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1453746, _1453748), tc_HOL_Obool)))))], (22273 ^ _780478) ^ [_1194617, _1194619] : [class_Rings_Olinordered__idom(_1194617), 22276 ^ _780478 : [(22283 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194617), _1194619), c_Groups_Ozero__class_Ozero(_1194617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194617), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194617), _1194619), _1194619)), c_Groups_Ozero__class_Ozero(_1194617))))], (22277 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194617), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1194617), _1194619), _1194619)), c_Groups_Ozero__class_Ozero(_1194617))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1194617), _1194619), c_Groups_Ozero__class_Ozero(_1194617))))]]], (3510 ^ _780478) ^ [_832874, _832876] : [_832876 = _832874, -(c_Int_Onumber__class_Onumber__of(_832876) = c_Int_Onumber__class_Onumber__of(_832874))], (18265 ^ _780478) ^ [_1122122, _1122124, _1122126] : [class_Groups_Omonoid__mult(_1122122), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1122122), _1122124), hAPP(c_Nat_OSuc, _1122126)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1122122), hAPP(hAPP(c_Power_Opower__class_Opower(_1122122), _1122124), _1122126)), _1122124))], (3496 ^ _780478) ^ [_832653, _832655, _832657, _832659, _832661, _832663] : [-(c_List_Osublist(_832663, _832659, _832655) = c_List_Osublist(_832661, _832657, _832653)), _832663 = _832661, _832659 = _832657, _832655 = _832653], (28522 ^ _780478) ^ [_1308474, _1308476] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1308474, _1308476)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1308476), _1308474)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (45805 ^ _780478) ^ [_1700147, _1700149, _1700151] : [hBOOL(hAPP(c_List_Odistinct(_1700147), _1700149)), -(c_List_Oremove1(_1700147, _1700151, c_List_Oremdups(_1700147, _1700149)) = c_List_Oremdups(_1700147, c_List_Oremove1(_1700147, _1700151, _1700149)))], (19006 ^ _780478) ^ [_1137281, _1137283, _1137285] : [class_Lattices_Olattice(_1137281), hAPP(_1137283, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1137281), 19011 ^ [_1137281, _1137283, _1137285]), 19012 ^ [_1137281, _1137283, _1137285])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1137281), hAPP(_1137283, 19011 ^ [_1137281, _1137283, _1137285])), hAPP(_1137283, 19012 ^ [_1137281, _1137283, _1137285])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1137281), _1137285)), -(_1137285 = c_Orderings_Obot__class_Obot(tc_fun(_1137281, tc_HOL_Obool))), -(hAPP(_1137283, c_Big__Operators_Olattice__class_OInf__fin(_1137281, _1137285)) = c_Big__Operators_Olattice__class_OInf__fin(_1137281, hAPP(c_Set_Oimage(_1137281, _1137281, _1137283), _1137285)))], (1774 ^ _780478) ^ [_805517, _805519] : [-(class_Groups_Omonoid__add(_805517)), _805519 = _805517, class_Groups_Omonoid__add(_805519)], (15055 ^ _780478) ^ [_1051407, _1051409, _1051411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051407), _1051409)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051407), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1051409), _1051411))))], (45891 ^ _780478) ^ [_1701757] : [-(c_List_Oconcat(_1701757, c_List_Olist_ONil(tc_List_Olist(_1701757))) = c_List_Olist_ONil(_1701757))], (40644 ^ _780478) ^ [_1576037, _1576039, _1576041, _1576043, _1576045] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576037, _1576037)), hAPP(hAPP(c_Product__Type_OPair(_1576037, _1576037), _1576039), _1576041)), _1576043)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1576037, _1576037)), hAPP(hAPP(c_Product__Type_OPair(_1576037, _1576037), _1576041), _1576045)), c_Transitive__Closure_Ortrancl(_1576037, _1576043))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576037, _1576037)), hAPP(hAPP(c_Product__Type_OPair(_1576037, _1576037), _1576039), _1576045)), c_Transitive__Closure_Otrancl(_1576037, _1576043))))], (31664 ^ _780478) ^ [_1377790, _1377792, _1377794] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377790, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377790), _1377792), _1377794), -(_1377792 = c_Orderings_Obot__class_Obot(tc_fun(_1377790, tc_HOL_Obool)))], (50916 ^ _780478) ^ [_1812501] : [-(c_Lazy__Sequence_Oflat(_1812501, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1812501))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1812501))], (51835 ^ _780478) ^ [_1828552, _1828554] : [class_Orderings_Oord(_1828552), -(class_Orderings_Oord(tc_fun(_1828554, _1828552)))], (34379 ^ _780478) ^ [_1428965] : [c_Int_OBit0(_1428965) = c_Int_OPls, -(_1428965 = c_Int_OPls)], (43311 ^ _780478) ^ [_1644469] : [class_Orderings_Olinorder(_1644469), -(c_List_Olinorder__class_Osorted__list__of__set(_1644469, c_Orderings_Obot__class_Obot(tc_fun(_1644469, tc_HOL_Obool))) = c_List_Olist_ONil(_1644469))], (51113 ^ _780478) ^ [_1816368, _1816370, _1816372, _1816374, _1816376] : [class_Divides_Osemiring__div(_1816368), -(_1816370 = c_Groups_Ozero__class_Ozero(_1816368)), -(_1816372 = c_Groups_Ozero__class_Ozero(_1816368)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816368), _1816370), _1816374)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816368), _1816372), _1816376)), 51132 ^ _780478 : [(51139 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1816368), _1816374), _1816372) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1816368), _1816370), _1816376), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1816368), _1816374), _1816370) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1816368), _1816376), _1816372))], (51133 ^ _780478) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1816368), _1816374), _1816370) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1816368), _1816376), _1816372), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1816368), _1816374), _1816372) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1816368), _1816370), _1816376))]]], (12544 ^ _780478) ^ [_1001925, _1001927] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1001925, _1001927)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1001925, _1001927), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001925), c_Orderings_Otop__class_Otop(tc_fun(_1001925, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1001927), c_Orderings_Otop__class_Otop(tc_fun(_1001927, tc_HOL_Obool))))], (22624 ^ _780478) ^ [_1201865] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1201865) = _1201865)], (35109 ^ _780478) ^ [_1442162] : [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, _1442162, 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, _1442162, 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))], (40520 ^ _780478) ^ [_1572917, _1572919] : [-(hAPP(c_Relation_ODomain(_1572917, _1572917), c_Transitive__Closure_Ortrancl(_1572917, _1572919)) = c_Orderings_Otop__class_Otop(tc_fun(_1572917, tc_HOL_Obool)))], (24943 ^ _780478) ^ [_1243636, _1243638, _1243640] : [hBOOL(hAPP(_1243636, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1243638), _1243640))), 24946 ^ _780478 : [(24953 ^ _780478) ^ [] : [-(_1243640 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24956 ^ _780478 : [(24957 ^ _780478) ^ [_1243888, _1243890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1243888), _1243640)), _1243638 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1243640), _1243890)), _1243888), -(hBOOL(hAPP(_1243636, _1243890)))]]], (24947 ^ _780478) ^ [] : [_1243640 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1243636, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (16721 ^ _780478) ^ [_1086823, _1086825, _1086827, _1086829, _1086831, _1086833] : [-(hBOOL(hAPP(hAPP(c_member(_1086823), _1086825), _1086827))), 16724 ^ _780478 : [(16731 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1086823), _1086829), _1086827))), -(hAPP(c_Set_Ovimage(_1086831, _1086823, hAPP(hAPP(c_COMBC(_1086831, _1086823, _1086823), hAPP(hAPP(c_COMBC(_1086831, _1086823, tc_fun(_1086823, _1086823)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1086823, tc_fun(_1086823, _1086823)), _1086831), c_If(_1086823)), hAPP(hAPP(c_COMBC(_1086831, tc_fun(_1086831, tc_HOL_Obool), tc_HOL_Obool), c_member(_1086831)), _1086833))), _1086825)), _1086829)), _1086827) = c_Orderings_Obot__class_Obot(tc_fun(_1086831, tc_HOL_Obool)))], (16725 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1086823), _1086829), _1086827)), -(hAPP(c_Set_Ovimage(_1086831, _1086823, hAPP(hAPP(c_COMBC(_1086831, _1086823, _1086823), hAPP(hAPP(c_COMBC(_1086831, _1086823, tc_fun(_1086823, _1086823)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1086823, tc_fun(_1086823, _1086823)), _1086831), c_If(_1086823)), hAPP(hAPP(c_COMBC(_1086831, tc_fun(_1086831, tc_HOL_Obool), tc_HOL_Obool), c_member(_1086831)), _1086833))), _1086825)), _1086829)), _1086827) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1086831, tc_HOL_Obool)), _1086833))]]], (44931 ^ _780478) ^ [_1680968, _1680970, _1680972] : [c_Fun_Oinj__on(_1680968, _1680970, _1680972, c_Orderings_Otop__class_Otop(tc_fun(_1680968, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1680968), tc_List_Olist(_1680970), hAPP(c_List_Omap(_1680968, _1680970), _1680972), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1680968), tc_HOL_Obool))))], (44821 ^ _780478) ^ [_1678488, _1678490, _1678492, _1678494, _1678496] : [-(hAPP(hAPP(c_List_Omap(_1678488, _1678490), _1678492), hAPP(hAPP(c_List_Oappend(_1678488), _1678494), _1678496)) = hAPP(hAPP(c_List_Oappend(_1678490), hAPP(hAPP(c_List_Omap(_1678488, _1678490), _1678492), _1678494)), hAPP(hAPP(c_List_Omap(_1678488, _1678490), _1678492), _1678496)))], (16398 ^ _780478) ^ [_1079217, _1079219, _1079221, _1079223] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1079217, tc_fun(_1079219, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1079217, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1079219, tc_HOL_Obool), tc_fun(_1079219, tc_HOL_Obool), _1079217), hAPP(c_COMBC(_1079219, tc_fun(_1079219, tc_HOL_Obool), tc_HOL_Obool), c_member(_1079219))), _1079221)), _1079223)), -(hBOOL(hAPP(hAPP(c_member(_1079219), _1079223), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1079217, tc_fun(_1079219, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1079217, tc_HOL_Obool))), _1079221))))], (50918 ^ _780478) ^ [_1812551, _1812553, _1812555] : [c_List_Olist__all(tc_Nat_Onat, _1812551, c_List_Oupt(_1812553, _1812555)), -(c_List_Oall__interval__nat(_1812551, _1812553, _1812555))], (11237 ^ _780478) ^ [_977005, _977007, _977009, _977011] : [class_Groups_Oab__group__add(_977005), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977007, _977005), hAPP(hAPP(c_COMBB(_977005, _977005, _977007), c_Groups_Ouminus__class_Ouminus(_977005)), _977009)), _977011) = hAPP(c_Groups_Ouminus__class_Ouminus(_977005), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977007, _977005), _977009), _977011)))], (23379 ^ _780478) ^ [_1215255, _1215257, _1215259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215255), _1215257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1215259), _1215255)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1215259), _1215257))))], (44738 ^ _780478) ^ [_1676294, _1676296, _1676298, _1676300, _1676302] : [44740 ^ _780478 : [(44743 ^ _780478) ^ [] : [hAPP(_1676298, 44739 ^ [_1676294, _1676296, _1676298, _1676300, _1676302]) = hAPP(_1676302, 44739 ^ [_1676294, _1676296, _1676298, _1676300, _1676302])], (44741 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676294), 44739 ^ [_1676294, _1676296, _1676298, _1676300, _1676302]), hAPP(c_List_Oset(_1676294), _1676300))))]], -(hAPP(hAPP(c_List_Omap(_1676294, _1676296), _1676298), _1676300) = hAPP(hAPP(c_List_Omap(_1676294, _1676296), _1676302), _1676300))], (43323 ^ _780478) ^ [_1644703, _1644705, _1644707, _1644709, _1644711] : [-(_1644703 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1644705, _1644707, _1644709), _1644703), _1644711) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1644707), _1644705), tc_prod(_1644707, _1644705), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644707), _1644705), c_List_Olist_ONil(_1644707)), _1644711), hAPP(c_Product__Type_Oprod_Oprod__case(_1644707, _1644705, tc_prod(tc_List_Olist(_1644707), _1644705)), hAPP(hAPP(c_COMBC(_1644707, tc_fun(_1644705, tc_prod(tc_List_Olist(_1644707), _1644705)), tc_fun(_1644705, tc_prod(tc_List_Olist(_1644707), _1644705))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1644707), _1644705), tc_prod(tc_List_Olist(_1644707), _1644705)), tc_fun(tc_fun(_1644705, tc_prod(tc_List_Olist(_1644707), _1644705)), tc_fun(_1644705, tc_prod(tc_List_Olist(_1644707), _1644705))), _1644707), c_COMBB(tc_prod(tc_List_Olist(_1644707), _1644705), tc_prod(tc_List_Olist(_1644707), _1644705), _1644705)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1644707), tc_fun(_1644705, tc_prod(tc_List_Olist(_1644707), _1644705))), tc_fun(tc_prod(tc_List_Olist(_1644707), _1644705), tc_prod(tc_List_Olist(_1644707), _1644705)), _1644707), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1644707), _1644705, tc_prod(tc_List_Olist(_1644707), _1644705))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1644707), tc_List_Olist(_1644707)), tc_fun(tc_List_Olist(_1644707), tc_fun(_1644705, tc_prod(tc_List_Olist(_1644707), _1644705))), _1644707), hAPP(c_COMBB(tc_List_Olist(_1644707), tc_fun(_1644705, tc_prod(tc_List_Olist(_1644707), _1644705)), tc_List_Olist(_1644707)), c_Product__Type_OPair(tc_List_Olist(_1644707), _1644705))), c_List_Olist_OCons(_1644707))))), hAPP(c_Lazy__Sequence_Oanamorph(_1644705, _1644707, _1644709), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1644703), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1644709, _1644711)))], (12996 ^ _780478) ^ [_1010768, _1010770] : [class_Lattices_Obounded__lattice__bot(_1010768), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010768), c_Orderings_Obot__class_Obot(_1010768)), _1010770) = _1010770)], (37981 ^ _780478) ^ [_1508360, _1508362, _1508364, _1508366] : [hAPP(hAPP(c_Relation_Orel__comp(_1508360, _1508360, _1508360), _1508362), _1508364) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1508360, _1508360), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1508360, _1508360, _1508360), _1508362), _1508366) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1508360, _1508360), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1508360, _1508360, _1508360), _1508362), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1508360, _1508360), tc_HOL_Obool)), _1508364), _1508366)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1508360, _1508360), tc_HOL_Obool)))], (30829 ^ _780478) ^ [_1353139, _1353141, _1353143] : [class_Complete__Lattice_Ocomplete__lattice(_1353139), -(c_Complete__Lattice_OSup__class_OSup(_1353139, hAPP(hAPP(c_Set_Oinsert(_1353139), _1353141), _1353143)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1353139), _1353141), c_Complete__Lattice_OSup__class_OSup(_1353139, _1353143)))], (49270 ^ _780478) ^ [_1775763, _1775765] : [c_Relation_Otrans(_1775763, hAPP(c_Relation_Oconverse(_1775763, _1775763), _1775765)), -(c_Relation_Otrans(_1775763, _1775765))], (37861 ^ _780478) ^ [_1504113, _1504115, _1504117] : [class_Rings_Oring__1(_1504113), -(hAPP(c_Int_Oring__1__class_Oof__int(_1504113), 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), _1504115), _1504117)), 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(_1504113), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1504113), _1504115)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1504113), _1504117)))], (34279 ^ _780478) ^ [_1427041, _1427043, _1427045] : [class_Int_Onumber__ring(_1427041), 34282 ^ _780478 : [(34289 ^ _780478) ^ [] : [c_Int_Oiszero(_1427041, hAPP(c_Int_Onumber__class_Onumber__of(_1427041), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1427043), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427045)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1427041), _1427043) = hAPP(c_Int_Onumber__class_Onumber__of(_1427041), _1427045))], (34283 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1427041), _1427043) = hAPP(c_Int_Onumber__class_Onumber__of(_1427041), _1427045), -(c_Int_Oiszero(_1427041, hAPP(c_Int_Onumber__class_Onumber__of(_1427041), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1427043), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1427045)))))]]], (31234 ^ _780478) ^ [_1361953, _1361955, _1361957] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1361953, tc_HOL_Obool)), _1361955), _1361957) = hAPP(c_Set_OCollect(_1361953), hAPP(hAPP(c_COMBS(_1361953, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361953), c_fdisj), hAPP(hAPP(c_COMBC(_1361953, tc_fun(_1361953, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361953)), _1361955))), hAPP(hAPP(c_COMBC(_1361953, tc_fun(_1361953, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361953)), _1361957))))], (23441 ^ _780478) ^ [_1216320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1216320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216320)))], (17749 ^ _780478) ^ [_1110994, _1110996, _1110998, _1111000, _1111002, _1111004] : [hBOOL(hAPP(hAPP(c_member(_1110994), _1110996), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1110998, tc_fun(_1110994, tc_HOL_Obool)), _1111000), _1111002))), hBOOL(hAPP(hAPP(c_member(_1110998), _1111004), _1111000)), -(hBOOL(hAPP(hAPP(c_member(_1110994), _1110996), hAPP(_1111002, _1111004))))], (41204 ^ _780478) ^ [_1589498, _1589500, _1589502, _1589504] : [-(hAPP(hAPP(c_Nat_Ocompow(_1589498, _1589498), _1589500), hAPP(hAPP(c_Nat_Ocompow(_1589498, _1589498), _1589502), _1589504)) = hAPP(hAPP(c_Nat_Ocompow(_1589498, _1589498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1589502), _1589500)), _1589504))], (2378 ^ _780478) ^ [_815314, _815316] : [_815316 = _815314, -(c_Divides_Oadjust(_815316) = c_Divides_Oadjust(_815314))], (10613 ^ _780478) ^ [_965590, _965592, _965594] : [class_Groups_Oordered__ab__group__add(_965590), 10616 ^ _780478 : [(10623 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965590), _965594), _965592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965590), hAPP(c_Groups_Ouminus__class_Ouminus(_965590), _965592)), hAPP(c_Groups_Ouminus__class_Ouminus(_965590), _965594))))], (10617 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965590), hAPP(c_Groups_Ouminus__class_Ouminus(_965590), _965592)), hAPP(c_Groups_Ouminus__class_Ouminus(_965590), _965594))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965590), _965594), _965592)))]]], (18033 ^ _780478) ^ [_1116095, _1116097, _1116099] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1116095)), _1116097)), hAPP(c_Nat_OSuc, _1116099)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116095), _1116097)), _1116099))], (25235 ^ _780478) ^ [_1249434, _1249436] : [class_Rings_Odivision__ring__inverse__zero(_1249434), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249434), _1249436), c_Groups_Ozero__class_Ozero(_1249434)) = c_Groups_Ozero__class_Ozero(_1249434))], (6208 ^ _780478) ^ [_879939, _879941, _879943] : [class_Orderings_Obot(_879939), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_879941, _879939)), _879943) = c_Orderings_Obot__class_Obot(_879939))], (24927 ^ _780478) ^ [_1243364, _1243366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1243364)), 24930 ^ _780478 : [(24937 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1243366), _1243364))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1243366), _1243364) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243366), _1243364)), _1243364)))], (24931 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1243366), _1243364)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1243366), _1243364) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (49846 ^ _780478) ^ [_1788138, _1788140] : [c_Equiv__Relations_Opart__equivp(_1788138, _1788140), 49850 ^ _780478 : [(49855 ^ _780478) ^ [] : [-(c_Predicate_Otransp(_1788138, _1788140))], (49853 ^ _780478) ^ [] : [-(c_Predicate_Osymp(_1788138, _1788140))], (49851 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1788140, 49849 ^ [_1788138, _1788140]), 49849 ^ [_1788138, _1788140])))]]], (42502 ^ _780478) ^ [_1627096, _1627098, _1627100, _1627102] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1627096, _1627096)), hAPP(hAPP(c_Product__Type_OPair(_1627096, _1627096), _1627098), _1627100)), hAPP(c_List_Oset(tc_prod(_1627096, _1627096)), hAPP(hAPP(c_List_Ozip(_1627096, _1627096), _1627102), _1627102)))), 42505 ^ _780478 : [(42508 ^ _780478) ^ [] : [-(_1627098 = _1627100)], (42506 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1627096), _1627098), hAPP(c_List_Oset(_1627096), _1627102))))]]], (16460 ^ _780478) ^ [_1080863, _1080865, _1080867, _1080869] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1080863), hAPP(c_Set_Ovimage(_1080863, _1080865, _1080867), _1080869))), hAPP(c_Set_Oimage(_1080863, _1080865, _1080867), c_Orderings_Otop__class_Otop(tc_fun(_1080863, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1080865, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1080865), _1080869)))], (28438 ^ _780478) ^ [_1306735, _1306737, _1306739] : [class_Orderings_Olinorder(_1306735), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1306735), _1306737), _1306739)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306735, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1306735, _1306737), _1306739)), hAPP(c_SetInterval_Oord__class_OatLeast(_1306735), _1306739)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1306735), _1306737))], (52109 ^ _780478) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (39275 ^ _780478) ^ [_1542973, _1542975, _1542977, _1542979, _1542981] : [c_Relation_Orefl__on(_1542973, _1542975, _1542977), c_Relation_Orefl__on(_1542973, _1542979, _1542981), -(c_Relation_Orefl__on(_1542973, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1542973, tc_HOL_Obool)), _1542975), _1542979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1542973, _1542973), tc_HOL_Obool)), _1542977), _1542981)))], (10187 ^ _780478) ^ [_957477, _957479, _957481, _957483] : [class_Orderings_Olinorder(_957477), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957477), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957477), _957479), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957477), _957481), _957483))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957477), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957477), _957479), _957481)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957477), _957479), _957483)))))], (45221 ^ _780478) ^ [_1686783] : [-(_1686783 = 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, _1686783)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1686783))))], (20872 ^ _780478) ^ [_1169180, _1169182] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1169180), c_Groups_Ozero__class_Ozero(_1169180)), hAPP(c_Nat_OSuc, _1169182)) = c_Groups_Ozero__class_Ozero(_1169180)), class_Power_Opower(_1169180), class_Rings_Osemiring__0(_1169180)], (27405 ^ _780478) ^ [_1287632] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1287632)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1287632))], (36622 ^ _780478) ^ [_1476844, _1476846] : [-(_1476844 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36625 ^ _780478 : [(36632 ^ _780478) ^ [] : [-(_1476846 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1476844, _1476846) = 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, _1476846))), 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)), _1476846)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476844))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1476846), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1476844), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1476844, _1476846)), 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), _1476846))))), c_Divides_Opdivmod(_1476844, _1476846)))))], (36626 ^ _780478) ^ [] : [_1476846 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1476844, _1476846) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476844))]]], (34491 ^ _780478) ^ [_1430886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430886), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430886)), c_Int_OPls)))], (3022 ^ _780478) ^ [_825240, _825242, _825244, _825246, _825248, _825250, _825252, _825254, _825256, _825258, _825260, _825262] : [-(c_Product__Type_Omap__pair(_825262, _825258, _825254, _825250, _825246, _825242) = c_Product__Type_Omap__pair(_825260, _825256, _825252, _825248, _825244, _825240)), _825262 = _825260, _825258 = _825256, _825254 = _825252, _825250 = _825248, _825246 = _825244, _825242 = _825240], (24803 ^ _780478) ^ [_1241330, _1241332, _1241334] : [-(_1241330 = 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), _1241330), _1241332)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1241330), _1241334)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1241332), _1241334))], (38822 ^ _780478) ^ [_1530173, _1530175] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530173, _1530173), tc_HOL_Obool)), c_Relation_OId__on(_1530173, _1530175)), hAPP(hAPP(c_Product__Type_OSigma(_1530173, _1530173), _1530175), hAPP(c_COMBK(tc_fun(_1530173, tc_HOL_Obool), _1530173), _1530175)))))], (38582 ^ _780478) ^ [_1523199, _1523201, _1523203, _1523205, _1523207] : [hBOOL(hAPP(hAPP(_1523199, _1523201), _1523203)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1523205, _1523207, _1523199), _1523203)))], (31728 ^ _780478) ^ [_1379772, _1379774, _1379776] : [-(hAPP(c_Relation_OImage(_1379772, _1379774, _1379776), c_Orderings_Obot__class_Obot(tc_fun(_1379772, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1379774, tc_HOL_Obool)))], (13002 ^ _780478) ^ [_1010863, _1010865] : [class_Lattices_Obounded__lattice__bot(_1010863), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010863), _1010865), c_Orderings_Obot__class_Obot(_1010863)) = _1010865)], (17815 ^ _780478) ^ [_1112530, _1112532, _1112534] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1112530, tc_HOL_Obool)), _1112532), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1112530, tc_HOL_Obool), _1112534)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1112530, tc_HOL_Obool), tc_fun(_1112530, tc_HOL_Obool)), _1112534), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1112530, tc_HOL_Obool)), _1112532)))], (3870 ^ _780478) ^ [_838530, _838532] : [_838532 = _838530, -(c_Groups_Oabs__class_Oabs(_838532) = c_Groups_Oabs__class_Oabs(_838530))], (42409 ^ _780478) ^ [_1623254, _1623256, _1623258] : [hBOOL(hAPP(hAPP(c_member(_1623254), _1623256), hAPP(c_List_Oset(_1623254), _1623258))), 42413 ^ _780478 : [(42416 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1623254), _1623258), 42412 ^ [_1623254, _1623256, _1623258]) = _1623256)], (42414 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42412 ^ [_1623254, _1623256, _1623258]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623254)), _1623258))))]]], (16004 ^ _780478) ^ [_1069977, _1069979, _1069981] : [class_Lattices_Olattice(_1069977), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1069977), _1069979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069977), _1069979), _1069981)) = _1069979)], (6568 ^ _780478) ^ [_887921, _887923, _887925] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_887921), _887923)), 6571 ^ _780478 : [(6578 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_887921), _887925)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_887921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887921, tc_HOL_Obool)), _887925), _887923))))], (6572 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_887921), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887921, tc_HOL_Obool)), _887925), _887923))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_887921), _887925)))]]], (18660 ^ _780478) ^ [_1130883, _1130885, _1130887, _1130889, _1130891] : [-(_1130883 = c_Orderings_Obot__class_Obot(tc_fun(_1130885, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130887, tc_HOL_Obool)), _1130889), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1130885, tc_fun(_1130887, tc_HOL_Obool)), _1130883), _1130891)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130885, tc_fun(_1130887, tc_HOL_Obool)), _1130883), hAPP(hAPP(c_COMBB(tc_fun(_1130887, tc_HOL_Obool), tc_fun(_1130887, tc_HOL_Obool), _1130885), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130887, tc_HOL_Obool)), _1130889)), _1130891)))], (7194 ^ _780478) ^ [_900466, _900468, _900470, _900472, _900474] : [class_Orderings_Oord(_900466), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900468, _900466)), _900470), _900472)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900466), hAPP(_900470, _900474)), hAPP(_900472, _900474))))], (40590 ^ _780478) ^ [_1574661, _1574663, _1574665, _1574667, _1574669] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574661, _1574661)), hAPP(hAPP(c_Product__Type_OPair(_1574661, _1574661), _1574663), _1574665)), _1574667)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1574661, _1574661)), hAPP(hAPP(c_Product__Type_OPair(_1574661, _1574661), _1574665), _1574669)), c_Transitive__Closure_Ortrancl(_1574661, _1574667))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574661, _1574661)), hAPP(hAPP(c_Product__Type_OPair(_1574661, _1574661), _1574663), _1574669)), c_Transitive__Closure_Ortrancl(_1574661, _1574667))))], (1204 ^ _780478) ^ [_798392, _798394] : [-(class_Groups_Oab__group__add(_798392)), _798394 = _798392, class_Groups_Oab__group__add(_798394)], (160 ^ _780478) ^ [_783080, _783082] : [-(class_Rings_Odivision__ring__inverse__zero(_783080)), _783082 = _783080, class_Rings_Odivision__ring__inverse__zero(_783082)], (7860 ^ _780478) ^ [_913856, _913858, _913860, _913862, _913864, _913866] : [c_Fun_Oinj__on(_913856, _913858, _913860, _913862), -(hBOOL(hAPP(hAPP(c_member(_913858), _913864), hAPP(c_Set_Oimage(_913856, _913858, _913860), _913862)))), -(c_Fun_Oinj__on(_913856, _913858, c_Fun_Ofun__upd(_913856, _913858, _913860, _913866, _913864), _913862))], (688 ^ _780478) ^ [_790854, _790856, _790858, _790860, _790862, _790864] : [-(c_List_Oall__interval__int(_790862, _790858, _790854)), c_List_Oall__interval__int(_790864, _790860, _790856), _790864 = _790862, _790860 = _790858, _790856 = _790854], (34443 ^ _780478) ^ [_1430057, _1430059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1430057), _1430059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1430057)), c_Int_OBit0(_1430059))))], (32094 ^ _780478) ^ [_1386534, _1386536, _1386538] : [class_Int_Onumber__ring(_1386534), class_Int_Oring__char__0(_1386534), 32101 ^ _780478 : [(32108 ^ _780478) ^ [] : [_1386536 = _1386538, -(hAPP(c_Int_Onumber__class_Onumber__of(_1386534), _1386536) = hAPP(c_Int_Onumber__class_Onumber__of(_1386534), _1386538))], (32102 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1386534), _1386536) = hAPP(c_Int_Onumber__class_Onumber__of(_1386534), _1386538), -(_1386536 = _1386538)]]], (5590 ^ _780478) ^ [_866084, _866086] : [_866086 = _866084, -(tc_Option_Ooption(_866086) = tc_Option_Ooption(_866084))], (46204 ^ _780478) ^ [_1710471, _1710473, _1710475] : [class_Groups_Oab__semigroup__add(_1710471), -(c_List_Ofoldr(_1710471, _1710471, c_Groups_Oplus__class_Oplus(_1710471), _1710473, _1710475) = hAPP(c_List_Ofoldl(_1710471, _1710471, c_Groups_Oplus__class_Oplus(_1710471), _1710475), _1710473))], (41156 ^ _780478) ^ [_1588310, _1588312, _1588314, _1588316, _1588318] : [c_Relation_Osingle__valued(_1588310, _1588312, hAPP(c_Relation_Oconverse(_1588312, _1588310), _1588314)), -(hAPP(c_Relation_OImage(_1588312, _1588310, _1588314), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1588312, tc_HOL_Obool)), _1588316), _1588318)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1588310, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1588312, _1588310, _1588314), _1588316)), hAPP(c_Relation_OImage(_1588312, _1588310, _1588314), _1588318)))], (47185 ^ _780478) ^ [_1729888, _1729890, _1729892] : [class_Orderings_Olinorder(_1729888), c_List_Olinorder__class_Osorted(_1729888, _1729890), -(c_List_Olinorder__class_Osorted(_1729888, c_List_OtakeWhile(_1729888, _1729892, _1729890)))], (37897 ^ _780478) ^ [_1505195, _1505197, _1505199, _1505201] : [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), _1505195), _1505197)), 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), _1505199), _1505201)), 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), _1505195), _1505201)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1505199), _1505197))))], (36806 ^ _780478) ^ [_1480561, _1480563, _1480565, _1480567, _1480569, _1480571, _1480573] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480561, _1480563), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1480565), _1480567))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480569, _1480563), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1480571), _1480573))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1480563)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1480561), _1480569), _1480563), 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), _1480565), _1480571)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1480567), _1480573)), _1480563))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1480567), _1480573), _1480563)))))], (51751 ^ _780478) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (6049 ^ _780478) ^ [_876722, _876724, _876726, _876728] : [-(hBOOL(hAPP(hAPP(c_member(_876722), _876724), _876726))), -(hBOOL(hAPP(hAPP(c_member(_876722), _876724), _876728))), 6056 ^ _780478 : [(6063 ^ _780478) ^ [] : [_876726 = _876728, -(hAPP(hAPP(c_Set_Oinsert(_876722), _876724), _876726) = hAPP(hAPP(c_Set_Oinsert(_876722), _876724), _876728))], (6057 ^ _780478) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_876722), _876724), _876726) = hAPP(hAPP(c_Set_Oinsert(_876722), _876724), _876728), -(_876726 = _876728)]]], (38007 ^ _780478) ^ [_1509041, _1509043, _1509045] : [38009 ^ _780478 : [(38012 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1509041), 38008 ^ [_1509041, _1509043, _1509045]), c_Wellfounded_Oacc(_1509041, _1509045)))], (38010 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1509041, _1509041)), hAPP(hAPP(c_Product__Type_OPair(_1509041, _1509041), 38008 ^ [_1509041, _1509043, _1509045]), _1509043)), _1509045)))]], -(hBOOL(hAPP(hAPP(c_member(_1509041), _1509043), c_Wellfounded_Oacc(_1509041, _1509045))))], (50034 ^ _780478) ^ [_1791823, _1791825, _1791827, _1791829, _1791831] : [c_Fun_Oinj__on(_1791823, _1791825, _1791827, _1791829), hBOOL(hAPP(hAPP(c_member(_1791823), _1791831), _1791829)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1791823, _1791825, _1791829, _1791827), hAPP(_1791827, _1791831)) = _1791831)], (30320 ^ _780478) ^ [_1343020, _1343022] : [class_Rings_Olinordered__idom(_1343020), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343020), hAPP(c_Groups_Oabs__class_Oabs(_1343020), _1343022)), hAPP(c_Groups_Oabs__class_Oabs(_1343020), _1343022)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343020), _1343022), _1343022))], (2210 ^ _780478) ^ [_812784, _812786, _812788, _812790] : [-(c_Nat__Transfer_Otsub(_812790, _812786) = c_Nat__Transfer_Otsub(_812788, _812784)), _812790 = _812788, _812786 = _812784], (38949 ^ _780478) ^ [_1533509, _1533511, _1533513, _1533515] : [-(_1533509 = c_Orderings_Obot__class_Obot(tc_fun(_1533511, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1533511, _1533513), _1533513, c_Product__Type_Osnd(_1533511, _1533513)), hAPP(hAPP(c_Product__Type_OSigma(_1533511, _1533513), _1533509), hAPP(c_COMBK(tc_fun(_1533513, tc_HOL_Obool), _1533511), _1533515))) = _1533515)], (49358 ^ _780478) ^ [_1777649, _1777651, _1777653] : [c_List_Olist__ex(_1777649, _1777651, _1777653), 49362 ^ _780478 : [(49365 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1777651, 49361 ^ [_1777649, _1777651, _1777653])))], (49363 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777649), 49361 ^ [_1777649, _1777651, _1777653]), hAPP(c_List_Oset(_1777649), _1777653))))]]], (38044 ^ _780478) ^ [_1510351, _1510353, _1510355, _1510357, _1510359] : [c_Typedef_Otype__definition(_1510351, _1510353, _1510355, _1510357, _1510359), -(hAPP(c_Set_Oimage(_1510351, _1510353, _1510355), c_Orderings_Otop__class_Otop(tc_fun(_1510351, tc_HOL_Obool))) = _1510359)], (31258 ^ _780478) ^ [_1362576, _1362578] : [-(hAPP(c_Set_OCollect(_1362576), hAPP(hAPP(c_COMBC(_1362576, _1362576, tc_HOL_Obool), c_fequal), _1362578)) = hAPP(hAPP(c_Set_Oinsert(_1362576), _1362578), c_Orderings_Obot__class_Obot(tc_fun(_1362576, tc_HOL_Obool))))], (46182 ^ _780478) ^ [_1709654, _1709656, _1709658, _1709660] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1709654, tc_Nat_Onat), _1709654), c_Product__Type_Ofst(_1709654, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1709654, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1709654, tc_Nat_Onat)), _1709656), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1709654, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1709654, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1709654, tc_Nat_Onat), _1709658), _1709660))) = hAPP(hAPP(c_List_Omap(tc_prod(_1709654, tc_Nat_Onat), _1709654), c_Product__Type_Ofst(_1709654, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1709654, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1709654, tc_Nat_Onat)), _1709656), c_Product__Type_Osnd(_1709654, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1709654, tc_Nat_Onat), _1709658), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1709660)))))], (19674 ^ _780478) ^ [_1147714] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147714) = _1147714)], (35507 ^ _780478) ^ [_1449045] : [class_Int_Onumber__ring(_1449045), -(hAPP(c_Int_Oring__1__class_Oof__int(_1449045), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1449045), c_Int_OMin))], (45875 ^ _780478) ^ [_1701501, _1701503, _1701505, _1701507] : [class_Orderings_Olinorder(_1701501), 45878 ^ _780478 : [(45885 ^ _780478) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1701503), _1701507)), -(hBOOL(hAPP(c_List_Odistinct(_1701503), c_List_Olinorder__class_Osort__key(_1701503, _1701501, _1701505, _1701507))))], (45879 ^ _780478) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1701503), c_List_Olinorder__class_Osort__key(_1701503, _1701501, _1701505, _1701507))), -(hBOOL(hAPP(c_List_Odistinct(_1701503), _1701507)))]]], (14983 ^ _780478) ^ [_1049799, _1049801, _1049803, _1049805, _1049807, _1049809] : [-(hBOOL(hAPP(hAPP(c_member(_1049799), _1049801), c_SetInterval_Oord_OatLeastLessThan(_1049799, _1049803, _1049805, _1049807, _1049809)))), hBOOL(hAPP(hAPP(_1049803, _1049807), _1049801)), hBOOL(hAPP(hAPP(_1049805, _1049801), _1049809))], (27082 ^ _780478) ^ [_1282357, _1282359, _1282361, _1282363] : [class_Fields_Olinordered__field(_1282357), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282357), c_Groups_Ozero__class_Ozero(_1282357)), _1282359)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282357), _1282361), _1282359)), _1282363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282357), _1282361), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1282357), _1282363), _1282359))))], (47183 ^ _780478) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (18572 ^ _780478) ^ [_1128820, _1128822] : [class_Complete__Lattice_Ocomplete__lattice(_1128820), -(c_Complete__Lattice_OInf__class_OInf(_1128820, hAPP(hAPP(c_Set_Oinsert(_1128820), _1128822), c_Orderings_Obot__class_Obot(tc_fun(_1128820, tc_HOL_Obool)))) = _1128822)], (23146 ^ _780478) ^ [_1211370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211370)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (45055 ^ _780478) ^ [_1683547, _1683549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1683547)), hAPP(c_Code__Numeral_Oof__nat, _1683549))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1683547), _1683549)))], (30290 ^ _780478) ^ [_1342437, _1342439] : [class_Groups_Oordered__ab__group__add__abs(_1342437), -(hAPP(c_Groups_Oabs__class_Oabs(_1342437), hAPP(c_Groups_Ouminus__class_Ouminus(_1342437), _1342439)) = hAPP(c_Groups_Oabs__class_Oabs(_1342437), _1342439))], (52053 ^ _780478) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (17624 ^ _780478) ^ [_1108380, _1108382, _1108384, _1108386, _1108388] : [class_Groups_Ocomm__monoid__mult(_1108380), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108382), _1108384)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108382), _1108386)), 17638 ^ _780478 : [(17641 ^ _780478) ^ [] : [hAPP(_1108388, 17637 ^ [_1108380, _1108382, _1108384, _1108386, _1108388]) = c_Groups_Oone__class_Oone(_1108380)], (17639 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1108382), 17637 ^ [_1108380, _1108382, _1108384, _1108386, _1108388]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1108382, tc_HOL_Obool)), _1108384), _1108386))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1108382, _1108380), _1108388), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1108382, tc_HOL_Obool)), _1108384), _1108386)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1108380), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1108382, _1108380), _1108388), _1108384)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1108382, _1108380), _1108388), _1108386)))], (41235 ^ _780478) ^ [_1590364, _1590366] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590364, _1590364), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590366) = c_Relation_OId(_1590364))], (43556 ^ _780478) ^ [_1650104, _1650106, _1650108] : [_1650108 = c_List_Olist_ONil(_1650106), -(_1650104 = hAPP(hAPP(c_List_Oappend(_1650106), _1650104), _1650108))], (45262 ^ _780478) ^ [_1687742, _1687744] : [-(hBOOL(hAPP(c_List_Olistsp(_1687742, _1687744), c_List_Olist_ONil(_1687742))))], (16568 ^ _780478) ^ [_1083214, _1083216, _1083218, _1083220] : [class_Lattices_Osemilattice__inf(_1083214), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083214), _1083216)), hBOOL(hAPP(hAPP(c_member(_1083214), _1083218), _1083216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083214), hAPP(hAPP(c_Finite__Set_Ofold(_1083214, _1083214, c_Lattices_Osemilattice__inf__class_Oinf(_1083214)), _1083220), _1083216)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1083214), _1083218), _1083220))))], (8878 ^ _780478) ^ [_933766, _933768, _933770] : [class_Orderings_Olinorder(_933766), -(_933768 = _933770), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933766), _933768), _933770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933766), _933770), _933768)))], (41251 ^ _780478) ^ [_1590640, _1590642, _1590644] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590640, _1590640)), hAPP(hAPP(c_Product__Type_OPair(_1590640, _1590640), _1590642), _1590642)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590640, _1590640), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590644))))], (48089 ^ _780478) ^ [_1749754, _1749756, _1749758] : [c_List_Olist__ex(_1749754, _1749756, _1749758), -(c_List_Olist__ex(_1749754, _1749756, hAPP(c_List_Orev(_1749754), _1749758)))], (12418 ^ _780478) ^ [_999733, _999735, _999737] : [class_Orderings_Olinorder(_999733), hBOOL(hAPP(c_Finite__Set_Ofinite(_999733), _999735)), -(_999735 = c_Orderings_Obot__class_Obot(tc_fun(_999733, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_999733), _999737)), -(_999737 = c_Orderings_Obot__class_Obot(tc_fun(_999733, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_999733, c_Orderings_Oord__class_Omin(_999733), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_999733, tc_HOL_Obool)), _999735), _999737)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_999733), c_Big__Operators_Olattice_OInf__fin(_999733, c_Orderings_Oord__class_Omin(_999733), _999735)), c_Big__Operators_Olattice_OInf__fin(_999733, c_Orderings_Oord__class_Omin(_999733), _999737)))], (5184 ^ _780478) ^ [_859699, _859701] : [_859701 = _859699, -(c_Finite__Set_Ocard(_859701) = c_Finite__Set_Ocard(_859699))], (2358 ^ _780478) ^ [_815016, _815018, _815020, _815022] : [-(c_Groups_Osgn__class_Osgn(_815022, _815018) = c_Groups_Osgn__class_Osgn(_815020, _815016)), _815022 = _815020, _815018 = _815016], (15445 ^ _780478) ^ [_1058772, _1058774, _1058776] : [class_Rings_Olinordered__semidom(_1058772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058772), c_Groups_Oone__class_Oone(_1058772)), _1058774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058772), c_Groups_Oone__class_Oone(_1058772)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1058772), _1058774), hAPP(hAPP(c_Power_Opower__class_Opower(_1058772), _1058774), _1058776)))))], (14054 ^ _780478) ^ [_1031679] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031679), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1031679)], (18602 ^ _780478) ^ [_1129459, _1129461, _1129463, _1129465, _1129467] : [-(_1129459 = c_Orderings_Obot__class_Obot(tc_fun(_1129461, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129461, tc_fun(_1129463, tc_HOL_Obool)), _1129459), hAPP(hAPP(c_COMBC(_1129461, tc_fun(_1129463, tc_HOL_Obool), tc_fun(_1129463, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1129463, tc_HOL_Obool), tc_fun(tc_fun(_1129463, tc_HOL_Obool), tc_fun(_1129463, tc_HOL_Obool)), _1129461), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129463, tc_HOL_Obool))), _1129465)), _1129467)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129463, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129461, tc_fun(_1129463, tc_HOL_Obool)), _1129459), _1129465)), _1129467))], (33382 ^ _780478) ^ [_1410710] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410710), 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), _1410710)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1410710)))], (2724 ^ _780478) ^ [_820687, _820689, _820691, _820693, _820695, _820697, _820699, _820701] : [-(c_Product__Type_Oapfst(_820701, _820697, _820693, _820689) = c_Product__Type_Oapfst(_820699, _820695, _820691, _820687)), _820701 = _820699, _820697 = _820695, _820693 = _820691, _820689 = _820687], (11885 ^ _780478) ^ [_989328, _989330, _989332] : [class_Orderings_Olinorder(_989328), hBOOL(hAPP(c_Finite__Set_Ofinite(_989328), _989330)), hBOOL(hAPP(hAPP(c_member(_989328), _989332), _989330)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_989328), _989332), c_Big__Operators_Olattice_OInf__fin(_989328, c_Orderings_Oord__class_Omin(_989328), _989330)) = c_Big__Operators_Olattice_OInf__fin(_989328, c_Orderings_Oord__class_Omin(_989328), _989330))], (48257 ^ _780478) ^ [_1753149, _1753151, _1753153, _1753155] : [-(c_List_Olist__all(_1753149, _1753151, hAPP(hAPP(c_List_Olist_OCons(_1753149), _1753153), _1753155))), hBOOL(hAPP(_1753151, _1753153)), c_List_Olist__all(_1753149, _1753151, _1753155)], (6124 ^ _780478) ^ [_878179] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_878179), c_Orderings_Obot__class_Obot(tc_fun(_878179, tc_HOL_Obool)))))], (18544 ^ _780478) ^ [_1128307, _1128309] : [class_Lattices_Olattice(_1128307), -(c_Big__Operators_Olattice__class_OInf__fin(_1128307, hAPP(hAPP(c_Set_Oinsert(_1128307), _1128309), c_Orderings_Obot__class_Obot(tc_fun(_1128307, tc_HOL_Obool)))) = _1128309)], (1814 ^ _780478) ^ [_806017, _806019] : [-(class_Orderings_Oorder(_806017)), _806019 = _806017, class_Orderings_Oorder(_806019)], (38660 ^ _780478) ^ [_1524846, _1524848, _1524850] : [-(hAPP(c_Set_Oimage(tc_prod(_1524846, _1524848), _1524846, c_Product__Type_Ofst(_1524846, _1524848)), _1524850) = hAPP(c_Relation_ODomain(_1524846, _1524848), _1524850))], (49205 ^ _780478) ^ [_1774416, _1774418] : [49208 ^ _780478 : [(49214 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774416, _1774416)), hAPP(hAPP(c_Product__Type_OPair(_1774416, _1774416), 49206 ^ [_1774416, _1774418]), 49210 ^ [_1774416, _1774418])), _1774418))], (49212 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774416, _1774416)), hAPP(hAPP(c_Product__Type_OPair(_1774416, _1774416), 49207 ^ [_1774416, _1774418]), 49210 ^ [_1774416, _1774418])), _1774418)))], (49209 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774416, _1774416)), hAPP(hAPP(c_Product__Type_OPair(_1774416, _1774416), 49206 ^ [_1774416, _1774418]), 49207 ^ [_1774416, _1774418])), _1774418)))]], -(c_Relation_Otrans(_1774416, _1774418))], (45227 ^ _780478) ^ [_1686834, _1686836, _1686838, _1686840, _1686842] : [class_Groups_Omonoid__add(_1686834), class_Groups_Oordered__ab__semigroup__add(_1686834), 45237 ^ _780478 : [(45240 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1686834), hAPP(_1686840, 45236 ^ [_1686834, _1686836, _1686838, _1686840, _1686842])), hAPP(_1686842, 45236 ^ [_1686834, _1686836, _1686838, _1686840, _1686842])))], (45238 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1686836), 45236 ^ [_1686834, _1686836, _1686838, _1686840, _1686842]), hAPP(c_List_Oset(_1686836), _1686838))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1686834), hAPP(c_List_Omonoid__add__class_Olistsum(_1686834), hAPP(hAPP(c_List_Omap(_1686836, _1686834), _1686840), _1686838))), hAPP(c_List_Omonoid__add__class_Olistsum(_1686834), hAPP(hAPP(c_List_Omap(_1686836, _1686834), _1686842), _1686838)))))], (19234 ^ _780478) ^ [_1141291, _1141293] : [class_Rings_Ocomm__semiring__1(_1141291), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141291), _1141293), c_Groups_Ozero__class_Ozero(_1141291)) = c_Groups_Ozero__class_Ozero(_1141291))], (8976 ^ _780478) ^ [_934889, _934891, _934893, _934895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934889, tc_HOL_Obool)), _934891), _934893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934889, tc_HOL_Obool)), _934893), _934895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934889, tc_HOL_Obool)), _934891), _934895)))], (40917 ^ _780478) ^ [_1582069, _1582071] : [-(c_Transitive__Closure_Ortrancl(_1582069, hAPP(c_Relation_Oconverse(_1582069, _1582069), _1582071)) = hAPP(c_Relation_Oconverse(_1582069, _1582069), c_Transitive__Closure_Ortrancl(_1582069, _1582071)))], (40498 ^ _780478) ^ [_1572424, _1572426, _1572428] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572424, _1572424)), _1572426), _1572428)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572424, _1572424)), _1572426), c_Transitive__Closure_Ortrancl(_1572424, _1572428))))], (45129 ^ _780478) ^ [_1685145, _1685147] : [-(c_Random_Oselect(_1685145, _1685147) = 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(_1685145, 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(_1685145)), _1685147)))), hAPP(hAPP(c_COMBB(_1685145, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1685145, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1685145, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1685145, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1685145), _1685147)), c_Code__Numeral_Onat__of))))], (9838 ^ _780478) ^ [_950731, _950733, _950735, _950737, _950739] : [class_Rings_Ocomm__semiring__1(_950731), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950731), _950733), _950735)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950731), _950737), _950739)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950731), _950733), _950737)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_950731), _950735), _950739)))], (27583 ^ _780478) ^ [_1290454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1290454)), -(c_Nat__Transfer_Ois__nat(_1290454))], (6614 ^ _780478) ^ [_888935, _888937, _888939, _888941] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888935, tc_HOL_Obool)), _888937), hAPP(hAPP(c_Set_Oinsert(_888935), _888939), _888941)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888935, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_888935, tc_HOL_Obool)), _888937), hAPP(hAPP(c_Set_Oinsert(_888935), _888939), c_Orderings_Obot__class_Obot(tc_fun(_888935, tc_HOL_Obool))))), _888941))], (30628 ^ _780478) ^ [_1348974, _1348976] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1348974), _1348976)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1348974) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (1664 ^ _780478) ^ [_804142, _804144] : [-(class_Rings_Ono__zero__divisors(_804142)), _804144 = _804142, class_Rings_Ono__zero__divisors(_804144)], (23615 ^ _780478) ^ [_1219337, _1219339, _1219341] : [class_Orderings_Oorder(_1219337), 23618 ^ _780478 : [(23625 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219337), _1219339), _1219341))), -(c_Orderings_Obot__class_Obot(tc_fun(_1219337, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219337, _1219339), _1219341))], (23619 ^ _780478) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1219337, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1219337, _1219339), _1219341), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219337), _1219339), _1219341))]]], (42203 ^ _780478) ^ [_1618202, _1618204, _1618206, _1618208] : [_1618202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1618204), hAPP(hAPP(c_List_Olist_OCons(_1618204), _1618206), _1618208)), _1618202) = _1618206)], (21420 ^ _780478) ^ [_1178209, _1178211, _1178213, _1178215] : [class_Rings_Olinordered__ring__strict(_1178209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178209), _1178211), c_Groups_Ozero__class_Ozero(_1178209))), 21427 ^ _780478 : [(21434 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178209), _1178215), _1178213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178209), _1178211), _1178213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178209), _1178211), _1178215))))], (21428 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178209), _1178211), _1178213)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178209), _1178211), _1178215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178209), _1178215), _1178213)))]]], (44767 ^ _780478) ^ [_1677216, _1677218, _1677220] : [class_Groups_Omonoid__add(_1677216), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677216), hAPP(hAPP(c_List_Omap(_1677218, _1677216), hAPP(c_COMBK(_1677216, _1677218), c_Groups_Ozero__class_Ozero(_1677216))), _1677220)) = c_Groups_Ozero__class_Ozero(_1677216))], (32306 ^ _780478) ^ [_1390910, _1390912, _1390914] : [class_Int_Onumber__ring(_1390910), -(hAPP(c_Int_Onumber__class_Onumber__of(_1390910), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1390912), _1390914)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1390910), hAPP(c_Int_Onumber__class_Onumber__of(_1390910), _1390912)), hAPP(c_Int_Onumber__class_Onumber__of(_1390910), _1390914)))], (46657 ^ _780478) ^ [_1718833, _1718835, _1718837, _1718839, _1718841] : [class_Orderings_Olinorder(_1718833), c_List_Olinorder__class_Osorted(_1718833, hAPP(hAPP(c_List_Omap(_1718835, _1718833), _1718837), _1718839)), -(c_List_Olinorder__class_Osorted(_1718833, hAPP(hAPP(c_List_Omap(_1718835, _1718833), _1718837), hAPP(c_List_Ofilter(_1718835, _1718841), _1718839))))], (37838 ^ _780478) ^ [_1503596, _1503598, _1503600, _1503602] : [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), _1503596), _1503598)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1503600), _1503602))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1503596), _1503602) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1503600), _1503598))], (51337 ^ _780478) ^ [_1820457, _1820459, _1820461] : [class_Rings_Odvd(_1820457), class_Rings_Osemiring__0(_1820457), 51344 ^ _780478 : [(51354 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1820459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1820457), _1820461), 51361 ^ [_1820457, _1820459, _1820461])))), 51355 ^ _780478 : [(51356 ^ _780478) ^ [_1820786] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820457), _1820461), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1820457), _1820786), c_Groups_Ozero__class_Ozero(_1820457)))), hBOOL(hAPP(_1820459, _1820786))]]], (51345 ^ _780478) ^ [] : [51346 ^ _780478 : [(51347 ^ _780478) ^ [_1820649] : [hBOOL(hAPP(_1820459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1820457), _1820461), _1820649)))]], 51349 ^ _780478 : [(51352 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1820459, 51348 ^ [_1820457, _1820459, _1820461])))], (51350 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820457), _1820461), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1820457), 51348 ^ [_1820457, _1820459, _1820461]), c_Groups_Ozero__class_Ozero(_1820457)))))]]]]], (51885 ^ _780478) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (46380 ^ _780478) ^ [_1713922] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1713922) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1713922))))], (1754 ^ _780478) ^ [_805267, _805269] : [-(class_Orderings_Olinorder(_805267)), _805269 = _805267, class_Orderings_Olinorder(_805269)], (34049 ^ _780478) ^ [_1423349] : [class_Int_Onumber__ring(_1423349), -(hAPP(c_Int_Onumber__class_Onumber__of(_1423349), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1423349))], (8330 ^ _780478) ^ [_923297, _923299, _923301, _923303] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_923297, _923299, _923301), _923303)), _923301 = c_Orderings_Obot__class_Obot(tc_fun(_923297, tc_HOL_Obool))], (31126 ^ _780478) ^ [_1359664, _1359666, _1359668] : [hBOOL(hAPP(_1359664, _1359666)), -(hBOOL(hAPP(hAPP(c_member(_1359668), _1359666), hAPP(c_Set_OCollect(_1359668), _1359664))))], (20136 ^ _780478) ^ [_1156070, _1156072, _1156074, _1156076, _1156078] : [class_Rings_Oordered__semiring(_1156070), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156070), _1156072), _1156074)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156070), _1156076), _1156078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156070), c_Groups_Ozero__class_Ozero(_1156070)), _1156074)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156070), c_Groups_Ozero__class_Ozero(_1156070)), _1156076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156070), _1156072), _1156076)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156070), _1156074), _1156078))))], (26416 ^ _780478) ^ [_1270149, _1270151, _1270153, _1270155, _1270157] : [class_Fields_Ofield(_1270149), -(_1270151 = c_Groups_Ozero__class_Ozero(_1270149)), -(_1270153 = c_Groups_Ozero__class_Ozero(_1270149)), 26427 ^ _780478 : [(26434 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270149), _1270155), _1270153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270149), _1270157), _1270151), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270149), _1270155), _1270151) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270149), _1270157), _1270153))], (26428 ^ _780478) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270149), _1270155), _1270151) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270149), _1270157), _1270153), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270149), _1270155), _1270153) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270149), _1270157), _1270151))]]], (29011 ^ _780478) ^ [_1318158, _1318160] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1318158, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1318158, tc_HOL_Obool))), hAPP(c_Set_OPow(_1318158), _1318160))))], (33174 ^ _780478) ^ [_1407295, _1407297, _1407299] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407295)))), 33177 ^ _780478 : [(33184 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407297)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407295)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407297)), _1407299)) = 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), _1407295), _1407297))), _1407299))], (33178 ^ _780478) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407297))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407295)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407297)), _1407299)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407295)), _1407299))]]], (35798 ^ _780478) ^ [_1459873, _1459875, _1459877, _1459879, _1459881, _1459883] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1459875, _1459877)), hAPP(hAPP(c_Product__Type_OPair(_1459875, _1459877), _1459881), _1459883)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1459873, tc_fun(tc_prod(_1459875, _1459877), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1459873, tc_HOL_Obool))), _1459879))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1459873, tc_fun(_1459875, tc_fun(_1459877, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1459873, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1459875, _1459877), tc_HOL_Obool), tc_fun(_1459875, tc_fun(_1459877, tc_HOL_Obool)), _1459873), hAPP(c_COMBC(_1459875, tc_fun(tc_prod(_1459875, _1459877), tc_HOL_Obool), tc_fun(_1459877, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459877, tc_fun(tc_fun(tc_prod(_1459875, _1459877), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1459875, _1459877), tc_HOL_Obool), tc_fun(_1459877, tc_HOL_Obool)), _1459875), c_COMBC(_1459877, tc_fun(tc_prod(_1459875, _1459877), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459877, tc_prod(_1459875, _1459877)), tc_fun(_1459877, tc_fun(tc_fun(tc_prod(_1459875, _1459877), tc_HOL_Obool), tc_HOL_Obool)), _1459875), hAPP(c_COMBB(tc_prod(_1459875, _1459877), tc_fun(tc_fun(tc_prod(_1459875, _1459877), tc_HOL_Obool), tc_HOL_Obool), _1459877), c_member(tc_prod(_1459875, _1459877)))), c_Product__Type_OPair(_1459875, _1459877))))), _1459879)), _1459881), _1459883)))], (4830 ^ _780478) ^ [_854104, _854106, _854108, _854110, _854112, _854114] : [-(c_Relation_OImage(_854114, _854110, _854106) = c_Relation_OImage(_854112, _854108, _854104)), _854114 = _854112, _854110 = _854108, _854106 = _854104], (7080 ^ _780478) ^ [_898679, _898681, _898683, _898685] : [class_Orderings_Opreorder(_898679), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898679), _898681), _898683)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898679), _898683), _898685)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898679), _898681), _898685)))], (28948 ^ _780478) ^ [_1316749, _1316751, _1316753, _1316755, _1316757] : [class_Groups_Ocomm__monoid__add(_1316749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316751), _1316753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316751, tc_HOL_Obool)), _1316755), _1316753)), 28962 ^ _780478 : [(28965 ^ _780478) ^ [] : [hAPP(_1316757, 28961 ^ [_1316749, _1316751, _1316753, _1316755, _1316757]) = c_Groups_Ozero__class_Ozero(_1316749)], (28963 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1316751), 28961 ^ [_1316749, _1316751, _1316753, _1316755, _1316757]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316751, tc_HOL_Obool)), _1316753), _1316755))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316751, _1316749), _1316757), _1316755) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316751, _1316749), _1316757), _1316753))], (19216 ^ _780478) ^ [_1140994, _1140996] : [class_Rings_Omult__zero(_1140994), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140994), c_Groups_Ozero__class_Ozero(_1140994)), _1140996) = c_Groups_Ozero__class_Ozero(_1140994))], (13172 ^ _780478) ^ [_1014195, _1014197, _1014199, _1014201, _1014203] : [-(hAPP(c_Set_Oimage(_1014195, _1014197, _1014199), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014195, tc_HOL_Obool)), _1014201), _1014203)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014197, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1014195, _1014197, _1014199), _1014201)), hAPP(c_Set_Oimage(_1014195, _1014197, _1014199), _1014203)))], (48479 ^ _780478) ^ [_1758034, _1758036, _1758038, _1758040, _1758042] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1758034, _1758036, _1758038), _1758040), _1758042)), -(hBOOL(hAPP(hAPP(_1758038, _1758042), _1758040)))], (48751 ^ _780478) ^ [_1763885, _1763887, _1763889] : [class_Fields_Olinordered__field(_1763885), 48757 ^ _780478 : [(48760 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1763885), _1763887), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1763885), _1763889), 48756 ^ [_1763885, _1763887, _1763889])))], (48758 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1763885), c_Groups_Ozero__class_Ozero(_1763885)), 48756 ^ [_1763885, _1763887, _1763889])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1763885), _1763887), _1763889)))], (38238 ^ _780478) ^ [] : [-(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)))))], (36606 ^ _780478) ^ [_1476546, _1476548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1476546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1476546), _1476548)), -(c_Divides_Odivmod__nat(_1476548, _1476546) = 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), _1476548), _1476546)), _1476546))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1476548), _1476546), _1476546)))], (50119 ^ _780478) ^ [_1793862, _1793864, _1793866, _1793868] : [c_Fun_Oinj__on(_1793862, _1793864, _1793866, c_Orderings_Otop__class_Otop(tc_fun(_1793862, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1793864, _1793862, c_Hilbert__Choice_Oinv__into(_1793862, _1793864, c_Orderings_Otop__class_Otop(tc_fun(_1793862, tc_HOL_Obool)), _1793866)), hAPP(c_Set_Oimage(_1793862, _1793864, _1793866), _1793868)) = _1793868)], (37187 ^ _780478) ^ [_1487910, _1487912, _1487914, _1487916] : [-(hAPP(c_Product__Type_Ofst(_1487910, _1487912), hAPP(hAPP(c_Product__Type_OPair(_1487910, _1487912), _1487914), _1487916)) = _1487914)], (13843 ^ _780478) ^ [_1027992, _1027994, _1027996] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027992), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027994), _1027996))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027992), _1027996)), _1027994)))], (48433 ^ _780478) ^ [_1757037, _1757039, _1757041, _1757043, _1757045] : [-(c_List_Osplice(_1757037, hAPP(hAPP(c_List_Olist_OCons(_1757037), _1757039), _1757041), hAPP(hAPP(c_List_Olist_OCons(_1757037), _1757043), _1757045)) = hAPP(hAPP(c_List_Olist_OCons(_1757037), _1757039), hAPP(hAPP(c_List_Olist_OCons(_1757037), _1757043), c_List_Osplice(_1757037, _1757041, _1757045))))], (23251 ^ _780478) ^ [_1213214, _1213216] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1213214)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213216))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1213214), _1213216)))], (6003 ^ _780478) ^ [_875979, _875981, _875983] : [_875979 = c_Orderings_Obot__class_Obot(tc_fun(_875981, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_875981), _875983), _875979))], (36194 ^ _780478) ^ [_1468603, _1468605, _1468607, _1468609, _1468611, _1468613] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1468603, tc_fun(_1468605, tc_HOL_Obool))), _1468607), _1468609), _1468611), _1468613)), -(hBOOL(hAPP(hAPP(_1468607, _1468611), _1468613))), -(hBOOL(hAPP(hAPP(_1468609, _1468611), _1468613)))], (15771 ^ _780478) ^ [_1065687, _1065689, _1065691, _1065693] : [class_Lattices_Olattice(_1065687), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065687), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065687), _1065689), _1065691)), _1065693) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065687), _1065689), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065687), _1065691), _1065693)))], (48509 ^ _780478) ^ [_1758615, _1758617, _1758619, _1758621] : [-(c_Predicate_Oconversep(_1758615, _1758617, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1758615, tc_fun(_1758617, tc_HOL_Obool))), _1758619), _1758621)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1758617, tc_fun(_1758615, tc_HOL_Obool))), c_Predicate_Oconversep(_1758615, _1758617, _1758619)), c_Predicate_Oconversep(_1758615, _1758617, _1758621)))], (17422 ^ _780478) ^ [_1102947, _1102949, _1102951, _1102953, _1102955] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102947, tc_fun(_1102949, tc_HOL_Obool)), _1102951), hAPP(hAPP(c_COMBB(tc_fun(_1102949, tc_HOL_Obool), tc_fun(_1102949, tc_HOL_Obool), _1102947), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102949, tc_HOL_Obool)), _1102953)), _1102955)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102949, tc_HOL_Obool)), _1102953), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1102947, tc_fun(_1102949, tc_HOL_Obool)), _1102951), _1102955)))], (17679 ^ _780478) ^ [_1109596, _1109598, _1109600] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1109596), _1109598)), hBOOL(hAPP(hAPP(c_member(_1109596), _1109600), _1109598)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1109596), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1109596, tc_HOL_Obool)), _1109598), hAPP(hAPP(c_Set_Oinsert(_1109596), _1109600), c_Orderings_Obot__class_Obot(tc_fun(_1109596, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1109596), _1109598))], (44682 ^ _780478) ^ [_1674423, _1674425, _1674427, _1674429, _1674431, _1674433, _1674435] : [-(hAPP(c_List_Ofoldl(_1674423, _1674425, _1674427, _1674429), hAPP(hAPP(c_List_Omap(_1674431, _1674425), _1674433), _1674435)) = hAPP(c_List_Ofoldl(_1674423, _1674431, hAPP(hAPP(c_COMBC(_1674423, tc_fun(_1674431, _1674425), tc_fun(_1674431, _1674423)), hAPP(hAPP(c_COMBB(tc_fun(_1674425, _1674423), tc_fun(tc_fun(_1674431, _1674425), tc_fun(_1674431, _1674423)), _1674423), c_COMBB(_1674425, _1674423, _1674431)), _1674427)), _1674433), _1674429), _1674435))], (15753 ^ _780478) ^ [_1065258, _1065260, _1065262, _1065264] : [class_Lattices_Olattice(_1065258), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065258), _1065260), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065258), _1065262), _1065264)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065258), _1065262), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065258), _1065260), _1065264)))], (52015 ^ _780478) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (23227 ^ _780478) ^ [_1212772, _1212774] : [_1212772 = _1212774, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212772) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212774))], (48772 ^ _780478) ^ [_1764321, _1764323] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1764321), _1764323))), -(c_Lazy__Sequence_Osmall__lazy_H(_1764321, _1764323) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1764323), c_Lazy__Sequence_Osmall__lazy_H(_1764321, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1764323), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48535 ^ _780478) ^ [_1759779, _1759781, _1759783] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759779)), c_List_Oreplicate(_1759779, _1759781, _1759783)) = _1759781)], (11143 ^ _780478) ^ [_975281, _975283, _975285, _975287, _975289] : [class_Groups_Ocomm__monoid__mult(_975281), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_975283, _975281), hAPP(hAPP(c_COMBS(_975283, _975281, _975281), hAPP(hAPP(c_COMBB(_975281, tc_fun(_975281, _975281), _975283), c_Groups_Otimes__class_Otimes(_975281)), _975285)), _975287)), _975289) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975281), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_975283, _975281), _975285), _975289)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_975283, _975281), _975287), _975289)))], (10347 ^ _780478) ^ [_960998, _961000, _961002, _961004] : [class_Groups_Ouminus(_960998), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_961000, _960998)), _961002), _961004) = hAPP(c_Groups_Ouminus__class_Ouminus(_960998), hAPP(_961002, _961004)))], (36391 ^ _780478) ^ [_1473019, _1473021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1473019), 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)), _1473021)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1473019, _1473021), c_Divides_OnegDivAlg(_1473019, _1473021))))], (15595 ^ _780478) ^ [_1062020, _1062022, _1062024, _1062026, _1062028, _1062030] : [hBOOL(hAPP(hAPP(c_member(_1062020), _1062022), _1062024)), hBOOL(hAPP(hAPP(_1062026, _1062022), _1062028)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1062020, tc_fun(_1062030, tc_HOL_Obool)), _1062024), _1062026), _1062028)))], (35395 ^ _780478) ^ [_1447371, _1447373] : [class_Int_Onumber__ring(_1447371), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1447371), hAPP(c_Int_Onumber__class_Onumber__of(_1447371), c_Int_OMin)), _1447373) = hAPP(c_Groups_Ouminus__class_Ouminus(_1447371), _1447373))], (14647 ^ _780478) ^ [_1042378, _1042380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042378), _1042380)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042378), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042380), _1042378)) = _1042380)], (42676 ^ _780478) ^ [_1631099, _1631101, _1631103] : [hBOOL(hAPP(hAPP(c_member(_1631099), _1631101), hAPP(c_List_Oset(_1631099), c_List_Obutlast(_1631099, _1631103)))), -(hBOOL(hAPP(hAPP(c_member(_1631099), _1631101), hAPP(c_List_Oset(_1631099), _1631103))))], (35371 ^ _780478) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (15085 ^ _780478) ^ [_1052024, _1052026] : [-(hBOOL(hAPP(hAPP(c_member(_1052024), _1052026), c_Orderings_Otop__class_Otop(tc_fun(_1052024, tc_HOL_Obool)))))], (26754 ^ _780478) ^ [_1276105, _1276107, _1276109, _1276111] : [class_Fields_Olinordered__field(_1276105), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276105), c_Groups_Ozero__class_Ozero(_1276105)), _1276107)), 26761 ^ _780478 : [(26768 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276105), _1276109), _1276107)), _1276111)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276105), _1276109), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276105), _1276111), _1276107))))], (26762 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276105), _1276109), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276105), _1276111), _1276107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276105), _1276109), _1276107)), _1276111)))]]], (42471 ^ _780478) ^ [_1626201, _1626203, _1626205, _1626207, _1626209] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1626201, _1626203)), _1626205), hAPP(hAPP(c_List_Ozip(_1626201, _1626203), _1626207), _1626209)) = hAPP(hAPP(c_List_Ozip(_1626201, _1626203), hAPP(hAPP(c_List_Otake(_1626201), _1626205), _1626207)), hAPP(hAPP(c_List_Otake(_1626203), _1626205), _1626209)))], (52263 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (26374 ^ _780478) ^ [_1269356, _1269358, _1269360] : [class_Fields_Olinordered__field(_1269356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269356), _1269358), c_Groups_Ozero__class_Ozero(_1269356))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269356), _1269360), c_Groups_Ozero__class_Ozero(_1269356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1269356), c_Groups_Ozero__class_Ozero(_1269356)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269356), _1269358), _1269360))))], (52271 ^ _780478) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (20931 ^ _780478) ^ [_1170210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170210)), -(_1170210 = hAPP(c_Nat_OSuc, 20934 ^ [_1170210]))], (30262 ^ _780478) ^ [_1341949, _1341951, _1341953] : [class_Groups_Oordered__ab__group__add__abs(_1341949), -(hAPP(c_Groups_Oabs__class_Oabs(_1341949), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1341949), _1341951), _1341953)) = hAPP(c_Groups_Oabs__class_Oabs(_1341949), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1341949), _1341953), _1341951)))], (11359 ^ _780478) ^ [_979343, _979345, _979347, _979349, _979351] : [class_Groups_Ocomm__monoid__mult(_979343), hBOOL(hAPP(c_Finite__Set_Ofinite(_979345), _979347)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_979345, _979343), hAPP(hAPP(c_COMBS(_979345, _979343, _979343), hAPP(hAPP(c_COMBB(_979343, tc_fun(_979343, _979343), _979345), c_Groups_Otimes__class_Otimes(_979343)), _979349)), _979351)), _979347) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979343), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_979345, _979343), _979349), _979347)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_979345, _979343), _979351), _979347)))], (27898 ^ _780478) ^ [_1296412, _1296414, _1296416, _1296418, _1296420] : [class_Orderings_Oorder(_1296412), 27901 ^ _780478 : [(27914 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296412, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1296412, _1296414, _1296416)), c_SetInterval_Oord__class_OatLeastAtMost(_1296412, _1296418, _1296420)))), 27915 ^ _780478 : [(27918 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296412), _1296418), _1296414)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296412), _1296416), _1296420))], (27916 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296412), _1296414), _1296416)))]]], (27902 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1296412, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1296412, _1296414, _1296416)), c_SetInterval_Oord__class_OatLeastAtMost(_1296412, _1296418, _1296420))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296412), _1296414), _1296416)), 27909 ^ _780478 : [(27912 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296412), _1296416), _1296420)))], (27910 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1296412), _1296418), _1296414)))]]]]], (40895 ^ _780478) ^ [_1581557, _1581559, _1581561, _1581563, _1581565] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581557, _1581559)), hAPP(hAPP(c_Product__Type_OPair(_1581557, _1581559), _1581561), _1581563)), hAPP(c_Relation_Oconverse(_1581559, _1581557), _1581565))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581559, _1581557)), hAPP(hAPP(c_Product__Type_OPair(_1581559, _1581557), _1581563), _1581561)), _1581565)))], (38824 ^ _780478) ^ [_1530232, _1530234, _1530236, _1530238, _1530240] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530232, _1530234), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1530232, tc_HOL_Obool)), _1530236), _1530238)), _1530240) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1530232, _1530234), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530232, _1530234), _1530236), _1530240)), hAPP(hAPP(c_Product__Type_OSigma(_1530232, _1530234), _1530238), _1530240)))], (12524 ^ _780478) ^ [_1001509] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1001509)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1001509), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1001509), c_Orderings_Otop__class_Otop(tc_fun(_1001509, tc_HOL_Obool)))))], (49151 ^ _780478) ^ [_1773096, _1773098, _1773100, _1773102, _1773104] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1773096), tc_List_Olist(_1773096))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773096), tc_List_Olist(_1773096)), _1773098), _1773100)), c_List_Olexord(_1773096, _1773102))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1773096), tc_List_Olist(_1773096))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773096), tc_List_Olist(_1773096)), _1773100), _1773104)), c_List_Olexord(_1773096, _1773102))), c_Relation_Otrans(_1773096, _1773102), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1773096), tc_List_Olist(_1773096))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1773096), tc_List_Olist(_1773096)), _1773098), _1773104)), c_List_Olexord(_1773096, _1773102))))], (51567 ^ _780478) ^ [_1824395] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824395), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1824395 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1424 ^ _780478) ^ [_801142, _801144] : [-(class_Lattices_Olattice(_801142)), _801144 = _801142, class_Lattices_Olattice(_801144)], (14773 ^ _780478) ^ [_1045030, _1045032, _1045034, _1045036, _1045038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045030), _1045032)), 14776 ^ _780478 : [(14783 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045036), 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), _1045032), _1045030)), _1045034)), _1045038))), -(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), _1045030), _1045034)), _1045036)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045032), _1045034)), _1045038))))], (14777 ^ _780478) ^ [] : [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), _1045030), _1045034)), _1045036)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045032), _1045034)), _1045038))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1045036), 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), _1045032), _1045030)), _1045034)), _1045038))))]]], (18972 ^ _780478) ^ [_1136616] : [-(hAPP(c_Nat_OSuc, _1136616) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1136616))], (52111 ^ _780478) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (49325 ^ _780478) ^ [_1777027] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1777027, tc_HOL_Obool) = c_Set_OBex(_1777027))], (2000 ^ _780478) ^ [_809429, _809431, _809433, _809435, _809437, _809439] : [-(c_Partial__Function_Oflat__lub(_809439, _809435, _809431) = c_Partial__Function_Oflat__lub(_809437, _809433, _809429)), _809439 = _809437, _809435 = _809433, _809431 = _809429], (43151 ^ _780478) ^ [_1640829, _1640831, _1640833] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1640829, tc_HOL_Obool)), hAPP(c_List_Oset(_1640829), c_List_Oremove1(_1640829, _1640831, _1640833))), hAPP(c_List_Oset(_1640829), _1640833))))], (31765 ^ _780478) ^ [_1380612, _1380614, _1380616, _1380618] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1380612, tc_Nat_Onat), _1380614), _1380616) = hAPP(c_Nat_OSuc, _1380618), 31769 ^ _780478 : [(31772 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1380614, 31768 ^ [_1380612, _1380614, _1380616, _1380618]))))], (31770 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1380612), 31768 ^ [_1380612, _1380614, _1380616, _1380618]), _1380616)))]]], (52001 ^ _780478) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (24783 ^ _780478) ^ [_1240958, _1240960, _1240962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1240958), _1240960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240958), _1240962)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240960), _1240962))))], (47065 ^ _780478) ^ [_1727264, _1727266, _1727268, _1727270] : [hAPP(c_List_Orev(_1727264), _1727266) = hAPP(hAPP(c_List_Olist_OCons(_1727264), _1727268), _1727270), -(_1727266 = hAPP(hAPP(c_List_Oappend(_1727264), hAPP(c_List_Orev(_1727264), _1727270)), hAPP(hAPP(c_List_Olist_OCons(_1727264), _1727268), c_List_Olist_ONil(_1727264))))], (32126 ^ _780478) ^ [_1387210, _1387212, _1387214] : [c_Com_Ocom_OLocal(_1387210, _1387212, _1387214) = c_Com_Ocom_OSKIP], (14271 ^ _780478) ^ [_1035466, _1035468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1035466), _1035468)), 14274 ^ _780478 : [(14277 ^ _780478) ^ [] : [_1035466 = _1035468], (14275 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1035466), _1035468)))]]], (41742 ^ _780478) ^ [_1604081, _1604083, _1604085] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604081)), hAPP(hAPP(c_List_Olist_OCons(_1604081), _1604083), _1604085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604081)), _1604085)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31266 ^ _780478) ^ [_1362800, _1362802, _1362804] : [-(hBOOL(hAPP(_1362800, _1362802))), -(hAPP(c_Set_OCollect(_1362804), hAPP(hAPP(c_COMBS(_1362804, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1362804), c_fconj), hAPP(c_fequal, _1362802))), _1362800)) = c_Orderings_Obot__class_Obot(tc_fun(_1362804, tc_HOL_Obool)))], (24809 ^ _780478) ^ [_1241394, _1241396] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1241394), _1241396)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241394)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241396)))], (41802 ^ _780478) ^ [_1606205, _1606207, _1606209, _1606211, _1606213, _1606215] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606205), tc_List_Olist(_1606205))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606205), tc_List_Olist(_1606205)), hAPP(hAPP(c_List_Olist_OCons(_1606205), _1606207), _1606209)), hAPP(hAPP(c_List_Olist_OCons(_1606205), _1606211), _1606213))), c_List_Olexord(_1606205, _1606215)))), 41803 ^ _780478 : [(41806 ^ _780478) ^ [] : [_1606207 = _1606211, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1606205), tc_List_Olist(_1606205))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1606205), tc_List_Olist(_1606205)), _1606209), _1606213)), c_List_Olexord(_1606205, _1606215)))], (41804 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606205, _1606205)), hAPP(hAPP(c_Product__Type_OPair(_1606205, _1606205), _1606207), _1606211)), _1606215))]]], (34677 ^ _780478) ^ [] : [-(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))))], (6508 ^ _780478) ^ [_886684, _886686, _886688, _886690] : [hBOOL(hAPP(hAPP(c_member(_886684), _886686), _886688)), -(hBOOL(hAPP(hAPP(c_member(_886684), _886686), _886690))), -(hBOOL(hAPP(hAPP(c_member(_886684), _886686), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886684, tc_HOL_Obool)), _886688), _886690))))], (17973 ^ _780478) ^ [_1115155, _1115157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115155), hAPP(c_Nat_OSuc, _1115157))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115155), _1115157))), -(_1115155 = hAPP(c_Nat_OSuc, _1115157))], (14237 ^ _780478) ^ [_1034940, _1034942, _1034944] : [class_Groups_Ocomm__monoid__mult(_1034940), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1034942, _1034940), _1034944), c_Orderings_Obot__class_Obot(tc_fun(_1034942, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1034940))], (38090 ^ _780478) ^ [_1511138, _1511140, _1511142, _1511144, _1511146, _1511148] : [c_Typedef_Otype__definition(_1511138, _1511140, _1511142, _1511144, _1511146), -(hAPP(_1511144, hAPP(_1511142, _1511148)) = _1511148)], (33805 ^ _780478) ^ [_1419152, _1419154, _1419156] : [-(hAPP(c_Nat_Onat_Onat__rec(_1419152, _1419154, _1419156), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1419154)], (42664 ^ _780478) ^ [_1630800, _1630802, _1630804, _1630806, _1630808, _1630810] : [-(_1630800 = _1630802), -(hAPP(hAPP(c_List_Olist__update(_1630804, hAPP(hAPP(c_List_Olist__update(_1630804, _1630806), _1630800), _1630808)), _1630802), _1630810) = hAPP(hAPP(c_List_Olist__update(_1630804, hAPP(hAPP(c_List_Olist__update(_1630804, _1630806), _1630802), _1630810)), _1630800), _1630808))], (52113 ^ _780478) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (35463 ^ _780478) ^ [_1448467, _1448469] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1448467), _1448469) = c_Groups_Oone__class_Oone(tc_Int_Oint), 35468 ^ _780478 : [(35471 ^ _780478) ^ [] : [-(_1448469 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35469 ^ _780478) ^ [] : [-(_1448467 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 35472 ^ _780478 : [(35475 ^ _780478) ^ [] : [-(_1448469 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35473 ^ _780478) ^ [] : [-(_1448467 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (28216 ^ _780478) ^ [_1302815, _1302817, _1302819] : [class_Orderings_Olinorder(_1302815), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302815), _1302817), _1302819)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302815, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1302815, _1302817, _1302819)), hAPP(c_SetInterval_Oord__class_OatLeast(_1302815), _1302819)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1302815), _1302817))], (7714 ^ _780478) ^ [_910787, _910789, _910791, _910793] : [c_Hoare__Mirabelle_Ohoare__derivs(_910787, _910789, _910791), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_910787), tc_HOL_Obool)), _910793), _910791)), -(c_Hoare__Mirabelle_Ohoare__derivs(_910787, _910789, _910793))], (22719 ^ _780478) ^ [_1203385] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1203385)) = 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), _1203385)))], (34533 ^ _780478) ^ [_1431629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1431629)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431629), c_Int_OPls)))], (11029 ^ _780478) ^ [_973008, _973010, _973012] : [class_Rings_Oring(_973008), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973008), hAPP(c_Groups_Ouminus__class_Ouminus(_973008), _973010)), hAPP(c_Groups_Ouminus__class_Ouminus(_973008), _973012)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973008), _973010), _973012))], (38026 ^ _780478) ^ [_1509496, _1509498, _1509500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1509496, _1509496), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1509496, _1509496, _1509496), _1509498), _1509500)), _1509498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1509496, tc_HOL_Obool), tc_fun(_1509496, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1509496, tc_HOL_Obool), tc_fun(_1509496, tc_HOL_Obool), tc_fun(_1509496, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1509496, _1509498)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1509496, tc_HOL_Obool), tc_fun(_1509496, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1509496, _1509500)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1509496, tc_HOL_Obool), tc_fun(_1509496, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1509496, tc_HOL_Obool), tc_fun(_1509496, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1509496, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1509496, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1509496, tc_HOL_Obool), tc_fun(_1509496, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1509496, _1509498))))], (27637 ^ _780478) ^ [_1291377, _1291379, _1291381, _1291383] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1291377), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1291379, tc_Int_Oint), _1291381), _1291383)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1291379, _1291377), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1291377, _1291379), c_Int_Oring__1__class_Oof__int(_1291377)), _1291381)), _1291383)), class_Groups_Ocomm__monoid__mult(_1291377), class_Rings_Oring__1(_1291377)], (15307 ^ _780478) ^ [_1056085, _1056087, _1056089, _1056091] : [class_Rings_Olinordered__semidom(_1056085), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1056087), _1056089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056085), c_Groups_Oone__class_Oone(_1056085)), _1056091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1056085), hAPP(hAPP(c_Power_Opower__class_Opower(_1056085), _1056091), _1056087)), hAPP(hAPP(c_Power_Opower__class_Opower(_1056085), _1056091), _1056089))))], (44698 ^ _780478) ^ [_1675384, _1675386] : [-(hAPP(hAPP(c_List_Ozip(_1675384, _1675384), _1675386), _1675386) = hAPP(hAPP(c_List_Omap(_1675384, tc_prod(_1675384, _1675384)), hAPP(hAPP(c_COMBS(_1675384, _1675384, tc_prod(_1675384, _1675384)), c_Product__Type_OPair(_1675384, _1675384)), c_COMBI(_1675384))), _1675386))], (35379 ^ _780478) ^ [_1447127] : [class_Int_Onumber__ring(_1447127), c_Int_Oiszero(_1447127, hAPP(c_Int_Onumber__class_Onumber__of(_1447127), c_Int_OMin))], (19622 ^ _780478) ^ [_1146868, _1146870, _1146872] : [19623 ^ _780478 : [(19626 ^ _780478) ^ [] : [_1146868 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19624 ^ _780478) ^ [] : [_1146870 = _1146872]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146868), _1146870) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146868), _1146872))], (29606 ^ _780478) ^ [_1330226, _1330228] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330226, _1330228) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1330226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1330226), _1330228)), _1330228)))], (31286 ^ _780478) ^ [_1363245, _1363247] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1363245), hAPP(c_Set_OCollect(_1363245), _1363247))), 31289 ^ _780478 : [(31296 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1363245), c_Orderings_Otop__class_Otop(tc_fun(_1363245, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1363245), hAPP(c_Set_OCollect(_1363245), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1363245), c_fNot), _1363247)))))], (31290 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1363245), hAPP(c_Set_OCollect(_1363245), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1363245), c_fNot), _1363247)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1363245), c_Orderings_Otop__class_Otop(tc_fun(_1363245, tc_HOL_Obool)))))]]], (52325 ^ _780478) ^ [_1833404] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1833404)))], (46465 ^ _780478) ^ [_1715780, _1715782, _1715784] : [class_Orderings_Olinorder(_1715780), c_List_Olinorder__class_Osorted(_1715780, _1715782), -(c_List_Olinorder__class_Osorted(_1715780, hAPP(hAPP(c_List_Odrop(_1715780), _1715784), _1715782)))], (44839 ^ _780478) ^ [_1678965] : [-(hAPP(c_List_Omap(_1678965, _1678965), c_COMBI(_1678965)) = c_Fun_Oid(tc_List_Olist(_1678965)))], (34623 ^ _780478) ^ [_1433187, _1433189] : [class_Int_Onumber__ring(_1433187), -(hAPP(c_Int_Onumber__class_Onumber__of(_1433187), c_Int_OBit0(_1433189)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433187), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433187), c_Groups_Ozero__class_Ozero(_1433187)), hAPP(c_Int_Onumber__class_Onumber__of(_1433187), _1433189))), hAPP(c_Int_Onumber__class_Onumber__of(_1433187), _1433189)))], (48305 ^ _780478) ^ [_1754113, _1754115, _1754117, _1754119] : [c_List_Olist__ex1(_1754113, _1754115, hAPP(hAPP(c_List_Olist_OCons(_1754113), _1754117), _1754119)), 48308 ^ _780478 : [(48315 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1754115, _1754117))), -(c_List_Olist__ex1(_1754113, _1754115, _1754119))], (48309 ^ _780478) ^ [] : [hBOOL(hAPP(_1754115, _1754117)), -(c_List_Olist__all(_1754113, hAPP(hAPP(c_COMBS(_1754113, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1754113), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1754113), c_fNot), _1754115))), hAPP(c_fequal, _1754117)), _1754119))]]], (50244 ^ _780478) ^ [_1796948, _1796950] : [50246 ^ _780478 : [(50249 ^ _780478) ^ [] : [hBOOL(hAPP(_1796948, hAPP(c_Code__Numeral_Oof__nat, 50245 ^ [_1796948, _1796950])))], (50247 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50245 ^ [_1796948, _1796950]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1796948, _1796950)))], (14331 ^ _780478) ^ [_1036349, _1036351, _1036353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036349), _1036351)), _1036353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036349), _1036353)))], (6740 ^ _780478) ^ [_891936] : [-(c_Finite__Set_Ofun__left__comm__idem(_891936, tc_fun(_891936, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_891936, tc_HOL_Obool), tc_fun(tc_fun(_891936, tc_HOL_Obool), tc_fun(_891936, tc_HOL_Obool)), _891936), hAPP(c_COMBC(tc_fun(_891936, tc_HOL_Obool), tc_fun(_891936, tc_HOL_Obool), tc_fun(_891936, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_891936, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_891936, tc_fun(_891936, tc_HOL_Obool), tc_fun(_891936, tc_HOL_Obool)), c_Set_Oinsert(_891936)), c_Orderings_Obot__class_Obot(tc_fun(_891936, tc_HOL_Obool))))))], (45635 ^ _780478) ^ [_1696567, _1696569] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1696567))), c_Enum_Osublists(_1696567, _1696569)) = 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(_1696567)), _1696569)))], (22308 ^ _780478) ^ [_1195291, _1195293, _1195295, _1195297, _1195299] : [class_Groups_Oordered__comm__monoid__add(_1195291), hBOOL(hAPP(c_Finite__Set_Ofinite(_1195293), _1195295)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1195293, tc_HOL_Obool)), _1195297), _1195295)), 22322 ^ _780478 : [(22325 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195291), c_Groups_Ozero__class_Ozero(_1195291)), hAPP(_1195299, 22321 ^ [_1195291, _1195293, _1195295, _1195297, _1195299])))], (22323 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1195293), 22321 ^ [_1195291, _1195293, _1195295, _1195297, _1195299]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1195293, tc_HOL_Obool)), _1195295), _1195297))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1195291), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1195293, _1195291), _1195299), _1195297)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1195293, _1195291), _1195299), _1195295))))], (18173 ^ _780478) ^ [_1119836, _1119838, _1119840, _1119842, _1119844] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119836, tc_HOL_Obool)), _1119838), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119840, tc_fun(_1119836, tc_HOL_Obool)), _1119842), _1119844)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1119840, tc_fun(_1119836, tc_HOL_Obool)), _1119842), hAPP(hAPP(c_COMBB(tc_fun(_1119836, tc_HOL_Obool), tc_fun(_1119836, tc_HOL_Obool), _1119840), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1119836, tc_HOL_Obool)), _1119838)), _1119844)))], (51997 ^ _780478) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (46961 ^ _780478) ^ [_1724990] : [-(hAPP(c_List_Orev(_1724990), c_List_Olist_ONil(_1724990)) = c_List_Olist_ONil(_1724990))], (8392 ^ _780478) ^ [_924519, _924521, _924523, _924525] : [_924523 = _924525, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_924519, _924521, hAPP(hAPP(c_Set_Oinsert(_924519), _924523), c_Orderings_Obot__class_Obot(tc_fun(_924519, tc_HOL_Obool)))), _924525)))], (33809 ^ _780478) ^ [_1419238, _1419240] : [class_Int_Onumber__ring(_1419238), 33812 ^ _780478 : [(33819 ^ _780478) ^ [] : [c_Int_Oiszero(_1419238, hAPP(c_Int_Onumber__class_Onumber__of(_1419238), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1419240), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1419238), _1419240) = c_Groups_Ozero__class_Ozero(_1419238))], (33813 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1419238), _1419240) = c_Groups_Ozero__class_Ozero(_1419238), -(c_Int_Oiszero(_1419238, hAPP(c_Int_Onumber__class_Onumber__of(_1419238), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1419240), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (292 ^ _780478) ^ [_784954, _784956, _784958, _784960] : [-(c_Nitpick_Owf_H(_784958, _784954)), c_Nitpick_Owf_H(_784960, _784956), _784960 = _784958, _784956 = _784954], (1104 ^ _780478) ^ [_797142, _797144] : [-(class_Groups_Oordered__ab__group__add__abs(_797142)), _797144 = _797142, class_Groups_Oordered__ab__group__add__abs(_797144)], (18738 ^ _780478) ^ [_1132396, _1132398, _1132400] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1132396), _1132398)), 18741 ^ _780478 : [(18748 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1132396), _1132400), _1132398))), -(hAPP(c_Finite__Set_Ocard(_1132396), hAPP(hAPP(c_Set_Oinsert(_1132396), _1132400), _1132398)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1132396), _1132398)))], (18742 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1132396), _1132400), _1132398)), -(hAPP(c_Finite__Set_Ocard(_1132396), hAPP(hAPP(c_Set_Oinsert(_1132396), _1132400), _1132398)) = hAPP(c_Finite__Set_Ocard(_1132396), _1132398))]]], (31540 ^ _780478) ^ [_1373007, _1373009, _1373011] : [class_Lattices_Odistrib__lattice(_1373007), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373007), _1373009)), -(_1373009 = c_Orderings_Obot__class_Obot(tc_fun(_1373007, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1373007), _1373011)), -(_1373011 = c_Orderings_Obot__class_Obot(tc_fun(_1373007, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1373007), c_Big__Operators_Olattice__class_OSup__fin(_1373007, _1373009)), c_Big__Operators_Olattice__class_OSup__fin(_1373007, _1373011)) = c_Big__Operators_Olattice__class_OSup__fin(_1373007, hAPP(c_Set_OCollect(_1373007), hAPP(hAPP(c_COMBB(tc_fun(_1373007, tc_HOL_Obool), tc_HOL_Obool, _1373007), c_HOL_OEx(_1373007)), hAPP(hAPP(c_COMBB(tc_fun(_1373007, tc_fun(_1373007, tc_HOL_Obool)), tc_fun(_1373007, tc_HOL_Obool), _1373007), hAPP(c_COMBB(tc_fun(_1373007, tc_HOL_Obool), tc_HOL_Obool, _1373007), c_HOL_OEx(_1373007))), hAPP(hAPP(c_COMBC(_1373007, tc_fun(_1373007, tc_fun(_1373007, tc_HOL_Obool)), tc_fun(_1373007, tc_fun(_1373007, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1373007, tc_fun(tc_fun(_1373007, tc_HOL_Obool), tc_fun(_1373007, tc_HOL_Obool))), tc_fun(tc_fun(_1373007, tc_fun(_1373007, tc_HOL_Obool)), tc_fun(_1373007, tc_fun(_1373007, tc_HOL_Obool))), _1373007), c_COMBS(_1373007, tc_fun(_1373007, tc_HOL_Obool), tc_fun(_1373007, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1373007, tc_fun(_1373007, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1373007, tc_fun(tc_fun(_1373007, tc_HOL_Obool), tc_fun(_1373007, tc_HOL_Obool))), _1373007), hAPP(c_COMBB(tc_fun(_1373007, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1373007, tc_HOL_Obool), tc_fun(_1373007, tc_HOL_Obool)), _1373007), c_COMBS(_1373007, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1373007, tc_fun(_1373007, tc_HOL_Obool)), tc_fun(_1373007, tc_fun(_1373007, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1373007), hAPP(c_COMBB(tc_fun(_1373007, tc_HOL_Obool), tc_fun(_1373007, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1373007), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1373007), c_fconj))), hAPP(hAPP(c_COMBC(_1373007, tc_fun(_1373007, tc_fun(_1373007, _1373007)), tc_fun(_1373007, tc_fun(_1373007, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1373007, _1373007), tc_fun(_1373007, tc_HOL_Obool)), tc_fun(tc_fun(_1373007, tc_fun(_1373007, _1373007)), tc_fun(_1373007, tc_fun(_1373007, tc_HOL_Obool))), _1373007), c_COMBB(tc_fun(_1373007, _1373007), tc_fun(_1373007, tc_HOL_Obool), _1373007)), hAPP(hAPP(c_COMBB(tc_fun(_1373007, tc_HOL_Obool), tc_fun(tc_fun(_1373007, _1373007), tc_fun(_1373007, tc_HOL_Obool)), _1373007), c_COMBB(_1373007, tc_HOL_Obool, _1373007)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1373007)))))), hAPP(hAPP(c_COMBC(_1373007, tc_fun(_1373007, tc_HOL_Obool), tc_fun(_1373007, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1373007, tc_HOL_Obool), tc_fun(_1373007, tc_HOL_Obool)), _1373007), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1373007)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1373007), c_fconj), hAPP(hAPP(c_COMBC(_1373007, tc_fun(_1373007, tc_HOL_Obool), tc_HOL_Obool), c_member(_1373007)), _1373009)))), hAPP(hAPP(c_COMBC(_1373007, tc_fun(_1373007, tc_HOL_Obool), tc_HOL_Obool), c_member(_1373007)), _1373011))))))))], (5132 ^ _780478) ^ [_858871, _858873, _858875, _858877, _858879, _858881] : [-(c_Set_Ovimage(_858881, _858877, _858873) = c_Set_Ovimage(_858879, _858875, _858871)), _858881 = _858879, _858877 = _858875, _858873 = _858871], (23245 ^ _780478) ^ [_1213109, _1213111] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1213109), _1213111)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1213109)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213111))))], (31230 ^ _780478) ^ [_1361783, _1361785, _1361787] : [-(hAPP(hAPP(c_Set_Oinsert(_1361783), _1361785), _1361787) = hAPP(c_Set_OCollect(_1361783), hAPP(hAPP(c_COMBS(_1361783, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361783), c_fdisj), hAPP(hAPP(c_COMBC(_1361783, _1361783, tc_HOL_Obool), c_fequal), _1361785))), hAPP(hAPP(c_COMBC(_1361783, tc_fun(_1361783, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361783)), _1361787))))], (5536 ^ _780478) ^ [_865289, _865291] : [_865291 = _865289, -(c_Groups_Ouminus__class_Ouminus(_865291) = c_Groups_Ouminus__class_Ouminus(_865289))], (37951 ^ _780478) ^ [_1507453, _1507455, _1507457, _1507459] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1507453, _1507455, _1507457), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507453, _1507455), tc_HOL_Obool))), _1507459) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1507453, _1507457), tc_HOL_Obool)))], (16158 ^ _780478) ^ [_1073144, _1073146, _1073148] : [16160 ^ _780478 : [(16166 ^ _780478) ^ [] : [-(16159 ^ [_1073144, _1073146, _1073148] = 16162 ^ [_1073144, _1073146, _1073148])], (16164 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1073144), 16162 ^ [_1073144, _1073146, _1073148]), _1073148)))], (16161 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1073144), 16159 ^ [_1073144, _1073146, _1073148]), _1073146)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073144, tc_HOL_Obool)), _1073146), _1073148) = c_Orderings_Obot__class_Obot(tc_fun(_1073144, tc_HOL_Obool)))], (50719 ^ _780478) ^ [_1806479, _1806481, _1806483] : [hBOOL(hAPP(hAPP(c_member(_1806479), _1806481), c_Quotient_ORespects(_1806479, _1806483))), -(hBOOL(hAPP(hAPP(_1806483, _1806481), _1806481)))], (50403 ^ _780478) ^ [_1800317, _1800319, _1800321, _1800323] : [-(c_Product__Type_Ocurry(_1800317, _1800319, _1800321, hAPP(c_Product__Type_Oprod_Oprod__case(_1800317, _1800319, _1800321), _1800323)) = _1800323)], (38568 ^ _780478) ^ [_1522433, _1522435] : [-(c_Nitpick_Onumber__of__frac(_1522433, _1522435) = c_Nitpick_OAbs__Frac(_1522433, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1522435), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (42760 ^ _780478) ^ [_1633014, _1633016, _1633018, _1633020] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633014), tc_List_Olist(_1633014))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633014), tc_List_Olist(_1633014)), _1633016), _1633018)), c_List_Olistrel1(_1633014, _1633020)))), 42761 ^ _780478 : [(42762 ^ _780478) ^ [_1633147, _1633149] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1633014, _1633014)), hAPP(hAPP(c_Product__Type_OPair(_1633014, _1633014), hAPP(hAPP(c_List_Onth(_1633014), _1633016), _1633147)), _1633149)), _1633020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1633147), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633014)), _1633016))), _1633018 = hAPP(hAPP(c_List_Olist__update(_1633014, _1633016), _1633147), _1633149)]]], (41212 ^ _780478) ^ [_1589727, _1589729, _1589731, _1589733] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589727, _1589727)), _1589729), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589727, _1589727), tc_HOL_Obool), _1589731), _1589733))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589727, _1589727)), _1589729), c_Transitive__Closure_Ortrancl(_1589727, _1589733))))], (10377 ^ _780478) ^ [_961509, _961511] : [class_Orderings_Olinorder(_961509), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_961509), _961511), _961511) = _961511)], (19476 ^ _780478) ^ [_1144818, _1144820, _1144822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1144818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1144818), _1144820)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1144818), _1144822))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1144820), _1144822)))], (12570 ^ _780478) ^ [_1002408, _1002410] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002408, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1002408, tc_HOL_Obool))), _1002410) = c_Orderings_Otop__class_Otop(tc_fun(_1002408, tc_HOL_Obool)))], (37143 ^ _780478) ^ [_1487029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487029)), 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), _1487029)) = 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), _1487029))))))], (52337 ^ _780478) ^ [_1833655, _1833657] : [hBOOL(hAPP(hAPP(c_fequal, _1833655), _1833657)), -(_1833655 = _1833657)], (452 ^ _780478) ^ [_787296, _787298, _787300, _787302, _787304, _787306] : [-(c_Nitpick_Oless__eq__frac(_787304, _787300, _787296)), c_Nitpick_Oless__eq__frac(_787306, _787302, _787298), _787306 = _787304, _787302 = _787300, _787298 = _787296], (48681 ^ _780478) ^ [_1762403, _1762405, _1762407] : [_1762405 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1762403, _1762405, _1762407) = c_List_Olist_ONil(_1762403))], (51981 ^ _780478) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (36842 ^ _780478) ^ [_1481269, _1481271] : [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), _1481269), _1481271))), 36845 ^ _780478 : [(36854 ^ _780478) ^ [] : [-(c_Divides_OposDivAlg(_1481269, _1481271) = hAPP(c_Divides_Oadjust(_1481271), c_Divides_OposDivAlg(_1481269, 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)))), _1481271)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481269), _1481271))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1481271), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36846 ^ _780478) ^ [] : [36847 ^ _780478 : [(36850 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1481271), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36848 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481269), _1481271))]], -(c_Divides_OposDivAlg(_1481269, _1481271) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1481269))]]], (34061 ^ _780478) ^ [_1423535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1423535))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1423535)))], (30436 ^ _780478) ^ [_1345468, _1345470] : [class_Groups_Oordered__ab__group__add__abs(_1345468), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345468), c_Groups_Ozero__class_Ozero(_1345468)), hAPP(c_Groups_Oabs__class_Oabs(_1345468), _1345470))))], (25253 ^ _780478) ^ [_1249757, _1249759, _1249761, _1249763] : [class_Rings_Odivision__ring(_1249757), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1249757), _1249759), _1249761)), _1249763) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1249757), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249757), _1249759), _1249763)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1249757), _1249761), _1249763)))], (52021 ^ _780478) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (31447 ^ _780478) ^ [_1369692, _1369694, _1369696, _1369698] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369692), hAPP(c_Set_OCollect(_1369692), _1369694))), 31450 ^ _780478 : [(31451 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369696), hAPP(c_Set_OCollect(_1369696), hAPP(hAPP(c_COMBB(tc_fun(_1369692, tc_HOL_Obool), tc_HOL_Obool, _1369696), c_HOL_OEx(_1369692)), hAPP(hAPP(c_COMBB(tc_fun(_1369692, tc_HOL_Obool), tc_fun(_1369692, tc_HOL_Obool), _1369696), hAPP(c_COMBS(_1369692, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1369692), c_fconj), _1369694))), _1369698))))), 31454 ^ _780478 : [(31455 ^ _780478) ^ [_1369975] : [hBOOL(hAPP(_1369694, _1369975)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1369696), hAPP(c_Set_OCollect(_1369696), hAPP(hAPP(c_COMBC(_1369696, _1369692, tc_HOL_Obool), _1369698), _1369975)))))]]], (31461 ^ _780478) ^ [] : [31463 ^ _780478 : [(31466 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1369696), hAPP(c_Set_OCollect(_1369696), hAPP(hAPP(c_COMBC(_1369696, _1369692, tc_HOL_Obool), _1369698), 31462 ^ [_1369692, _1369694, _1369696, _1369698]))))], (31464 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1369694, 31462 ^ [_1369692, _1369694, _1369696, _1369698])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1369696), hAPP(c_Set_OCollect(_1369696), hAPP(hAPP(c_COMBB(tc_fun(_1369692, tc_HOL_Obool), tc_HOL_Obool, _1369696), c_HOL_OEx(_1369692)), hAPP(hAPP(c_COMBB(tc_fun(_1369692, tc_HOL_Obool), tc_fun(_1369692, tc_HOL_Obool), _1369696), hAPP(c_COMBS(_1369692, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1369692), c_fconj), _1369694))), _1369698))))))]]], (29590 ^ _780478) ^ [_1329878, _1329880] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329878, _1329880) = 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), _1329878), _1329880) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1329880), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1329878, _1329880)))], (29063 ^ _780478) ^ [_1319556, _1319558, _1319560] : [hBOOL(hAPP(c_Predicate_OPowp(_1319556, hAPP(hAPP(c_COMBC(_1319556, tc_fun(_1319556, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319556)), _1319558)), _1319560)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1319556, tc_HOL_Obool)), _1319560), hAPP(c_Set_OPow(_1319556), _1319558))))], (47195 ^ _780478) ^ [_1730027, _1730029, _1730031] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730027)), c_List_OtakeWhile(_1730027, _1730029, _1730031))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730027)), _1730031))))], (33933 ^ _780478) ^ [_1421482, _1421484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421482), _1421484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1421482)), c_Int_OBit1(_1421484))))], (45053 ^ _780478) ^ [_1683486, _1683488] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1683486)), hAPP(c_Code__Numeral_Oof__nat, _1683488)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1683486), _1683488)))], (38374 ^ _780478) ^ [_1517782, _1517784, _1517786] : [c_Wellfounded_Owf(_1517782, _1517784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1517782, tc_HOL_Obool)), _1517786), hAPP(c_Relation_OImage(_1517782, _1517782, _1517784), _1517786))), -(_1517786 = c_Orderings_Obot__class_Obot(tc_fun(_1517782, tc_HOL_Obool)))], (40919 ^ _780478) ^ [_1582112, _1582114] : [c_Wellfounded_Owf(_1582112, hAPP(c_Relation_Oconverse(_1582112, _1582112), _1582114)), -(c_Wellfounded_Owf(_1582112, hAPP(c_Relation_Oconverse(_1582112, _1582112), c_Transitive__Closure_Otrancl(_1582112, _1582114))))], (17805 ^ _780478) ^ [_1112219] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112219), hAPP(c_Nat_OSuc, _1112219))))], (22349 ^ _780478) ^ [_1196127] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1196127)) = _1196127)], (31144 ^ _780478) ^ [_1360044, _1360046, _1360048] : [-(hAPP(c_Set_OCollect(_1360044), hAPP(hAPP(c_COMBS(_1360044, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1360044), c_fdisj), _1360046)), _1360048)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1360044, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1360044), _1360046)), hAPP(c_Set_OCollect(_1360044), _1360048)))], (25541 ^ _780478) ^ [_1254703] : [hAPP(c_Int_Onat, _1254703) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254703), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30671 ^ _780478) ^ [_1349969] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349969, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1349969, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1349969, tc_HOL_Obool)))], (39368 ^ _780478) ^ [_1545270, _1545272] : [c_Wellfounded_OwfP(_1545270, _1545272), -(c_Wellfounded_Oacyclic(_1545270, hAPP(c_Set_OCollect(tc_prod(_1545270, _1545270)), hAPP(c_Product__Type_Oprod_Oprod__case(_1545270, _1545270, tc_HOL_Obool), _1545272))))], (32130 ^ _780478) ^ [_1387287, _1387289, _1387291] : [class_Int_Onumber(_1387287), class_Orderings_Olinorder(_1387287), 32137 ^ _780478 : [(32144 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387287), hAPP(c_Int_Onumber__class_Onumber__of(_1387287), _1387291)), hAPP(c_Int_Onumber__class_Onumber__of(_1387287), _1387289)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387287), hAPP(c_Int_Onumber__class_Onumber__of(_1387287), _1387289)), hAPP(c_Int_Onumber__class_Onumber__of(_1387287), _1387291))))], (32138 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1387287), hAPP(c_Int_Onumber__class_Onumber__of(_1387287), _1387289)), hAPP(c_Int_Onumber__class_Onumber__of(_1387287), _1387291))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1387287), hAPP(c_Int_Onumber__class_Onumber__of(_1387287), _1387291)), hAPP(c_Int_Onumber__class_Onumber__of(_1387287), _1387289)))]]], (12936 ^ _780478) ^ [_1009667, _1009669, _1009671, _1009673] : [class_Lattices_Osemilattice__sup(_1009667), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009667), _1009669), _1009671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009667), _1009673), _1009671)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009667), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009667), _1009669), _1009673)), _1009671)))], (38679 ^ _780478) ^ [_1525383, _1525385, _1525387, _1525389] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1525383, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1525383, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1525383, _1525385), _1525387)), hAPP(c_Relation_ODomain(_1525383, _1525385), _1525389))), hAPP(c_Relation_ODomain(_1525383, _1525385), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1525383, _1525385), tc_HOL_Obool)), _1525387), _1525389)))))], (36640 ^ _780478) ^ [_1477222, _1477224, _1477226, _1477228, _1477230, _1477232] : [-(hAPP(c_Product__Type_Oapsnd(_1477222, _1477224, _1477226, _1477228), hAPP(hAPP(c_Product__Type_OPair(_1477226, _1477222), _1477230), _1477232)) = hAPP(hAPP(c_Product__Type_OPair(_1477226, _1477224), _1477230), hAPP(_1477228, _1477232)))], (47260 ^ _780478) ^ [_1731337, _1731339, _1731341, _1731343, _1731345] : [hBOOL(hAPP(hAPP(c_member(_1731337), _1731339), hAPP(c_List_Oset(_1731337), _1731341))), -(hBOOL(hAPP(_1731343, _1731339))), -(c_List_OtakeWhile(_1731337, _1731343, hAPP(hAPP(c_List_Oappend(_1731337), _1731341), _1731345)) = c_List_OtakeWhile(_1731337, _1731343, _1731341))], (22014 ^ _780478) ^ [_1189464, _1189466, _1189468, _1189470, _1189472] : [class_Groups_Ocomm__monoid__add(_1189464), hBOOL(hAPP(c_Finite__Set_Ofinite(_1189466), _1189468)), 22021 ^ _780478 : [(22028 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1189466), _1189470), _1189468))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1189466, _1189464), hAPP(hAPP(c_COMBC(_1189466, _1189464, _1189464), hAPP(hAPP(c_COMBS(_1189466, _1189464, tc_fun(_1189464, _1189464)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1189464, tc_fun(_1189464, _1189464)), _1189466), c_If(_1189464)), hAPP(c_fequal, _1189470))), _1189472)), c_Groups_Ozero__class_Ozero(_1189464))), _1189468) = c_Groups_Ozero__class_Ozero(_1189464))], (22022 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1189466), _1189470), _1189468)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1189466, _1189464), hAPP(hAPP(c_COMBC(_1189466, _1189464, _1189464), hAPP(hAPP(c_COMBS(_1189466, _1189464, tc_fun(_1189464, _1189464)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1189464, tc_fun(_1189464, _1189464)), _1189466), c_If(_1189464)), hAPP(c_fequal, _1189470))), _1189472)), c_Groups_Ozero__class_Ozero(_1189464))), _1189468) = hAPP(_1189472, _1189470))]]], (37429 ^ _780478) ^ [] : [-(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))], (48243 ^ _780478) ^ [_1752906, _1752908, _1752910] : [c_List_Olist__all(_1752906, _1752908, _1752910), -(c_List_Olist__all(_1752906, _1752908, hAPP(c_List_Orev(_1752906), _1752910)))], (25615 ^ _780478) ^ [_1255889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255889)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1255889)) = _1255889)], (11011 ^ _780478) ^ [_972621, _972623, _972625] : [class_Rings_Oring(_972621), -(hAPP(c_Groups_Ouminus__class_Ouminus(_972621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972621), _972623), _972625)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972621), _972623), hAPP(c_Groups_Ouminus__class_Ouminus(_972621), _972625)))], (14523 ^ _780478) ^ [_1040016, _1040018] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040016), _1040018)), _1040018) = _1040016)], (8296 ^ _780478) ^ [_922576, _922578, _922580] : [class_Groups_Ogroup__add(_922576), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_922576), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_922576), _922578), _922580)), _922580) = _922578)], (24092 ^ _780478) ^ [_1228950, _1228952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1228950), _1228952)), -(c_Nat__Transfer_Otsub(_1228952, _1228950) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1228952), _1228950))], (13781 ^ _780478) ^ [_1026852, _1026854, _1026856] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1026852), _1026854)), hBOOL(hAPP(hAPP(c_member(_1026852), _1026856), _1026854)), -(hAPP(c_Finite__Set_Ocard(_1026852), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026852, tc_HOL_Obool)), _1026854), hAPP(hAPP(c_Set_Oinsert(_1026852), _1026856), c_Orderings_Obot__class_Obot(tc_fun(_1026852, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1026852), _1026854)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12808 ^ _780478) ^ [_1007464, _1007466] : [class_Lattices_Oboolean__algebra(_1007464), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007464), _1007466), hAPP(c_Groups_Ouminus__class_Ouminus(_1007464), _1007466)) = c_Orderings_Otop__class_Otop(_1007464))], (33891 ^ _780478) ^ [_1420752, _1420754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1420752)), c_Int_OBit1(_1420754))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420752), _1420754)))], (47063 ^ _780478) ^ [_1727186, _1727188, _1727190, _1727192, _1727194] : [-(hAPP(c_List_Ofoldl(_1727186, _1727188, _1727190, _1727192), _1727194) = c_List_Ofoldr(_1727188, _1727186, hAPP(c_COMBC(_1727186, _1727188, _1727186), _1727190), hAPP(c_List_Orev(_1727188), _1727194), _1727192))], (34021 ^ _780478) ^ [_1422848] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1422848))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1422848)))))], (38826 ^ _780478) ^ [_1530315, _1530317, _1530319, _1530321, _1530323] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1530315, _1530317), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1530315, tc_HOL_Obool)), _1530319), _1530321)), hAPP(c_COMBK(tc_fun(_1530317, tc_HOL_Obool), _1530315), _1530323)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1530315, _1530317), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1530315, _1530317), _1530319), hAPP(c_COMBK(tc_fun(_1530317, tc_HOL_Obool), _1530315), _1530323))), hAPP(hAPP(c_Product__Type_OSigma(_1530315, _1530317), _1530321), hAPP(c_COMBK(tc_fun(_1530317, tc_HOL_Obool), _1530315), _1530323))))], (41172 ^ _780478) ^ [_1588786, _1588788, _1588790] : [c_Relation_Ototal__on(_1588786, _1588788, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1588786, _1588786), tc_HOL_Obool)), _1588790), c_Relation_OId(_1588786))), -(c_Relation_Ototal__on(_1588786, _1588788, _1588790))], (14529 ^ _780478) ^ [_1040141, _1040143, _1040145] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040141), _1040143)), _1040145) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040141), _1040145)), _1040143))], (47021 ^ _780478) ^ [_1726400, _1726402, _1726404, _1726406, _1726408] : [c_List_Olist__all2(_1726400, _1726402, _1726404, _1726406, hAPP(c_List_Orev(_1726402), _1726408)), -(c_List_Olist__all2(_1726400, _1726402, _1726404, hAPP(c_List_Orev(_1726400), _1726406), _1726408))], (34419 ^ _780478) ^ [_1429631, _1429633] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1429631)), c_Int_OBit0(_1429633)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1429631), _1429633)))], (10483 ^ _780478) ^ [_963363, _963365, _963367, _963369] : [class_Orderings_Olinorder(_963363), 10486 ^ _780478 : [(10495 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963363), hAPP(hAPP(c_Orderings_Oord__class_Omax(_963363), _963365), _963367)), _963369))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963363), _963365), _963369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963363), _963367), _963369))], (10487 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963363), hAPP(hAPP(c_Orderings_Oord__class_Omax(_963363), _963365), _963367)), _963369)), 10490 ^ _780478 : [(10493 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963363), _963367), _963369)))], (10491 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963363), _963365), _963369)))]]]]], (1354 ^ _780478) ^ [_800267, _800269] : [-(class_Complete__Lattice_Ocomplete__lattice(_800267)), _800269 = _800267, class_Complete__Lattice_Ocomplete__lattice(_800269)], (44714 ^ _780478) ^ [_1675742, _1675744, _1675746, _1675748] : [c_List_Olist_ONil(_1675742) = hAPP(hAPP(c_List_Omap(_1675744, _1675742), _1675746), _1675748), -(_1675748 = c_List_Olist_ONil(_1675744))], (30725 ^ _780478) ^ [_1351203, _1351205, _1351207, _1351209, _1351211] : [class_Groups_Oordered__ab__group__add__abs(_1351203), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351203), hAPP(c_Groups_Oabs__class_Oabs(_1351203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351203), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351203), _1351205), _1351207)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351203), _1351209), _1351211)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1351203), hAPP(c_Groups_Oabs__class_Oabs(_1351203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351203), _1351205), _1351209))), hAPP(c_Groups_Oabs__class_Oabs(_1351203), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351203), _1351207), _1351211))))))], (34733 ^ _780478) ^ [_1435429, _1435431] : [class_Rings_Oring__1__no__zero__divisors(_1435429), 34736 ^ _780478 : [(34743 ^ _780478) ^ [] : [_1435431 = c_Groups_Ozero__class_Ozero(_1435429), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1435429), _1435431), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1435429))], (34737 ^ _780478) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1435429), _1435431), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1435429), -(_1435431 = c_Groups_Ozero__class_Ozero(_1435429))]]], (6414 ^ _780478) ^ [_884726, _884728, _884730, _884732, _884734, _884736, _884738, _884740] : [c_Finite__Set_Ofolding__image__simple(_884726, _884728, _884730, _884732, _884734, _884736), hBOOL(hAPP(c_Finite__Set_Ofinite(_884728), _884738)), -(hBOOL(hAPP(hAPP(c_member(_884728), _884740), _884738))), -(hAPP(_884736, hAPP(hAPP(c_Set_Oinsert(_884728), _884740), _884738)) = hAPP(hAPP(_884730, hAPP(_884734, _884740)), hAPP(_884736, _884738)))], (1284 ^ _780478) ^ [_799392, _799394] : [-(class_Groups_Osgn__if(_799392)), _799394 = _799392, class_Groups_Osgn__if(_799394)], (48729 ^ _780478) ^ [_1763226, _1763228, _1763230] : [-(hAPP(c_List_Oset(_1763226), c_List_Oreplicate(_1763226, hAPP(c_Nat_OSuc, _1763228), _1763230)) = hAPP(hAPP(c_Set_Oinsert(_1763226), _1763230), c_Orderings_Obot__class_Obot(tc_fun(_1763226, tc_HOL_Obool))))], (51895 ^ _780478) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (50977 ^ _780478) ^ [_1813648] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1813648), _1813648)))], (50447 ^ _780478) ^ [_1801211, _1801213, _1801215, _1801217] : [c_Fun_Obij__betw(_1801211, _1801213, _1801215, _1801217, c_Orderings_Otop__class_Otop(tc_fun(_1801213, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1801211, _1801213, _1801215), c_Orderings_Otop__class_Otop(tc_fun(_1801211, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1801213, tc_HOL_Obool)))], (38404 ^ _780478) ^ [_1518342, _1518344] : [c_FunDef_Oreduction__pair(_1518342, _1518344), 38407 ^ _780478 : [(38410 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518342, _1518342), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518342, _1518342, _1518342), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518342, _1518342), tc_HOL_Obool), tc_fun(tc_prod(_1518342, _1518342), tc_HOL_Obool)), _1518344)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1518342, _1518342), tc_HOL_Obool), tc_fun(tc_prod(_1518342, _1518342), tc_HOL_Obool)), _1518344))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518342, _1518342), tc_HOL_Obool), tc_fun(tc_prod(_1518342, _1518342), tc_HOL_Obool)), _1518344))))], (38408 ^ _780478) ^ [] : [-(c_Wellfounded_Owf(_1518342, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518342, _1518342), tc_HOL_Obool), tc_fun(tc_prod(_1518342, _1518342), tc_HOL_Obool)), _1518344)))]]], (44692 ^ _780478) ^ [_1674966, _1674968, _1674970, _1674972, _1674974, _1674976, _1674978, _1674980] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674966, _1674968), _1674970), _1674972), hAPP(hAPP(c_List_Ozip(_1674966, _1674968), hAPP(hAPP(c_List_Omap(_1674974, _1674966), _1674976), _1674978)), _1674980)) = hAPP(hAPP(c_List_Omap(tc_prod(_1674974, _1674968), _1674970), hAPP(c_Product__Type_Oprod_Oprod__case(_1674974, _1674968, _1674970), hAPP(hAPP(c_COMBB(tc_fun(_1674968, tc_prod(_1674966, _1674968)), tc_fun(_1674968, _1674970), _1674974), hAPP(c_COMBB(tc_prod(_1674966, _1674968), _1674970, _1674968), _1674972)), hAPP(hAPP(c_COMBB(_1674966, tc_fun(_1674968, tc_prod(_1674966, _1674968)), _1674974), c_Product__Type_OPair(_1674966, _1674968)), _1674976)))), hAPP(hAPP(c_List_Ozip(_1674974, _1674968), _1674978), _1674980)))], (352 ^ _780478) ^ [_785818, _785820, _785822, _785824, _785826, _785828, _785830, _785832] : [-(c_Finite__Set_Ofolding__idem(_785830, _785826, _785822, _785818)), c_Finite__Set_Ofolding__idem(_785832, _785828, _785824, _785820), _785832 = _785830, _785828 = _785826, _785824 = _785822, _785820 = _785818], (15777 ^ _780478) ^ [_1065830, _1065832, _1065834, _1065836] : [class_Lattices_Osemilattice__inf(_1065830), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065830), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065830), _1065832), _1065834)), _1065836) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065830), _1065832), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065830), _1065834), _1065836)))], (35461 ^ _780478) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (10311 ^ _780478) ^ [_960344, _960346, _960348] : [class_Orderings_Olinorder(_960344), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_960344), _960346), hAPP(hAPP(c_Orderings_Oord__class_Omax(_960344), _960346), _960348)) = _960346)], (30063 ^ _780478) ^ [_1338316, _1338318, _1338320] : [hBOOL(hAPP(_1338316, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338318, _1338320))), 30066 ^ _780478 : [(30073 ^ _780478) ^ [] : [-(_1338320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 30076 ^ _780478 : [(30077 ^ _780478) ^ [_1338564, _1338566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1338564), _1338320)), _1338318 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338320), _1338566)), _1338564), -(hBOOL(hAPP(_1338316, _1338564)))]]], (30067 ^ _780478) ^ [] : [_1338320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1338316, _1338318)))]]], (21440 ^ _780478) ^ [_1178590, _1178592, _1178594, _1178596, _1178598] : [class_Rings_Olinordered__semiring__strict(_1178590), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178590), _1178592), _1178594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178590), _1178596), _1178598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178590), c_Groups_Ozero__class_Ozero(_1178590)), _1178594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1178590), c_Groups_Ozero__class_Ozero(_1178590)), _1178596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1178590), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178590), _1178592), _1178596)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1178590), _1178594), _1178598))))], (28247 ^ _780478) ^ [_1303422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303422), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1303422 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 28250 ^ [_1303422]))))], (30011 ^ _780478) ^ [_1337250, _1337252, _1337254] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1337250), _1337252)), _1337254) = 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), _1337250), _1337254)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1337252), _1337254))), 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, _1337250, _1337254)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1337252, _1337254))), _1337254)))], (40937 ^ _780478) ^ [_1582467, _1582469, _1582471, _1582473] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582467, _1582467)), hAPP(hAPP(c_Product__Type_OPair(_1582467, _1582467), _1582469), _1582471)), c_Transitive__Closure_Ortrancl(_1582467, _1582473))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582467, _1582467)), hAPP(hAPP(c_Product__Type_OPair(_1582467, _1582467), _1582471), _1582469)), c_Transitive__Closure_Ortrancl(_1582467, hAPP(c_Relation_Oconverse(_1582467, _1582467), _1582473)))))], (16308 ^ _780478) ^ [_1076959, _1076961, _1076963] : [class_Lattices_Oboolean__algebra(_1076959), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1076959), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1076959), _1076961), _1076963)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1076959), hAPP(c_Groups_Ouminus__class_Ouminus(_1076959), _1076961)), hAPP(c_Groups_Ouminus__class_Ouminus(_1076959), _1076963)))], (43530 ^ _780478) ^ [_1649664, _1649666, _1649668] : [c_List_Olist_ONil(_1649664) = hAPP(hAPP(c_List_Oappend(_1649664), _1649666), _1649668), 43533 ^ _780478 : [(43536 ^ _780478) ^ [] : [-(_1649668 = c_List_Olist_ONil(_1649664))], (43534 ^ _780478) ^ [] : [-(_1649666 = c_List_Olist_ONil(_1649664))]]], (8477 ^ _780478) ^ [_926329, _926331, _926333, _926335, _926337] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_926329, _926331, hAPP(hAPP(c_Set_Oinsert(_926329), _926333), _926335)), _926337)), 8482 ^ _780478 : [(8487 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_926329), 8480 ^ [_926329, _926331, _926333, _926335, _926337]), 8481 ^ [_926329, _926331, _926333, _926335, _926337]))], (8485 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_926329, _926329, _926331, 8480 ^ [_926329, _926331, _926333, _926335, _926337], 8481 ^ [_926329, _926331, _926333, _926335, _926337]), _926337)))], (8483 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_926329), _926333), _926335) = hAPP(hAPP(c_Set_Oinsert(_926329), 8480 ^ [_926329, _926331, _926333, _926335, _926337]), 8481 ^ [_926329, _926331, _926333, _926335, _926337]))]]], (36590 ^ _780478) ^ [_1476318, _1476320] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476318))), 36593 ^ _780478 : [(36600 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476320))), -(c_Divides_Odivmod__int(_1476318, _1476320) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1476318), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1476320))))], (36594 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1476320)), -(c_Divides_Odivmod__int(_1476318, _1476320) = c_Divides_OnegDivAlg(_1476318, _1476320))]]], (42221 ^ _780478) ^ [_1618515, _1618517, _1618519, _1618521] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618515) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1618517), hAPP(hAPP(c_List_Olist_OCons(_1618517), _1618519), _1618521)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618515)) = hAPP(hAPP(c_List_Onth(_1618517), _1618521), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618515)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (11087 ^ _780478) ^ [_974061, _974063] : [class_Orderings_Olinorder(_974061), hBOOL(hAPP(c_Finite__Set_Ofinite(_974061), _974063)), -(c_Big__Operators_Olinorder__class_OMax(_974061, _974063) = hAPP(c_Finite__Set_Ofold1(_974061, c_Orderings_Oord__class_Omax(_974061)), _974063))], (17291 ^ _780478) ^ [_1099492, _1099494, _1099496, _1099498, _1099500] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099492, tc_fun(_1099494, tc_HOL_Obool)), _1099496), _1099498), _1099500))), 17292 ^ _780478 : [(17293 ^ _780478) ^ [_1099564] : [hBOOL(hAPP(hAPP(c_member(_1099492), _1099564), _1099496)), hBOOL(hAPP(hAPP(_1099498, _1099564), _1099500))]]], (29808 ^ _780478) ^ [_1333989, _1333991] : [-(_1333989 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29811 ^ _780478 : [(29818 ^ _780478) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333991, _1333989) = 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), _1333991)), _1333989) = 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), _1333991), _1333989))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29812 ^ _780478) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333991, _1333989) = 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), _1333991)), _1333989) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333991), _1333989)))]]], (34271 ^ _780478) ^ [_1426843, _1426845] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1426843, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426845)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1426843, 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)))), _1426845)))], (9440 ^ _780478) ^ [_942264, _942266, _942268, _942270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_942264, tc_HOL_Obool)), _942266), _942268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942264, tc_HOL_Obool)), _942268), _942270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_942264, tc_HOL_Obool)), _942266), _942270)))], (37431 ^ _780478) ^ [_1493708, _1493710, _1493712] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1493708, tc_HOL_Obool), tc_fun(_1493708, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1493708, tc_HOL_Obool), tc_fun(_1493708, tc_HOL_Obool)), _1493710), _1493712)), c_Wellfounded_Ofinite__psubset(_1493708))), 37434 ^ _780478 : [(37437 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1493708), _1493712)))], (37435 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1493708, tc_HOL_Obool)), _1493710), _1493712)))]]], (50173 ^ _780478) ^ [_1795159, _1795161, _1795163] : [hAPP(c_Fun_Ocomp(_1795159, _1795161, _1795161, _1795163), c_Hilbert__Choice_Oinv__into(_1795159, _1795161, c_Orderings_Otop__class_Otop(tc_fun(_1795159, tc_HOL_Obool)), _1795163)) = c_Fun_Oid(_1795161), -(hAPP(c_Set_Oimage(_1795159, _1795161, _1795163), c_Orderings_Otop__class_Otop(tc_fun(_1795159, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1795161, tc_HOL_Obool)))], (41132 ^ _780478) ^ [_1587703, _1587705] : [-(c_Relation_Orefl__on(_1587703, c_Orderings_Otop__class_Otop(tc_fun(_1587703, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587703, _1587703), tc_HOL_Obool)), _1587705), c_Relation_OId(_1587703))))], (50871 ^ _780478) ^ [_1811251, _1811253, _1811255, _1811257, _1811259, _1811261] : [50874 ^ _780478 : [(50881 ^ _780478) ^ [] : [hAPP(hAPP(_1811259, 50872 ^ [_1811251, _1811253, _1811255, _1811257, _1811259, _1811261]), 50876 ^ [_1811251, _1811253, _1811255, _1811257, _1811259, _1811261]) = hAPP(hAPP(_1811259, 50873 ^ [_1811251, _1811253, _1811255, _1811257, _1811259, _1811261]), 50877 ^ [_1811251, _1811253, _1811255, _1811257, _1811259, _1811261])], (50879 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1811255, _1811255)), hAPP(hAPP(c_Product__Type_OPair(_1811255, _1811255), 50876 ^ [_1811251, _1811253, _1811255, _1811257, _1811259, _1811261]), 50877 ^ [_1811251, _1811253, _1811255, _1811257, _1811259, _1811261])), _1811257)))], (50875 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1811251, _1811251)), hAPP(hAPP(c_Product__Type_OPair(_1811251, _1811251), 50872 ^ [_1811251, _1811253, _1811255, _1811257, _1811259, _1811261]), 50873 ^ [_1811251, _1811253, _1811255, _1811257, _1811259, _1811261])), _1811253)))]], -(c_Equiv__Relations_Ocongruent2(_1811251, _1811255, _1811261, _1811253, _1811257, _1811259))], (36500 ^ _780478) ^ [_1474958, _1474960] : [-(c_Divides_OposDivAlg(_1474958, _1474960) = hAPP(c_Divides_Oadjust(_1474960), c_Divides_OposDivAlg(_1474958, 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)))), _1474960)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1474958), _1474960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1474960), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17582 ^ _780478) ^ [_1107342, _1107344, _1107346, _1107348, _1107350] : [class_Groups_Ocomm__monoid__mult(_1107342), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107344), _1107346)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1107344), _1107348)), 17596 ^ _780478 : [(17599 ^ _780478) ^ [] : [hAPP(_1107350, 17595 ^ [_1107342, _1107344, _1107346, _1107348, _1107350]) = c_Groups_Oone__class_Oone(_1107342)], (17597 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1107344), 17595 ^ [_1107342, _1107344, _1107346, _1107348, _1107350]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107344, tc_HOL_Obool)), _1107346), _1107348))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1107342, _1107344, c_Groups_Otimes__class_Otimes(_1107342)), _1107350), c_Groups_Oone__class_Oone(_1107342)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1107344, tc_HOL_Obool)), _1107346), _1107348)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1107342), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1107342, _1107344, c_Groups_Otimes__class_Otimes(_1107342)), _1107350), c_Groups_Oone__class_Oone(_1107342)), _1107346)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1107342, _1107344, c_Groups_Otimes__class_Otimes(_1107342)), _1107350), c_Groups_Oone__class_Oone(_1107342)), _1107348)))], (27553 ^ _780478) ^ [_1289929, _1289931] : [class_Rings_Oring__1(_1289929), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289929), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1289931)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1289929), _1289931))], (47560 ^ _780478) ^ [_1737670, _1737672, _1737674] : [-(c_List_Oinsert(_1737670, _1737672, c_List_Oremdups(_1737670, _1737674)) = c_List_Oremdups(_1737670, c_List_Oinsert(_1737670, _1737672, _1737674)))], (16034 ^ _780478) ^ [_1070672, _1070674, _1070676, _1070678] : [class_Lattices_Odistrib__lattice(_1070672), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070672), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070672), _1070674), _1070676)), _1070678) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070672), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070672), _1070674), _1070678)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070672), _1070676), _1070678)))], (15215 ^ _780478) ^ [_1054359, _1054361, _1054363] : [class_Lattices_Olattice(_1054359), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054359), _1054361)), -(hBOOL(hAPP(hAPP(c_member(_1054359), _1054363), _1054361))), -(_1054361 = c_Orderings_Obot__class_Obot(tc_fun(_1054359, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1054359, hAPP(hAPP(c_Set_Oinsert(_1054359), _1054363), _1054361)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1054359), _1054363), c_Big__Operators_Olattice__class_OSup__fin(_1054359, _1054361)))], (9384 ^ _780478) ^ [_941196, _941198, _941200, _941202, _941204] : [class_Groups_Oordered__cancel__ab__semigroup__add(_941196), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941196), _941198), _941200)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941196), _941202), _941204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941196), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941196), _941198), _941202)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941196), _941200), _941204))))], (35575 ^ _780478) ^ [_1450244, _1450246, _1450248, _1450250] : [-(c_Nitpick_Oprod(_1450244, _1450246, _1450248, _1450250) = hAPP(c_Set_OCollect(tc_prod(_1450244, _1450246)), hAPP(c_Product__Type_Oprod_Oprod__case(_1450244, _1450246, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1450244, tc_fun(_1450246, tc_HOL_Obool), tc_fun(_1450246, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1450246, tc_HOL_Obool), tc_fun(_1450246, tc_HOL_Obool)), _1450244), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1450246)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1450244), c_fconj), hAPP(hAPP(c_COMBC(_1450244, tc_fun(_1450244, tc_HOL_Obool), tc_HOL_Obool), c_member(_1450244)), _1450248)))), hAPP(hAPP(c_COMBC(_1450246, tc_fun(_1450246, tc_HOL_Obool), tc_HOL_Obool), c_member(_1450246)), _1450250)))))], (14885 ^ _780478) ^ [_1047760, _1047762, _1047764] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047760), _1047762)), _1047764) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1047762), _1047764)))], (8198 ^ _780478) ^ [_920659, _920661, _920663, _920665] : [class_Groups_Oab__semigroup__add(_920659), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920659), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920659), _920661), _920663)), _920665) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920659), _920661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920659), _920663), _920665)))], (13738 ^ _780478) ^ [_1025961, _1025963, _1025965, _1025967] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1025961), _1025963)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1025965), _1025967)), 13745 ^ _780478 : [(13746 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1025961), _1025963)), hAPP(c_Finite__Set_Ocard(_1025965), _1025967)))), 13747 ^ _780478 : [(13748 ^ _780478) ^ [_1026172] : [c_Fun_Oinj__on(_1025961, _1025965, _1026172, _1025963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025965, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1025961, _1025965, _1026172), _1025963)), _1025967))]]], (13756 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1025961), _1025963)), hAPP(c_Finite__Set_Ocard(_1025965), _1025967))), 13760 ^ _780478 : [(13763 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025965, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1025961, _1025965, 13759 ^ [_1025961, _1025963, _1025965, _1025967]), _1025963)), _1025967)))], (13761 ^ _780478) ^ [] : [-(c_Fun_Oinj__on(_1025961, _1025965, 13759 ^ [_1025961, _1025963, _1025965, _1025967], _1025963))]]]]], (23647 ^ _780478) ^ [_1219843, _1219845, _1219847, _1219849] : [class_Groups_Ocomm__monoid__add(_1219843), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219843), _1219845), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1219847)), hAPP(c_Nat_OSuc, _1219849))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1219843), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1219843, tc_Nat_Onat), _1219845), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1219847), _1219849)))], (31312 ^ _780478) ^ [_1363873, _1363875, _1363877, _1363879, _1363881, _1363883, _1363885] : [class_Groups_Ocomm__monoid__add(_1363873), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363875), _1363877)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1363879), _1363881)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363875, _1363873), hAPP(hAPP(c_COMBS(_1363875, tc_fun(_1363879, tc_HOL_Obool), _1363873), hAPP(hAPP(c_COMBB(tc_fun(_1363879, _1363873), tc_fun(tc_fun(_1363879, tc_HOL_Obool), _1363873), _1363875), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363879, _1363873)), _1363883)), hAPP(hAPP(c_COMBB(tc_fun(_1363879, tc_HOL_Obool), tc_fun(_1363879, tc_HOL_Obool), _1363875), c_Set_OCollect(_1363879)), hAPP(hAPP(c_COMBB(tc_fun(_1363879, tc_HOL_Obool), tc_fun(_1363879, tc_HOL_Obool), _1363875), hAPP(c_COMBS(_1363879, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1363879), c_fconj), hAPP(hAPP(c_COMBC(_1363879, tc_fun(_1363879, tc_HOL_Obool), tc_HOL_Obool), c_member(_1363879)), _1363881)))), _1363885)))), _1363877) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363879, _1363873), hAPP(hAPP(c_COMBS(_1363879, tc_fun(_1363875, tc_HOL_Obool), _1363873), hAPP(hAPP(c_COMBB(tc_fun(_1363875, _1363873), tc_fun(tc_fun(_1363875, tc_HOL_Obool), _1363873), _1363879), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363875, _1363873)), hAPP(c_COMBC(_1363875, _1363879, _1363873), _1363883))), hAPP(hAPP(c_COMBB(tc_fun(_1363875, tc_HOL_Obool), tc_fun(_1363875, tc_HOL_Obool), _1363879), c_Set_OCollect(_1363875)), hAPP(hAPP(c_COMBB(tc_fun(_1363875, tc_HOL_Obool), tc_fun(_1363875, tc_HOL_Obool), _1363879), hAPP(c_COMBS(_1363875, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1363875), c_fconj), hAPP(hAPP(c_COMBC(_1363875, tc_fun(_1363875, tc_HOL_Obool), tc_HOL_Obool), c_member(_1363875)), _1363877)))), hAPP(c_COMBC(_1363875, _1363879, tc_HOL_Obool), _1363885))))), _1363881))], (48537 ^ _780478) ^ [_1759817, _1759819, _1759821, _1759823] : [-(hAPP(hAPP(c_List_Omap(_1759817, _1759819), hAPP(c_COMBK(_1759819, _1759817), _1759821)), _1759823) = c_List_Oreplicate(_1759819, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759817)), _1759823), _1759821))], (18422 ^ _780478) ^ [_1125191, _1125193, _1125195] : [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, _1125191)), _1125193)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1125191)), _1125195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125193), _1125195)))], (35904 ^ _780478) ^ [_1462214, _1462216, _1462218, _1462220, _1462222, _1462224, _1462226] : [c_Equiv__Relations_Oequiv(_1462214, _1462216, _1462218), hBOOL(hAPP(hAPP(c_member(tc_fun(_1462214, tc_HOL_Obool)), _1462220), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462214), _1462216), _1462218))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1462214, tc_HOL_Obool)), _1462222), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1462214), _1462216), _1462218))), hBOOL(hAPP(hAPP(c_member(_1462214), _1462224), _1462220)), hBOOL(hAPP(hAPP(c_member(_1462214), _1462226), _1462222)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1462214, _1462214)), hAPP(hAPP(c_Product__Type_OPair(_1462214, _1462214), _1462224), _1462226)), _1462218)), -(_1462220 = _1462222)], (52139 ^ _780478) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (33054 ^ _780478) ^ [_1405163] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405163)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1405163)))], (19540 ^ _780478) ^ [_1145700] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145700) = _1145700)], (42368 ^ _780478) ^ [_1622308, _1622310, _1622312, _1622314, _1622316] : [hBOOL(hAPP(hAPP(c_member(_1622308), _1622310), hAPP(c_List_Oset(_1622308), _1622312))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1622314), hAPP(_1622316, _1622310))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1622314), c_List_Olist_Olist__size(_1622308, _1622316, _1622312))))], (29486 ^ _780478) ^ [_1327919, _1327921] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327919, _1327921)), _1327921) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8818 ^ _780478) ^ [_932848, _932850, _932852] : [class_Orderings_Opreorder(_932848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932848), _932850), _932852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932848), _932852), _932850))], (13821 ^ _780478) ^ [_1027627, _1027629, _1027631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027627), _1027629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027627), _1027631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027631), _1027629)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027631), _1027627))))], (18106 ^ _780478) ^ [_1117781, _1117783, _1117785, _1117787, _1117789] : [-(hAPP(hAPP(c_Set_Oinsert(_1117781), _1117783), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117785, tc_fun(_1117781, tc_HOL_Obool)), _1117787), _1117789)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117785, tc_fun(_1117781, tc_HOL_Obool)), _1117787), hAPP(hAPP(c_COMBB(tc_fun(_1117781, tc_HOL_Obool), tc_fun(_1117781, tc_HOL_Obool), _1117785), hAPP(c_Set_Oinsert(_1117781), _1117783)), _1117789)))], (49871 ^ _780478) ^ [_1788496, _1788498] : [c_Equiv__Relations_Oequivp(_1788496, _1788498), -(c_Equiv__Relations_Opart__equivp(_1788496, _1788498))], (10223 ^ _780478) ^ [_958427, _958429, _958431, _958433] : [class_Orderings_Olinorder(_958427), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_958427), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958427), _958429), _958431)), _958433) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_958427), _958429), hAPP(hAPP(c_Orderings_Oord__class_Omax(_958427), _958431), _958433)))], (24275 ^ _780478) ^ [_1232088, _1232090, _1232092, _1232094] : [class_Divides_Osemiring__div(_1232088), -(_1232090 = c_Groups_Ozero__class_Ozero(_1232088)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1232088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232088), _1232090), _1232092)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1232088), _1232090), _1232094)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1232088), _1232092), _1232094))], (40877 ^ _780478) ^ [_1581046, _1581048, _1581050, _1581052, _1581054] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581046, _1581048)), hAPP(hAPP(c_Product__Type_OPair(_1581046, _1581048), _1581050), _1581052)), hAPP(c_Relation_Oconverse(_1581048, _1581046), _1581054))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581048, _1581046)), hAPP(hAPP(c_Product__Type_OPair(_1581048, _1581046), _1581052), _1581050)), _1581054)))], (388 ^ _780478) ^ [_786364, _786366, _786368, _786370, _786372, _786374] : [-(c_Relation_Osingle__valued(_786372, _786368, _786364)), c_Relation_Osingle__valued(_786374, _786370, _786366), _786374 = _786372, _786370 = _786368, _786366 = _786364], (46125 ^ _780478) ^ [_1707756, _1707758, _1707760, _1707762, _1707764] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707756)), hAPP(c_List_Ofilter(_1707756, _1707758), hAPP(hAPP(c_List_Omap(_1707760, _1707756), _1707762), _1707764))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707760)), hAPP(c_List_Ofilter(_1707760, hAPP(c_Fun_Ocomp(_1707756, tc_HOL_Obool, _1707760, _1707758), _1707762)), _1707764)))], (19188 ^ _780478) ^ [_1140563, _1140565] : [class_Rings_Ocomm__semiring__1(_1140563), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140563), c_Groups_Ozero__class_Ozero(_1140563)), _1140565) = _1140565)], (43159 ^ _780478) ^ [_1640989, _1640991] : [-(_1640991 = c_List_Olist_ONil(_1640989)), -(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(_1640989)), _1640991))))], (48661 ^ _780478) ^ [_1762069, _1762071] : [-(c_List_Oreplicate(_1762069, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1762071) = c_List_Olist_ONil(_1762069))], (16028 ^ _780478) ^ [_1070513, _1070515, _1070517, _1070519] : [class_Lattices_Odistrib__lattice(_1070513), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070513), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070513), _1070515), _1070517)), _1070519) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070513), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070513), _1070515), _1070519)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070513), _1070517), _1070519)))], (18279 ^ _780478) ^ [_1122423, _1122425] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122423), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122425), _1122423)))))], (11161 ^ _780478) ^ [_975640, _975642, _975644] : [class_Orderings_Olinorder(_975640), hBOOL(hAPP(c_Finite__Set_Ofinite(_975640), _975642)), hBOOL(hAPP(hAPP(c_member(_975640), _975644), _975642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975640), hAPP(c_Finite__Set_Ofold1(_975640, c_Orderings_Oord__class_Omin(_975640)), _975642)), _975644)))], (31236 ^ _780478) ^ [_1362046, _1362048, _1362050] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1362046, tc_HOL_Obool)), _1362048), _1362050) = hAPP(c_Set_OCollect(_1362046), hAPP(hAPP(c_COMBS(_1362046, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1362046), c_fconj), hAPP(hAPP(c_COMBC(_1362046, tc_fun(_1362046, tc_HOL_Obool), tc_HOL_Obool), c_member(_1362046)), _1362048))), hAPP(hAPP(c_COMBC(_1362046, tc_fun(_1362046, tc_HOL_Obool), tc_HOL_Obool), c_member(_1362046)), _1362050))))], (22211 ^ _780478) ^ [_1193308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193308)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1193308), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1193308)], (31789 ^ _780478) ^ [_1381052, _1381054, _1381056] : [_1381052 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1381054, _1381054), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1381054, _1381054), tc_HOL_Obool)), _1381052), _1381056)))], (6682 ^ _780478) ^ [_890580, _890582, _890584, _890586, _890588] : [class_Groups_Ominus(_890580), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890582, _890580)), _890584), _890586), _890588) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_890580), hAPP(_890584, _890588)), hAPP(_890586, _890588)))], (23033 ^ _780478) ^ [_1209171, _1209173] : [class_Int_Oring__char__0(_1209171), hBOOL(hAPP(hAPP(c_member(_1209171), _1209173), c_Int_Oring__1__class_OInts(_1209171))), 23040 ^ _780478 : [(23047 ^ _780478) ^ [] : [_1209173 = c_Groups_Ozero__class_Ozero(_1209171), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209171), _1209173), _1209173) = c_Groups_Ozero__class_Ozero(_1209171))], (23041 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209171), _1209173), _1209173) = c_Groups_Ozero__class_Ozero(_1209171), -(_1209173 = c_Groups_Ozero__class_Ozero(_1209171))]]], (52169 ^ _780478) ^ [_1831763, _1831765] : [-(class_Enum_Oenum(tc_sum(_1831763, _1831765))), class_Enum_Oenum(_1831763), class_Enum_Oenum(_1831765)], (22620 ^ _780478) ^ [_1201751, _1201753, _1201755] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1201751), _1201753)), _1201755) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201751), _1201755)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201753), _1201755)))], (41073 ^ _780478) ^ [_1586281] : [-(hAPP(c_Relation_ORange(_1586281, _1586281), c_Relation_OId(_1586281)) = c_Orderings_Otop__class_Otop(tc_fun(_1586281, tc_HOL_Obool)))], (44155 ^ _780478) ^ [_1664179, _1664181, _1664183] : [_1664183 = c_List_Olist_ONil(_1664179), -(hAPP(c_List_Orotate(_1664179, _1664181), _1664183) = c_List_Olist_ONil(_1664179))], (34693 ^ _780478) ^ [_1434601, _1434603] : [class_Int_Onumber__ring(_1434601), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1434601), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434601), c_Groups_Oone__class_Oone(_1434601)), c_Groups_Oone__class_Oone(_1434601))), hAPP(c_Int_Onumber__class_Onumber__of(_1434601), _1434603)) = hAPP(c_Int_Onumber__class_Onumber__of(_1434601), c_Int_OBit0(_1434603)))], (34771 ^ _780478) ^ [] : [-(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))))))], (29297 ^ _780478) ^ [_1324467, _1324469, _1324471, _1324473] : [class_Divides_Oring__div(_1324467), c_Divides_Odiv__class_Omod(_1324467, _1324469, _1324471) = c_Divides_Odiv__class_Omod(_1324467, _1324473, _1324471), -(c_Divides_Odiv__class_Omod(_1324467, hAPP(c_Groups_Ouminus__class_Ouminus(_1324467), _1324469), _1324471) = c_Divides_Odiv__class_Omod(_1324467, hAPP(c_Groups_Ouminus__class_Ouminus(_1324467), _1324473), _1324471))], (35279 ^ _780478) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (49165 ^ _780478) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (36644 ^ _780478) ^ [_1477313, _1477315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1477313), _1477315)), -(c_Divides_Odivmod__nat(_1477313, _1477315) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1477313))], (11899 ^ _780478) ^ [_989575, _989577, _989579] : [class_Orderings_Olinorder(_989575), hBOOL(hAPP(c_Finite__Set_Ofinite(_989575), _989577)), hBOOL(hAPP(hAPP(c_member(_989575), _989579), _989577)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_989575), _989579), c_Big__Operators_Olattice_OSup__fin(_989575, c_Orderings_Oord__class_Omax(_989575), _989577)) = c_Big__Operators_Olattice_OSup__fin(_989575, c_Orderings_Oord__class_Omax(_989575), _989577))], (19486 ^ _780478) ^ [_1145008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1145008), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46036 ^ _780478) ^ [_1705868, _1705870, _1705872] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705868)), hAPP(c_List_Ofilter(_1705868, _1705870), _1705872))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705868)), hAPP(c_List_Ofilter(_1705868, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1705868), c_fNot), _1705870)), _1705872))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705868)), _1705872))], (42510 ^ _780478) ^ [_1627295, _1627297, _1627299, _1627301] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1627295, _1627295)), hAPP(hAPP(c_Product__Type_OPair(_1627295, _1627295), _1627297), _1627299)), hAPP(c_List_Oset(tc_prod(_1627295, _1627295)), hAPP(hAPP(c_List_Ozip(_1627295, _1627295), _1627301), _1627301))))), hBOOL(hAPP(hAPP(c_member(_1627295), _1627297), hAPP(c_List_Oset(_1627295), _1627301))), _1627297 = _1627299], (11175 ^ _780478) ^ [_975877, _975879, _975881] : [class_Orderings_Olinorder(_975877), hBOOL(hAPP(c_Finite__Set_Ofinite(_975877), _975879)), -(_975879 = c_Orderings_Obot__class_Obot(tc_fun(_975877, tc_HOL_Obool))), 11186 ^ _780478 : [(11196 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975877), hAPP(c_Finite__Set_Ofold1(_975877, c_Orderings_Oord__class_Omin(_975877)), _975879)), _975881))), 11197 ^ _780478 : [(11198 ^ _780478) ^ [_976266] : [hBOOL(hAPP(hAPP(c_member(_975877), _976266), _975879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975877), _976266), _975881))]]], (11187 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975877), hAPP(c_Finite__Set_Ofold1(_975877, c_Orderings_Oord__class_Omin(_975877)), _975879)), _975881)), 11191 ^ _780478 : [(11194 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975877), 11190 ^ [_975877, _975879, _975881]), _975881)))], (11192 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_975877), 11190 ^ [_975877, _975879, _975881]), _975879)))]]]]], (15659 ^ _780478) ^ [_1063299, _1063301, _1063303] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063299, tc_HOL_Obool)), _1063301), _1063303) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063299, tc_HOL_Obool)), _1063303), _1063301))], (52359 ^ _780478) ^ [_1833951] : [-(hBOOL(_1833951)), -(hBOOL(hAPP(c_fNot, _1833951)))], (51371 ^ _780478) ^ [_1821058] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821058, _1821058) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1821058), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (34031 ^ _780478) ^ [_1423002, _1423004] : [class_Int_Onumber__ring(_1423002), -(hAPP(c_Int_Onumber__class_Onumber__of(_1423002), c_Int_OBit1(_1423004)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1423002), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1423002), c_Groups_Oone__class_Oone(_1423002)), hAPP(c_Int_Onumber__class_Onumber__of(_1423002), _1423004))), hAPP(c_Int_Onumber__class_Onumber__of(_1423002), _1423004)))], (52333 ^ _780478) ^ [_1833548, _1833550, _1833552, _1833554, _1833556, _1833558] : [-(hAPP(hAPP(hAPP(c_COMBC(_1833548, _1833550, _1833552), _1833554), _1833556), _1833558) = hAPP(hAPP(_1833554, _1833558), _1833556))], (35127 ^ _780478) ^ [_1442445, _1442447, _1442449] : [class_Int_Onumber__ring(_1442445), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1442445), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1442445), _1442447), _1442449)), 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(_1442445), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1442445), hAPP(hAPP(c_Power_Opower__class_Opower(_1442445), _1442447), 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(_1442445), _1442449), 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(_1442445), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1442445), hAPP(c_Int_Onumber__class_Onumber__of(_1442445), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1442447)), _1442449)))], (35327 ^ _780478) ^ [_1446379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1446379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1446379)))], (33034 ^ _780478) ^ [_1404836] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404836)))), -(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), _1404836)) = 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), _1404836))))], (31208 ^ _780478) ^ [_1361250, _1361252, _1361254] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1361250), hAPP(c_Set_OCollect(_1361250), hAPP(hAPP(c_COMBS(_1361250, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1361250), c_fdisj), _1361252)), _1361254)))), 31211 ^ _780478 : [(31214 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1361250), hAPP(c_Set_OCollect(_1361250), _1361254))))], (31212 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1361250), hAPP(c_Set_OCollect(_1361250), _1361252))))]]], (7329 ^ _780478) ^ [_902938, _902940, _902942, _902944, _902946] : [c_Fun_Oinj__on(_902938, _902940, _902942, _902944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902938, tc_HOL_Obool)), _902946), _902944)), -(c_Fun_Oinj__on(_902938, _902940, _902942, _902946))], (47611 ^ _780478) ^ [_1738924, _1738926, _1738928, _1738930, _1738932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1738924, _1738926)), hAPP(_1738924, _1738928))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1738930, _1738930)), hAPP(hAPP(c_Product__Type_OPair(_1738930, _1738930), _1738926), _1738928)), c_List_Omeasures(_1738930, _1738932))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1738930, _1738930)), hAPP(hAPP(c_Product__Type_OPair(_1738930, _1738930), _1738926), _1738928)), c_List_Omeasures(_1738930, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1738930, tc_Nat_Onat)), _1738924), _1738932)))))], (28214 ^ _780478) ^ [_1302743, _1302745, _1302747] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1302743, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1302745)), _1302747) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302743, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1302743, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1302745)), _1302747)), hAPP(_1302747, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37616 ^ _780478) ^ [_1498403, _1498405] : [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), _1498403), _1498405)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1498403), _1498405)))], (14625 ^ _780478) ^ [_1041952, _1041954, _1041956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041952), _1041954)), 14628 ^ _780478 : [(14635 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041956), _1041952)), _1041954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041956), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041954), _1041952))))], (14629 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1041956), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1041954), _1041952))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1041956), _1041952)), _1041954)))]]], (33196 ^ _780478) ^ [_1407717] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407717)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407717)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407717))], (10121 ^ _780478) ^ [_956381, _956383, _956385] : [class_Groups_Ogroup__add(_956381), 10124 ^ _780478 : [(10131 ^ _780478) ^ [] : [_956383 = _956385, -(hAPP(c_Groups_Ouminus__class_Ouminus(_956381), _956383) = hAPP(c_Groups_Ouminus__class_Ouminus(_956381), _956385))], (10125 ^ _780478) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_956381), _956383) = hAPP(c_Groups_Ouminus__class_Ouminus(_956381), _956385), -(_956383 = _956385)]]], (6810 ^ _780478) ^ [_893105, _893107, _893109, _893111, _893113] : [c_Finite__Set_Ofun__left__comm__idem(_893105, _893107, _893109), -(c_Finite__Set_Ofun__left__comm__idem(_893111, _893107, hAPP(hAPP(c_COMBB(_893105, tc_fun(_893107, _893107), _893111), _893109), _893113)))], (11063 ^ _780478) ^ [_973615, _973617, _973619] : [hBOOL(hAPP(hAPP(c_member(_973615), _973617), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973615, tc_HOL_Obool)), _973619))), hBOOL(hAPP(hAPP(c_member(_973615), _973617), _973619))], (2980 ^ _780478) ^ [_824615, _824617] : [_824617 = _824615, -(c_Nitpick_Odenom(_824617) = c_Nitpick_Odenom(_824615))], (47334 ^ _780478) ^ [_1733041, _1733043, _1733045] : [-(c_List_OdropWhile(_1733041, _1733043, _1733045) = c_List_Olist_ONil(_1733041)), hBOOL(hAPP(_1733043, hAPP(c_List_Ohd(_1733041), c_List_OdropWhile(_1733041, _1733043, _1733045))))], (18181 ^ _780478) ^ [_1120215, _1120217, _1120219, _1120221, _1120223] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120215, tc_fun(_1120217, tc_HOL_Obool)), _1120219), hAPP(hAPP(c_COMBS(_1120215, tc_fun(_1120217, tc_HOL_Obool), tc_fun(_1120217, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1120217, tc_HOL_Obool), tc_fun(tc_fun(_1120217, tc_HOL_Obool), tc_fun(_1120217, tc_HOL_Obool)), _1120215), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1120217, tc_HOL_Obool))), _1120221)), _1120223)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1120217, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120215, tc_fun(_1120217, tc_HOL_Obool)), _1120219), _1120221)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120215, tc_fun(_1120217, tc_HOL_Obool)), _1120219), _1120223)))], (47041 ^ _780478) ^ [_1726784, _1726786, _1726788] : [hAPP(c_List_Orev(_1726784), _1726786) = hAPP(c_List_Orev(_1726784), _1726788), -(_1726786 = _1726788)], (32042 ^ _780478) ^ [_1385700, _1385702] : [class_Int_Onumber__ring(_1385700), -(hAPP(c_Int_Onumber__class_Onumber__of(_1385700), _1385702) = hAPP(c_Int_Oring__1__class_Oof__int(_1385700), _1385702))], (47308 ^ _780478) ^ [_1732340, _1732342] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1732340), _1732342) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1732340)), c_List_Oembed__list(_1732342))))], (3620 ^ _780478) ^ [_834631, _834633, _834635, _834637] : [-(c_List_Orotate(_834637, _834633) = c_List_Orotate(_834635, _834631)), _834637 = _834635, _834633 = _834631], (51653 ^ _780478) ^ [_1825807, _1825809, _1825811, _1825813] : [class_Divides_Osemiring__div(_1825807), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825807), _1825809), _1825811)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825807), _1825809), _1825813)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825807), _1825809), c_Divides_Odiv__class_Omod(_1825807, _1825811, _1825813))))], (19428 ^ _780478) ^ [_1144133] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1144133) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11035 ^ _780478) ^ [_973137, _973139, _973141] : [class_Rings_Oidom(_973137), 11038 ^ _780478 : [(11039 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973137), _973139), _973139) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973137), _973141), _973141), -(_973139 = _973141), -(_973139 = hAPP(c_Groups_Ouminus__class_Ouminus(_973137), _973141))], (11049 ^ _780478) ^ [] : [11050 ^ _780478 : [(11053 ^ _780478) ^ [] : [_973139 = hAPP(c_Groups_Ouminus__class_Ouminus(_973137), _973141)], (11051 ^ _780478) ^ [] : [_973139 = _973141]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973137), _973139), _973139) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_973137), _973141), _973141))]]], (42444 ^ _780478) ^ [_1624509, _1624511, _1624513, _1624515] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1624509), tc_List_Olist(_1624509))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1624509), tc_List_Olist(_1624509)), _1624511), _1624513)), c_List_Olistrel(_1624509, _1624515))), 42447 ^ _780478 : [(42450 ^ _780478) ^ [_1624845] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624509, _1624509)), _1624845), hAPP(c_List_Oset(tc_prod(_1624509, _1624509)), hAPP(hAPP(c_List_Ozip(_1624509, _1624509), _1624511), _1624513)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1624509, _1624509, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1624509, tc_fun(tc_prod(_1624509, _1624509), tc_HOL_Obool), tc_fun(_1624509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1624509, tc_fun(tc_fun(tc_prod(_1624509, _1624509), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1624509, _1624509), tc_HOL_Obool), tc_fun(_1624509, tc_HOL_Obool)), _1624509), c_COMBC(_1624509, tc_fun(tc_prod(_1624509, _1624509), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1624509, tc_prod(_1624509, _1624509)), tc_fun(_1624509, tc_fun(tc_fun(tc_prod(_1624509, _1624509), tc_HOL_Obool), tc_HOL_Obool)), _1624509), hAPP(c_COMBB(tc_prod(_1624509, _1624509), tc_fun(tc_fun(tc_prod(_1624509, _1624509), tc_HOL_Obool), tc_HOL_Obool), _1624509), c_member(tc_prod(_1624509, _1624509)))), c_Product__Type_OPair(_1624509, _1624509)))), _1624515)), _1624845)))], (42448 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624509)), _1624511) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1624509)), _1624513))]]], (18454 ^ _780478) ^ [_1126117, _1126119] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126117), hAPP(c_Nat_OSuc, _1126119)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1126117), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126117), _1126119)))], (2898 ^ _780478) ^ [_823386, _823388, _823390, _823392, _823394, _823396] : [-(c_Nitpick_Oof__frac(_823396, _823392, _823388) = c_Nitpick_Oof__frac(_823394, _823390, _823386)), _823396 = _823394, _823392 = _823390, _823388 = _823386], (2338 ^ _780478) ^ [_814718, _814720, _814722, _814724] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_814724, _814720) = c_Code__Numeral_Odiv__mod__code__numeral(_814722, _814718)), _814724 = _814722, _814720 = _814718], (47053 ^ _780478) ^ [_1726980, _1726982] : [class_Groups_Ocomm__monoid__add(_1726980), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1726980), hAPP(c_List_Orev(_1726980), _1726982)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1726980), _1726982))], (38360 ^ _780478) ^ [_1517478, _1517480] : [c_Wellfounded_Owf(_1517478, _1517480), 38364 ^ _780478 : [(38365 ^ _780478) ^ [_1517614] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517478, _1517478)), hAPP(hAPP(c_Product__Type_OPair(_1517478, _1517478), hAPP(_1517614, hAPP(c_Nat_OSuc, 38363 ^ [_1517478, _1517480, _1517614]))), hAPP(_1517614, 38363 ^ [_1517478, _1517480, _1517614]))), _1517480))]]], (47252 ^ _780478) ^ [_1731206, _1731208, _1731210] : [hBOOL(hAPP(c_List_Odistinct(_1731206), _1731208)), -(hBOOL(hAPP(c_List_Odistinct(_1731206), c_List_OtakeWhile(_1731206, _1731210, _1731208))))], (16582 ^ _780478) ^ [_1083481, _1083483, _1083485] : [class_Lattices_Osemilattice__inf(_1083481), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083481), _1083483)), hBOOL(hAPP(hAPP(c_member(_1083481), _1083485), _1083483)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1083481), hAPP(c_Finite__Set_Ofold1(_1083481, c_Lattices_Osemilattice__inf__class_Oinf(_1083481)), _1083483)), _1083485)))], (51807 ^ _780478) ^ [_1828186, _1828188] : [-(class_Finite__Set_Ofinite(tc_fun(_1828186, _1828188))), class_Finite__Set_Ofinite(_1828186), class_Finite__Set_Ofinite(_1828188)], (47868 ^ _780478) ^ [_1745237, _1745239, _1745241, _1745243, _1745245] : [hAPP(c_List_Ofilter(_1745237, _1745239), _1745241) = hAPP(hAPP(c_List_Olist_OCons(_1745237), _1745243), _1745245), 47873 ^ _780478 : [(47882 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1745239, _1745243)))], (47884 ^ _780478) ^ [] : [-(_1745245 = hAPP(c_List_Ofilter(_1745237, _1745239), 47872 ^ [_1745237, _1745239, _1745241, _1745243, _1745245]))], (47876 ^ _780478) ^ [_1745551] : [hBOOL(hAPP(hAPP(c_member(_1745237), _1745551), hAPP(c_List_Oset(_1745237), 47871 ^ [_1745237, _1745239, _1745241, _1745243, _1745245]))), hBOOL(hAPP(_1745239, _1745551))], (47874 ^ _780478) ^ [] : [-(_1745241 = hAPP(hAPP(c_List_Oappend(_1745237), 47871 ^ [_1745237, _1745239, _1745241, _1745243, _1745245]), hAPP(hAPP(c_List_Olist_OCons(_1745237), _1745243), 47872 ^ [_1745237, _1745239, _1745241, _1745243, _1745245])))]]], (41001 ^ _780478) ^ [_1584276, _1584278, _1584280, _1584282, _1584284, _1584286] : [c_Relation_Osingle__valued(_1584276, _1584278, hAPP(c_Relation_Oconverse(_1584278, _1584276), _1584280)), -(_1584282 = c_Orderings_Obot__class_Obot(tc_fun(_1584284, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1584278, _1584276, _1584280), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1584284, tc_fun(_1584278, tc_HOL_Obool)), _1584282), _1584286)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1584284, tc_fun(_1584276, tc_HOL_Obool)), _1584282), hAPP(hAPP(c_COMBB(tc_fun(_1584278, tc_HOL_Obool), tc_fun(_1584276, tc_HOL_Obool), _1584284), c_Relation_OImage(_1584278, _1584276, _1584280)), _1584286)))], (46679 ^ _780478) ^ [_1719298, _1719300, _1719302] : [class_Orderings_Olinorder(_1719298), 46682 ^ _780478 : [(46695 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1719298, hAPP(hAPP(c_List_Olist_OCons(_1719298), _1719300), _1719302))), c_List_Olinorder__class_Osorted(_1719298, _1719302), 46701 ^ _780478 : [(46704 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719298), _1719300), 46700 ^ [_1719298, _1719300, _1719302]))], (46702 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1719298), 46700 ^ [_1719298, _1719300, _1719302]), hAPP(c_List_Oset(_1719298), _1719302))))]]], (46683 ^ _780478) ^ [] : [c_List_Olinorder__class_Osorted(_1719298, hAPP(hAPP(c_List_Olist_OCons(_1719298), _1719300), _1719302)), 46686 ^ _780478 : [(46689 ^ _780478) ^ [_1719484] : [hBOOL(hAPP(hAPP(c_member(_1719298), _1719484), hAPP(c_List_Oset(_1719298), _1719302))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719298), _1719300), _1719484)))], (46687 ^ _780478) ^ [] : [-(c_List_Olinorder__class_Osorted(_1719298, _1719302))]]]]], (23771 ^ _780478) ^ [_1222446, _1222448] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1222446, 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(_1222446, tc_HOL_Obool)), tc_fun(_1222446, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1222446, tc_HOL_Obool)), tc_fun(_1222446, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1222446, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1222448)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1222446, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1222448))], (24797 ^ _780478) ^ [_1241221, _1241223, _1241225] : [_1241221 = 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), _1241221), _1241223)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1241221), _1241225)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42872 ^ _780478) ^ [_1635675, _1635677, _1635679, _1635681] : [hBOOL(hAPP(c_List_Odistinct(_1635675), _1635677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1635679), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635675)), _1635677))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1635681), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635675)), _1635677))), 42883 ^ _780478 : [(42890 ^ _780478) ^ [] : [_1635679 = _1635681, -(hAPP(hAPP(c_List_Onth(_1635675), _1635677), _1635679) = hAPP(hAPP(c_List_Onth(_1635675), _1635677), _1635681))], (42884 ^ _780478) ^ [] : [hAPP(hAPP(c_List_Onth(_1635675), _1635677), _1635679) = hAPP(hAPP(c_List_Onth(_1635675), _1635677), _1635681), -(_1635679 = _1635681)]]], (48645 ^ _780478) ^ [_1761798, _1761800, _1761802, _1761804] : [-(c_List_Oreplicate(_1761798, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1761800), _1761802), _1761804) = hAPP(hAPP(c_List_Oappend(_1761798), c_List_Oreplicate(_1761798, _1761800, _1761804)), c_List_Oreplicate(_1761798, _1761802, _1761804)))], (12746 ^ _780478) ^ [_1006059, _1006061, _1006063, _1006065] : [class_Lattices_Osemilattice__sup(_1006059), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006059), _1006061), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006059), _1006063), _1006065)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006059), _1006063), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006059), _1006061), _1006065)))], (50725 ^ _780478) ^ [_1806584, _1806586, _1806588] : [hBOOL(hAPP(hAPP(_1806588, _1806586), _1806586)), -(hBOOL(hAPP(hAPP(c_member(_1806584), _1806586), c_Quotient_ORespects(_1806584, _1806588))))], (13174 ^ _780478) ^ [_1014269, _1014271, _1014273] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014269, tc_HOL_Obool)), _1014271), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014269, tc_HOL_Obool)), _1014273), _1014271)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1014269, tc_HOL_Obool)), _1014271), _1014273))], (42644 ^ _780478) ^ [_1630284, _1630286, _1630288, _1630290] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630284)), hAPP(hAPP(c_List_Olist__update(_1630284, _1630286), _1630288), _1630290)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630284)), _1630286))], (13348 ^ _780478) ^ [_1018025, _1018027, _1018029, _1018031, _1018033] : [_1018025 = hAPP(_1018027, _1018029), -(hBOOL(hAPP(hAPP(c_member(_1018031), _1018025), hAPP(c_Set_Oimage(_1018033, _1018031, _1018027), c_Orderings_Otop__class_Otop(tc_fun(_1018033, tc_HOL_Obool))))))], (42292 ^ _780478) ^ [_1620577, _1620579, _1620581, _1620583] : [-(hBOOL(hAPP(hAPP(c_member(_1620577), _1620579), hAPP(c_List_Oset(_1620577), _1620581)))), hBOOL(hAPP(hAPP(c_member(_1620577), _1620579), hAPP(c_List_Oset(_1620577), c_List_Osublist(_1620577, _1620581, _1620583))))], (52321 ^ _780478) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (28716 ^ _780478) ^ [_1312230, _1312232, _1312234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1312230)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1312232), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1312234)), 28726 ^ _780478 : [(28732 ^ _780478) ^ [] : [-(_1312232 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28728 ^ [_1312230, _1312232, _1312234]), 28725 ^ [_1312230, _1312232, _1312234]))], (28730 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28728 ^ [_1312230, _1312232, _1312234]), _1312234)))], (28727 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28725 ^ [_1312230, _1312232, _1312234]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1312230))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1312232), _1312230) = _1312232)], (7521 ^ _780478) ^ [_906858, _906860, _906862, _906864, _906866, _906868] : [c_Fun_Oinj__on(_906858, _906860, _906862, _906864), -(_906866 = _906868), hBOOL(hAPP(hAPP(c_member(_906858), _906866), _906864)), hBOOL(hAPP(hAPP(c_member(_906858), _906868), _906864)), hAPP(_906862, _906866) = hAPP(_906862, _906868)], (18770 ^ _780478) ^ [_1132989, _1132991, _1132993] : [class_Complete__Lattice_Ocomplete__lattice(_1132989), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132989), _1132991)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1132989), _1132993), c_Complete__Lattice_OInf__class_OInf(_1132989, _1132991)) = hAPP(hAPP(c_Finite__Set_Ofold(_1132989, _1132989, c_Lattices_Osemilattice__inf__class_Oinf(_1132989)), _1132993), _1132991))], (43273 ^ _780478) ^ [_1643428, _1643430, _1643432, _1643434, _1643436, _1643438] : [-(hAPP(c_List_Olist_Olist__case(_1643428, _1643430, _1643432, _1643434), hAPP(hAPP(c_List_Olist_OCons(_1643430), _1643436), _1643438)) = hAPP(hAPP(_1643434, _1643436), _1643438))], (3694 ^ _780478) ^ [_835786, _835788] : [_835788 = _835786, -(c_List_Oembed__list(_835788) = c_List_Oembed__list(_835786))], (52239 ^ _780478) ^ [_1832624] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1832624)))], (45373 ^ _780478) ^ [_1690079, _1690081] : [-(c_List_Opartition(_1690079, _1690081, c_List_Olist_ONil(_1690079)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1690079), tc_List_Olist(_1690079)), c_List_Olist_ONil(_1690079)), c_List_Olist_ONil(_1690079)))], (41620 ^ _780478) ^ [_1600687, _1600689, _1600691] : [-(c_Nitpick_Otimes__frac(_1600687, _1600689, _1600691) = hAPP(hAPP(c_Nitpick_Ofrac(_1600687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1600687), _1600689)), hAPP(c_Nitpick_Onum(_1600687), _1600691))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1600687), _1600689)), hAPP(c_Nitpick_Odenom(_1600687), _1600691))))], (38957 ^ _780478) ^ [_1533740, _1533742, _1533744, _1533746] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1533740), _1533742)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533740, _1533740), tc_HOL_Obool)), _1533744), hAPP(hAPP(c_Product__Type_OSigma(_1533740, _1533740), _1533742), hAPP(c_COMBK(tc_fun(_1533740, tc_HOL_Obool), _1533740), _1533742)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1533740, tc_HOL_Obool)), _1533746), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1533740), _1533742), _1533744))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1533740), _1533746)))], (42029 ^ _780478) ^ [_1613662, _1613664, _1613666, _1613668, _1613670, _1613672] : [hBOOL(hAPP(hAPP(_1613662, _1613664), _1613666)), c_List_Olistrelp(_1613668, _1613662, _1613670, _1613672), -(c_List_Olistrelp(_1613668, _1613662, hAPP(hAPP(c_List_Olist_OCons(_1613668), _1613664), _1613670), hAPP(hAPP(c_List_Olist_OCons(_1613668), _1613666), _1613672)))], (16192 ^ _780478) ^ [_1073866, _1073868, _1073870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073866, tc_HOL_Obool)), _1073868), _1073870)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073866, tc_HOL_Obool)), _1073870), _1073868) = _1073868)], (33060 ^ _780478) ^ [_1405270, _1405272] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405270)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405272)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1405270), _1405272)))], (49191 ^ _780478) ^ [_1773974, _1773976] : [c_Relation_Otrans(_1773974, _1773976), 49194 ^ _780478 : [(49195 ^ _780478) ^ [_1774110, _1774112] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773974, _1773974)), hAPP(hAPP(c_Product__Type_OPair(_1773974, _1773974), _1774112), _1774110)), _1773976)), 49198 ^ _780478 : [(49199 ^ _780478) ^ [_1774253] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773974, _1773974)), hAPP(hAPP(c_Product__Type_OPair(_1773974, _1773974), _1774110), _1774253)), _1773976)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773974, _1773974)), hAPP(hAPP(c_Product__Type_OPair(_1773974, _1773974), _1774112), _1774253)), _1773976)))]]]]], (31730 ^ _780478) ^ [_1379816, _1379818, _1379820, _1379822, _1379824, _1379826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1379816, _1379818), tc_HOL_Obool)), _1379820), _1379822)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379816, tc_HOL_Obool)), _1379824), _1379826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379818, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379816, _1379818, _1379820), _1379824)), hAPP(c_Relation_OImage(_1379816, _1379818, _1379822), _1379826))))], (37816 ^ _780478) ^ [] : [-(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)))], (13416 ^ _780478) ^ [_1019542, _1019544, _1019546, _1019548, _1019550, _1019552, _1019554, _1019556] : [c_Finite__Set_Ofolding__image__simple__idem(_1019542, _1019544, _1019546, _1019548, _1019550, _1019552), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019544), _1019554)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019544), _1019556)), -(hAPP(_1019552, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1019544, tc_HOL_Obool)), _1019554), _1019556)) = hAPP(hAPP(_1019546, hAPP(_1019552, _1019554)), hAPP(_1019552, _1019556)))], (49379 ^ _780478) ^ [_1778183, _1778185, _1778187, _1778189] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1778183, tc_fun(_1778185, tc_HOL_Obool)), _1778187), _1778189) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1778185, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1778185, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1778183, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1778185, tc_HOL_Obool)), c_HOL_OEx(_1778183)), hAPP(hAPP(c_COMBB(tc_fun(_1778183, tc_HOL_Obool), tc_fun(_1778183, tc_HOL_Obool), tc_fun(_1778185, tc_HOL_Obool)), hAPP(c_COMBS(_1778183, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1778183), c_fconj), hAPP(hAPP(c_COMBC(_1778183, tc_fun(_1778183, tc_HOL_Obool), tc_HOL_Obool), c_member(_1778183)), _1778187)))), hAPP(hAPP(c_COMBC(tc_fun(_1778185, tc_HOL_Obool), tc_fun(_1778183, tc_fun(_1778185, tc_HOL_Obool)), tc_fun(_1778183, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778185, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1778183, tc_fun(_1778185, tc_HOL_Obool)), tc_fun(_1778183, tc_HOL_Obool)), tc_fun(_1778185, tc_HOL_Obool)), c_COMBB(tc_fun(_1778185, tc_HOL_Obool), tc_HOL_Obool, _1778183)), c_fequal)), _1778189))))))], (43275 ^ _780478) ^ [_1643483, _1643485, _1643487, _1643489] : [-(hAPP(c_List_Olist_Olist__case(_1643483, _1643485, _1643487, _1643489), c_List_Olist_ONil(_1643485)) = _1643487)], (50672 ^ _780478) ^ [_1805557, _1805559] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805557), _1805559)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1805557, 50675 ^ [_1805557, _1805559], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1805557), _1805559)), _1805559))], (41732 ^ _780478) ^ [_1603906, _1603908, _1603910, _1603912, _1603914] : [-(hAPP(hAPP(c_List_Olist_OCons(_1603906), _1603908), _1603910) = hAPP(hAPP(c_List_Olist_OCons(_1603906), _1603912), _1603914)), _1603908 = _1603912, _1603910 = _1603914], (12794 ^ _780478) ^ [_1007179, _1007181] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007179), c_Orderings_Otop__class_Otop(tc_fun(_1007179, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1007179), _1007181) = hAPP(c_Finite__Set_Ocard(_1007179), c_Orderings_Otop__class_Otop(tc_fun(_1007179, tc_HOL_Obool))), -(_1007181 = c_Orderings_Otop__class_Otop(tc_fun(_1007179, tc_HOL_Obool)))], (12642 ^ _780478) ^ [_1004057, _1004059, _1004061, _1004063] : [12646 ^ _780478 : [(12649 ^ _780478) ^ [] : [hBOOL(hAPP(_1004063, 12645 ^ [_1004057, _1004059, _1004061, _1004063]))], (12647 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1004057), 12645 ^ [_1004057, _1004059, _1004061, _1004063]), _1004059)))]], 12651 ^ _780478 : [(12654 ^ _780478) ^ [] : [hBOOL(hAPP(_1004063, 12650 ^ [_1004057, _1004059, _1004061, _1004063]))], (12652 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1004057), 12650 ^ [_1004057, _1004059, _1004061, _1004063]), _1004061)))]], 12655 ^ _780478 : [(12656 ^ _780478) ^ [_1004390] : [hBOOL(hAPP(hAPP(c_member(_1004057), _1004390), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004057, tc_HOL_Obool)), _1004059), _1004061))), -(hBOOL(hAPP(_1004063, _1004390)))]]], (29059 ^ _780478) ^ [_1319410, _1319412] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1319410)), _1319412) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1319410), 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), _1319410)), _1319412))], (18351 ^ _780478) ^ [_1123769, _1123771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123769)), _1123771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123769), _1123771)))], (26636 ^ _780478) ^ [_1273944, _1273946, _1273948] : [class_Fields_Olinordered__field(_1273944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273944), _1273946), c_Groups_Ozero__class_Ozero(_1273944))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273944), _1273948), c_Groups_Ozero__class_Ozero(_1273944))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273944), c_Groups_Ozero__class_Ozero(_1273944)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273944), _1273946), _1273948))))], (30644 ^ _780478) ^ [_1349361, _1349363, _1349365] : [30646 ^ _780478 : [(30649 ^ _780478) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349361, tc_HOL_Obool)), 30645 ^ [_1349361, _1349363, _1349365]), _1349365) = c_Orderings_Obot__class_Obot(tc_fun(_1349361, tc_HOL_Obool))], (30647 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1349361, tc_HOL_Obool)), 30645 ^ [_1349361, _1349363, _1349365]), _1349363)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349361, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349361, tc_HOL_Obool), _1349363)), _1349365) = c_Orderings_Obot__class_Obot(tc_fun(_1349361, tc_HOL_Obool)))], (37818 ^ _780478) ^ [] : [-(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)))], (52257 ^ _780478) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (18478 ^ _780478) ^ [_1126611, _1126613, _1126615] : [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, _1126611)), _1126613)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126611)), _1126615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1126613), _1126615)))], (9290 ^ _780478) ^ [_939589, _939591, _939593] : [class_Orderings_Olinorder(_939589), 9293 ^ _780478 : [(9300 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939589), _939593), _939591)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939589), _939591), _939593))], (9294 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939589), _939591), _939593))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939589), _939593), _939591)))]]], (41206 ^ _780478) ^ [_1589560, _1589562, _1589564, _1589566] : [-(hAPP(_1589560, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1589562, _1589562), _1589564), _1589560), _1589566)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1589562, _1589562), _1589564), _1589560), hAPP(_1589560, _1589566)))], (9808 ^ _780478) ^ [_950050, _950052, _950054, _950056] : [class_Rings_Ocomm__semiring__1(_950050), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950050), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950050), _950052), _950054)), _950056) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950050), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_950050), _950052), _950056)), _950054))], (1524 ^ _780478) ^ [_802392, _802394] : [-(class_Groups_Olinordered__ab__semigroup__add(_802392)), _802394 = _802392, class_Groups_Olinordered__ab__semigroup__add(_802394)], (25886 ^ _780478) ^ [_1260325, _1260327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260325)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1260325), _1260327)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1260325)), hAPP(c_Int_Onat, _1260327)))], (44588 ^ _780478) ^ [_1672761, _1672763] : [-(_1672761 = c_List_Olist_ONil(_1672763)), -(hBOOL(hAPP(hAPP(c_member(_1672763), c_List_Olast(_1672763, _1672761)), hAPP(c_List_Oset(_1672763), _1672761))))], (42674 ^ _780478) ^ [_1631031, _1631033, _1631035, _1631037, _1631039] : [-(hAPP(hAPP(c_List_Olist__update(_1631031, hAPP(hAPP(c_List_Olist_OCons(_1631031), _1631033), _1631035)), hAPP(c_Nat_OSuc, _1631037)), _1631039) = hAPP(hAPP(c_List_Olist_OCons(_1631031), _1631033), hAPP(hAPP(c_List_Olist__update(_1631031, _1631035), _1631037), _1631039)))], (20794 ^ _780478) ^ [_1167869, _1167871] : [class_Groups_Ogroup__add(_1167869), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167869), _1167871), hAPP(c_Groups_Ouminus__class_Ouminus(_1167869), _1167871)) = c_Groups_Ozero__class_Ozero(_1167869))], (31142 ^ _780478) ^ [_1360013] : [-(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)), _1360013)))))], (45391 ^ _780478) ^ [_1690980, _1690982, _1690984, _1690986, _1690988] : [-(c_Enum_Oproduct(_1690980, _1690982, hAPP(hAPP(c_List_Olist_OCons(_1690980), _1690984), _1690986), _1690988) = hAPP(hAPP(c_List_Oappend(tc_prod(_1690980, _1690982)), hAPP(hAPP(c_List_Omap(_1690982, tc_prod(_1690980, _1690982)), hAPP(c_Product__Type_OPair(_1690980, _1690982), _1690984)), _1690988)), c_Enum_Oproduct(_1690980, _1690982, _1690986, _1690988)))], (3326 ^ _780478) ^ [_830026, _830028, _830030, _830032] : [-(c_List_Olists(_830032, _830028) = c_List_Olists(_830030, _830026)), _830032 = _830030, _830028 = _830026], (37024 ^ _780478) ^ [_1484671, _1484673, _1484675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484671, tc_fun(_1484671, tc_HOL_Obool))), _1484673), _1484675)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484671, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1484671, _1484675)), c_Wellfounded_Oaccp(_1484671, _1484673))))], (39355 ^ _780478) ^ [_1544923, _1544925, _1544927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1544923, _1544923), tc_HOL_Obool)), _1544925), hAPP(hAPP(c_Product__Type_OSigma(_1544923, _1544923), _1544927), hAPP(c_COMBK(tc_fun(_1544923, tc_HOL_Obool), _1544923), _1544927)))), 39361 ^ _780478 : [(39364 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544923, _1544923)), hAPP(hAPP(c_Product__Type_OPair(_1544923, _1544923), 39360 ^ [_1544923, _1544925, _1544927]), 39360 ^ [_1544923, _1544925, _1544927])), _1544925))], (39362 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544923), 39360 ^ [_1544923, _1544925, _1544927]), _1544927)))]], -(c_Relation_Orefl__on(_1544923, _1544927, _1544925))], (18596 ^ _780478) ^ [_1129252, _1129254, _1129256, _1129258, _1129260] : [_1129252 = c_Orderings_Obot__class_Obot(tc_fun(_1129254, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129254, tc_fun(_1129256, tc_HOL_Obool)), _1129252), hAPP(hAPP(c_COMBC(_1129254, tc_fun(_1129256, tc_HOL_Obool), tc_fun(_1129256, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1129256, tc_HOL_Obool), tc_fun(tc_fun(_1129256, tc_HOL_Obool), tc_fun(_1129256, tc_HOL_Obool)), _1129254), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129256, tc_HOL_Obool))), _1129258)), _1129260)) = c_Orderings_Otop__class_Otop(tc_fun(_1129256, tc_HOL_Obool)))], (35856 ^ _780478) ^ [_1461128, _1461130, _1461132] : [class_Rings_Osemiring__1(_1461128), hBOOL(hAPP(hAPP(c_member(_1461128), _1461130), c_Nat_Osemiring__1__class_ONats(_1461128))), hBOOL(hAPP(hAPP(c_member(_1461128), _1461132), c_Nat_Osemiring__1__class_ONats(_1461128))), -(hBOOL(hAPP(hAPP(c_member(_1461128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1461128), _1461130), _1461132)), c_Nat_Osemiring__1__class_ONats(_1461128))))], (48206 ^ _780478) ^ [_1752193, _1752195, _1752197] : [c_List_Olist__all(_1752193, _1752195, _1752197), 48209 ^ _780478 : [(48210 ^ _780478) ^ [_1752274] : [hBOOL(hAPP(hAPP(c_member(_1752193), _1752274), hAPP(c_List_Oset(_1752193), _1752197))), -(hBOOL(hAPP(_1752195, _1752274)))]]], (12710 ^ _780478) ^ [_1005357, _1005359, _1005361] : [class_Lattices_Osemilattice__sup(_1005357), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005357), _1005359), _1005361) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005357), _1005361), _1005359))], (7373 ^ _780478) ^ [_903934, _903936, _903938, _903940, _903942, _903944] : [c_Fun_Oinj__on(_903934, _903936, _903938, _903940), hAPP(_903938, _903942) = _903944, hBOOL(hAPP(hAPP(c_member(_903934), _903942), _903940)), -(hAPP(c_Fun_Othe__inv__into(_903934, _903936, _903940, _903938), _903944) = _903942)], (35187 ^ _780478) ^ [_1443763] : [_1443763 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1443763) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35677 ^ _780478) ^ [_1455875, _1455877, _1455879, _1455881, _1455883, _1455885] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1455875, _1455877)), hAPP(hAPP(c_Product__Type_OPair(_1455875, _1455877), _1455883), _1455885)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool)), _1455879), _1455881))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455875, tc_fun(_1455877, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1455875, tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_fun(_1455877, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455877, tc_fun(tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_fun(_1455877, tc_HOL_Obool)), _1455875), c_COMBC(_1455877, tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455877, tc_prod(_1455875, _1455877)), tc_fun(_1455877, tc_fun(tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_HOL_Obool)), _1455875), hAPP(c_COMBB(tc_prod(_1455875, _1455877), tc_fun(tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_HOL_Obool), _1455877), c_member(tc_prod(_1455875, _1455877)))), c_Product__Type_OPair(_1455875, _1455877)))), _1455879)), hAPP(hAPP(c_COMBC(_1455875, tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_fun(_1455877, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455877, tc_fun(tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_fun(_1455877, tc_HOL_Obool)), _1455875), c_COMBC(_1455877, tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1455877, tc_prod(_1455875, _1455877)), tc_fun(_1455877, tc_fun(tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_HOL_Obool)), _1455875), hAPP(c_COMBB(tc_prod(_1455875, _1455877), tc_fun(tc_fun(tc_prod(_1455875, _1455877), tc_HOL_Obool), tc_HOL_Obool), _1455877), c_member(tc_prod(_1455875, _1455877)))), c_Product__Type_OPair(_1455875, _1455877)))), _1455881)), _1455883), _1455885)))], (23923 ^ _780478) ^ [_1225262, _1225264, _1225266, _1225268, _1225270] : [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), _1225262), _1225264)), _1225266)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225262), _1225268)), _1225270))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225266), _1225262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225270), _1225262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225264), _1225268)))], (17458 ^ _780478) ^ [_1104505, _1104507, _1104509, _1104511, _1104513] : [hBOOL(hAPP(hAPP(c_member(_1104505), _1104507), _1104509)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1104511, tc_HOL_Obool)), hAPP(_1104513, _1104507)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104505, tc_fun(_1104511, tc_HOL_Obool)), _1104509), _1104513))))], (50293 ^ _780478) ^ [_1797877, _1797879, _1797881, _1797883, _1797885, _1797887] : [c_Fun_Obij__betw(_1797877, _1797879, _1797881, _1797883, _1797885), hBOOL(hAPP(hAPP(c_member(_1797877), _1797887), _1797883)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1797879, _1797877, _1797885, c_Hilbert__Choice_Oinv__into(_1797877, _1797879, _1797883, _1797881)), _1797887) = hAPP(_1797881, _1797887))], (40955 ^ _780478) ^ [_1583022, _1583024, _1583026, _1583028] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583022, _1583022)), hAPP(hAPP(c_Product__Type_OPair(_1583022, _1583022), _1583024), _1583026)), c_Transitive__Closure_Otrancl(_1583022, hAPP(c_Relation_Oconverse(_1583022, _1583022), _1583028)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583022, _1583022)), hAPP(hAPP(c_Product__Type_OPair(_1583022, _1583022), _1583024), _1583026)), hAPP(c_Relation_Oconverse(_1583022, _1583022), c_Transitive__Closure_Otrancl(_1583022, _1583028)))))], (41995 ^ _780478) ^ [_1612157, _1612159, _1612161, _1612163, _1612165, _1612167] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1612157, _1612157)), hAPP(hAPP(c_Product__Type_OPair(_1612157, _1612157), _1612159), _1612161)), _1612163)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612157), tc_List_Olist(_1612157))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612157), tc_List_Olist(_1612157)), _1612165), _1612167)), c_List_Olistrel(_1612157, _1612163))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612157), tc_List_Olist(_1612157))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612157), tc_List_Olist(_1612157)), hAPP(hAPP(c_List_Olist_OCons(_1612157), _1612159), _1612165)), hAPP(hAPP(c_List_Olist_OCons(_1612157), _1612161), _1612167))), c_List_Olistrel(_1612157, _1612163))))], (42184 ^ _780478) ^ [_1617718, _1617720, _1617722] : [-(_1617718 = _1617720), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617722)), _1617718) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617722)), _1617720), 42190 ^ _780478 : [(42193 ^ _780478) ^ [] : [hAPP(hAPP(c_List_Onth(_1617722), _1617718), 42189 ^ [_1617718, _1617720, _1617722]) = hAPP(hAPP(c_List_Onth(_1617722), _1617720), 42189 ^ [_1617718, _1617720, _1617722])], (42191 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42189 ^ [_1617718, _1617720, _1617722]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617722)), _1617718))))]]], (33977 ^ _780478) ^ [_1422119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1422119)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422119), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (47312 ^ _780478) ^ [_1732411, _1732413, _1732415] : [hBOOL(hAPP(c_List_Odistinct(_1732411), _1732413)), hBOOL(hAPP(hAPP(c_member(_1732411), _1732415), hAPP(c_List_Oset(_1732411), _1732413))), -(c_List_OtakeWhile(_1732411, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732411), c_fNot), hAPP(hAPP(c_COMBC(_1732411, _1732411, tc_HOL_Obool), c_fequal), _1732415)), hAPP(c_List_Orev(_1732411), _1732413)) = hAPP(c_List_Orev(_1732411), hAPP(c_List_Otl(_1732411), c_List_OdropWhile(_1732411, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732411), c_fNot), hAPP(hAPP(c_COMBC(_1732411, _1732411, tc_HOL_Obool), c_fequal), _1732415)), _1732413))))], (27062 ^ _780478) ^ [_1281976, _1281978, _1281980, _1281982] : [class_Fields_Olinordered__field(_1281976), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281976), _1281978), c_Groups_Ozero__class_Ozero(_1281976))), 27069 ^ _780478 : [(27076 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281976), _1281982), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281976), _1281980), _1281978))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281976), _1281980), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281976), _1281982), _1281978))))], (27070 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281976), _1281980), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281976), _1281982), _1281978))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281976), _1281982), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281976), _1281980), _1281978))))]]], (41259 ^ _780478) ^ [_1590841, _1590843, _1590845, _1590847, _1590849, _1590851] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590841, _1590841)), hAPP(hAPP(c_Product__Type_OPair(_1590841, _1590841), _1590843), _1590845)), _1590847)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590841, _1590841)), hAPP(hAPP(c_Product__Type_OPair(_1590841, _1590841), _1590845), _1590849)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590841, _1590841), tc_HOL_Obool), _1590851), _1590847))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590841, _1590841)), hAPP(hAPP(c_Product__Type_OPair(_1590841, _1590841), _1590843), _1590849)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590841, _1590841), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1590851)), _1590847))))], (38601 ^ _780478) ^ [_1523558, _1523560, _1523562] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1523558), _1523560), _1523562) = c_Nitpick_OAbs__Frac(_1523558, c_Nitpick_Onorm__frac(_1523560, _1523562)))], (45995 ^ _780478) ^ [_1704629, _1704631, _1704633] : [-(c_Enum_On__lists(_1704629, hAPP(c_Nat_OSuc, _1704631), _1704633) = c_List_Oconcat(tc_List_Olist(_1704629), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1704629), tc_List_Olist(tc_List_Olist(_1704629))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1704629), tc_List_Olist(_1704629), tc_List_Olist(tc_List_Olist(_1704629))), hAPP(hAPP(c_COMBB(tc_fun(_1704629, tc_List_Olist(_1704629)), tc_fun(tc_List_Olist(_1704629), tc_List_Olist(tc_List_Olist(_1704629))), tc_List_Olist(_1704629)), c_List_Omap(_1704629, tc_List_Olist(_1704629))), hAPP(c_COMBC(_1704629, tc_List_Olist(_1704629), tc_List_Olist(_1704629)), c_List_Olist_OCons(_1704629)))), _1704633)), c_Enum_On__lists(_1704629, _1704631, _1704633))))], (42550 ^ _780478) ^ [_1628406, _1628408] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1628406, _1628408) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1628406), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1628408), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (42057 ^ _780478) ^ [_1614238, _1614240, _1614242, _1614244, _1614246] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614238), tc_List_Olist(_1614238))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614238), tc_List_Olist(_1614238)), hAPP(hAPP(c_List_Olist_OCons(_1614238), _1614240), _1614242)), _1614244)), c_List_Olistrel(_1614238, _1614246))), 42062 ^ _780478 : [(42067 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1614238), tc_List_Olist(_1614238))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1614238), tc_List_Olist(_1614238)), _1614242), 42061 ^ [_1614238, _1614240, _1614242, _1614244, _1614246])), c_List_Olistrel(_1614238, _1614246))))], (42065 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1614238, _1614238)), hAPP(hAPP(c_Product__Type_OPair(_1614238, _1614238), _1614240), 42060 ^ [_1614238, _1614240, _1614242, _1614244, _1614246])), _1614246)))], (42063 ^ _780478) ^ [] : [-(_1614244 = hAPP(hAPP(c_List_Olist_OCons(_1614238), 42060 ^ [_1614238, _1614240, _1614242, _1614244, _1614246]), 42061 ^ [_1614238, _1614240, _1614242, _1614244, _1614246]))]]], (22466 ^ _780478) ^ [_1198599, _1198601, _1198603, _1198605, _1198607] : [class_Groups_Ocomm__monoid__add(_1198599), hBOOL(hAPP(c_Finite__Set_Ofinite(_1198601), _1198603)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1198601), _1198605)), 22480 ^ _780478 : [(22483 ^ _780478) ^ [] : [hAPP(_1198607, 22479 ^ [_1198599, _1198601, _1198603, _1198605, _1198607]) = c_Groups_Ozero__class_Ozero(_1198599)], (22481 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1198601), 22479 ^ [_1198599, _1198601, _1198603, _1198605, _1198607]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1198601, tc_HOL_Obool)), _1198603), _1198605))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198601, _1198599), _1198607), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1198601, tc_HOL_Obool)), _1198603), _1198605)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1198599), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198601, _1198599), _1198607), _1198603)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198601, _1198599), _1198607), _1198605)))], (37541 ^ _780478) ^ [_1496881, _1496883] : [-(c_Equiv__Relations_Oequivp(_1496881, _1496883)), 37546 ^ _780478 : [(37549 ^ _780478) ^ [] : [hAPP(_1496883, 37542 ^ [_1496881, _1496883]) = hAPP(_1496883, 37543 ^ [_1496881, _1496883])], (37547 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1496883, 37542 ^ [_1496881, _1496883]), 37543 ^ [_1496881, _1496883])))]], 37550 ^ _780478 : [(37553 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1496883, 37542 ^ [_1496881, _1496883]), 37543 ^ [_1496881, _1496883]))], (37551 ^ _780478) ^ [] : [-(hAPP(_1496883, 37542 ^ [_1496881, _1496883]) = hAPP(_1496883, 37543 ^ [_1496881, _1496883]))]]], (22931 ^ _780478) ^ [_1207289, _1207291, _1207293] : [class_Rings_Oring__1(_1207289), hBOOL(hAPP(hAPP(c_member(_1207289), _1207291), c_Int_Oring__1__class_OInts(_1207289))), hBOOL(hAPP(hAPP(c_member(_1207289), _1207293), c_Int_Oring__1__class_OInts(_1207289))), -(hBOOL(hAPP(hAPP(c_member(_1207289), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207289), _1207291), _1207293)), c_Int_Oring__1__class_OInts(_1207289))))], (14323 ^ _780478) ^ [_1036214, _1036216] : [14324 ^ _780478 : [(14327 ^ _780478) ^ [] : [_1036214 = _1036216], (14325 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036214), _1036216))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1036214), _1036216)))], (31160 ^ _780478) ^ [_1360422, _1360424, _1360426] : [hBOOL(hAPP(hAPP(c_member(_1360422), _1360424), hAPP(c_Set_OCollect(_1360422), _1360426))), -(hBOOL(hAPP(_1360426, _1360424)))], (24159 ^ _780478) ^ [_1230301, _1230303] : [class_Divides_Osemiring__div(_1230301), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1230301), c_Groups_Ozero__class_Ozero(_1230301)), _1230303) = c_Groups_Ozero__class_Ozero(_1230301))], (28028 ^ _780478) ^ [_1299001, _1299003, _1299005, _1299007, _1299009] : [class_Orderings_Oorder(_1299001), 28031 ^ _780478 : [(28052 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1299001, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1299001, _1299003, _1299005)), c_SetInterval_Oord__class_OatLeastAtMost(_1299001, _1299007, _1299009)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299001), _1299007), _1299009)), 28055 ^ _780478 : [(28058 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299001), _1299007), _1299003)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299001), _1299005), _1299009)), 28065 ^ _780478 : [(28068 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299001), _1299005), _1299009))], (28066 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299001), _1299007), _1299003))]]], (28056 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299001), _1299003), _1299005)))]]], (28032 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1299001, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1299001, _1299003, _1299005)), c_SetInterval_Oord__class_OatLeastAtMost(_1299001, _1299007, _1299009))), 28035 ^ _780478 : [(28036 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299001), _1299003), _1299005)), 28039 ^ _780478 : [(28044 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299001), _1299007), _1299003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1299001), _1299005), _1299009)))], (28042 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299001), _1299005), _1299009)))], (28040 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299001), _1299007), _1299003)))]]], (28050 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299001), _1299007), _1299009)))]]]]], (16781 ^ _780478) ^ [_1088185, _1088187, _1088189, _1088191, _1088193, _1088195, _1088197, _1088199] : [c_Finite__Set_Ofolding__image__simple(_1088185, _1088187, _1088189, _1088191, _1088193, _1088195), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088187), _1088197)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088187), _1088199)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088187, tc_HOL_Obool)), _1088197), _1088199) = c_Orderings_Obot__class_Obot(tc_fun(_1088187, tc_HOL_Obool)), -(hAPP(_1088195, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088187, tc_HOL_Obool)), _1088197), _1088199)) = hAPP(hAPP(_1088189, hAPP(_1088195, _1088197)), hAPP(_1088195, _1088199)))], (7824 ^ _780478) ^ [_913062, _913064, _913066, _913068, _913070, _913072, _913074] : [-(hBOOL(hAPP(hAPP(c_member(_913062), _913064), _913066))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_913062, _913068, _913070, _913072, _913066), _913074)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_913062, _913068, _913070, _913072, hAPP(hAPP(c_Set_Oinsert(_913062), _913064), _913066)), hAPP(hAPP(_913070, _913064), _913074))))], (6744 ^ _780478) ^ [_892060, _892062, _892064, _892066] : [-(c_Fun_Ofun__upd(_892060, _892062, _892064, _892066, hAPP(_892064, _892066)) = _892064)], (10825 ^ _780478) ^ [_969281, _969283, _969285, _969287] : [class_Orderings_Olinorder(_969281), 10828 ^ _780478 : [(10837 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969281), hAPP(hAPP(c_Orderings_Oord__class_Omax(_969281), _969283), _969285)), _969287))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969281), _969283), _969287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969281), _969285), _969287))], (10829 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969281), hAPP(hAPP(c_Orderings_Oord__class_Omax(_969281), _969283), _969285)), _969287)), 10832 ^ _780478 : [(10835 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969281), _969285), _969287)))], (10833 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969281), _969283), _969287)))]]]]], (50361 ^ _780478) ^ [_1799444, _1799446, _1799448, _1799450, _1799452, _1799454, _1799456, _1799458] : [c_Fun_Obij__betw(_1799444, _1799446, _1799448, _1799450, _1799452), 50364 ^ _780478 : [(50371 ^ _780478) ^ [] : [c_Fun_Obij__betw(_1799444, _1799454, hAPP(c_Fun_Ocomp(_1799446, _1799454, _1799444, _1799456), _1799448), _1799450, _1799458), -(c_Fun_Obij__betw(_1799446, _1799454, _1799456, _1799452, _1799458))], (50365 ^ _780478) ^ [] : [c_Fun_Obij__betw(_1799446, _1799454, _1799456, _1799452, _1799458), -(c_Fun_Obij__betw(_1799444, _1799454, hAPP(c_Fun_Ocomp(_1799446, _1799454, _1799444, _1799456), _1799448), _1799450, _1799458))]]], (37203 ^ _780478) ^ [_1488239, _1488241, _1488243, _1488245] : [-(_1488239 = _1488241), hAPP(c_Product__Type_Ofst(_1488243, _1488245), _1488239) = hAPP(c_Product__Type_Ofst(_1488243, _1488245), _1488241), hAPP(c_Product__Type_Osnd(_1488243, _1488245), _1488239) = hAPP(c_Product__Type_Osnd(_1488243, _1488245), _1488241)], (20 ^ _780478) ^ [_780738, _780740, _780742, _780744, _780746, _780748, _780750, _780752, _780754, _780756, _780758, _780760] : [-(c_Nitpick_Ofold__graph_H(_780758, _780754, _780750, _780746, _780742, _780738)), c_Nitpick_Ofold__graph_H(_780760, _780756, _780752, _780748, _780744, _780740), _780760 = _780758, _780756 = _780754, _780752 = _780750, _780748 = _780746, _780744 = _780742, _780740 = _780738], (39735 ^ _780478) ^ [_1554178, _1554180, _1554182, _1554184, _1554186] : [c_Fun_Oinj__on(_1554178, _1554180, _1554182, c_Orderings_Otop__class_Otop(tc_fun(_1554178, tc_HOL_Obool))), c_Fun_Oinj__on(_1554184, _1554178, _1554186, c_Orderings_Otop__class_Otop(tc_fun(_1554184, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1554184, _1554180, hAPP(c_Fun_Ocomp(_1554178, _1554180, _1554184, _1554182), _1554186), c_Orderings_Otop__class_Otop(tc_fun(_1554184, tc_HOL_Obool))))], (33921 ^ _780478) ^ [_1421259, _1421261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421259), _1421261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1421259)), c_Int_OBit1(_1421261))))], (34417 ^ _780478) ^ [_1429600] : [-(c_Int_OBit0(_1429600) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1429600), _1429600))], (41053 ^ _780478) ^ [_1585883, _1585885, _1585887] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1585883, _1585885, _1585885), _1585887), c_Relation_OId(_1585885)) = _1585887)], (41955 ^ _780478) ^ [_1610975, _1610977, _1610979, _1610981] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610975), tc_List_Olist(_1610975))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610975), tc_List_Olist(_1610975)), _1610977), _1610979)), c_List_Olistrel(_1610975, _1610981))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610975)), _1610977) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610975)), _1610979))], (5989 ^ _780478) ^ [_875658, _875660, _875662, _875664] : [5990 ^ _780478 : [(5993 ^ _780478) ^ [] : [hBOOL(hAPP(_875662, _875664))], (5991 ^ _780478) ^ [] : [_875660 = _875664]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_875658), _875660), _875662), _875664)))], (40420 ^ _780478) ^ [_1570314, _1570316] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570314, _1570314)), _1570316)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570314, _1570314)), c_Transitive__Closure_Otrancl(_1570314, _1570316))))], (45801 ^ _780478) ^ [_1700028, _1700030, _1700032, _1700034] : [-(hAPP(c_List_OremoveAll(_1700028, _1700030), hAPP(hAPP(c_List_Oappend(_1700028), _1700032), _1700034)) = hAPP(hAPP(c_List_Oappend(_1700028), hAPP(c_List_OremoveAll(_1700028, _1700030), _1700032)), hAPP(c_List_OremoveAll(_1700028, _1700030), _1700034)))], (11465 ^ _780478) ^ [_981396, _981398, _981400, _981402] : [class_Orderings_Olinorder(_981396), hBOOL(hAPP(c_Finite__Set_Ofinite(_981396), _981398)), hBOOL(hAPP(hAPP(c_member(_981396), _981400), _981398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_981396), hAPP(hAPP(c_Orderings_Oord__class_Omax(_981396), _981400), _981402)), hAPP(hAPP(c_Finite__Set_Ofold(_981396, _981396, c_Orderings_Oord__class_Omax(_981396)), _981402), _981398))))], (23969 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (13216 ^ _780478) ^ [_1015070, _1015072, _1015074, _1015076, _1015078] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1015070, _1015072, _1015074), _1015076), _1015078), c_Orderings_Obot__class_Obot(tc_fun(_1015072, tc_HOL_Obool))) = _1015078)], (21618 ^ _780478) ^ [_1181988, _1181990] : [-(_1181988 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1181988), _1181990) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1181990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1181988), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1181990)))], (32488 ^ _780478) ^ [_1393889, _1393891, _1393893, _1393895] : [class_Int_Onumber__ring(_1393889), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1393889), hAPP(c_Int_Onumber__class_Onumber__of(_1393889), _1393891)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1393889), hAPP(c_Int_Onumber__class_Onumber__of(_1393889), _1393893)), _1393895)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1393889), hAPP(c_Int_Onumber__class_Onumber__of(_1393889), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393891), _1393893))), _1393895))], (51905 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (39512 ^ _780478) ^ [_1548201, _1548203, _1548205] : [hBOOL(hAPP(hAPP(c_member(_1548203), _1548201), c_Orderings_Obot__class_Obot(tc_fun(_1548203, tc_HOL_Obool)))), -(hBOOL(hAPP(_1548205, _1548201)))], (46589 ^ _780478) ^ [_1717666, _1717668, _1717670] : [class_Orderings_Olinorder(_1717666), c_List_Olinorder__class_Osorted(_1717666, _1717668), hBOOL(hAPP(c_List_Odistinct(_1717666), _1717668)), c_List_Olinorder__class_Osorted(_1717666, _1717670), hBOOL(hAPP(c_List_Odistinct(_1717666), _1717670)), hAPP(c_List_Oset(_1717666), _1717668) = hAPP(c_List_Oset(_1717666), _1717670), -(_1717668 = _1717670)], (6712 ^ _780478) ^ [_891338, _891340, _891342, _891344, _891346, _891348] : [-(hBOOL(hAPP(hAPP(c_member(_891338), _891340), _891342))), -(hAPP(c_Set_Oimage(_891338, _891344, c_Fun_Ofun__upd(_891338, _891344, _891346, _891340, _891348)), _891342) = hAPP(c_Set_Oimage(_891338, _891344, _891346), _891342))], (37339 ^ _780478) ^ [_1490990, _1490992, _1490994] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1490990, _1490992), _1490994))), _1490990 = 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), _1490994)), _1490992)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490994)), 37346 ^ _780478 : [(37349 ^ _780478) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1490994) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37347 ^ _780478) ^ [] : [-(_1490992 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 37350 ^ _780478 : [(37353 ^ _780478) ^ [] : [37354 ^ _780478 : [(37357 ^ _780478) ^ [] : [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), _1490994))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490994)), _1490992))], (37355 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490992)))]], 37362 ^ _780478 : [(37365 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1490992), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490994))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1490994)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37363 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490992))]]], (37351 ^ _780478) ^ [] : [_1490992 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (45217 ^ _780478) ^ [_1686708, _1686710] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1686708), _1686710) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1686708), _1686710))], (28016 ^ _780478) ^ [_1298711, _1298713, _1298715, _1298717] : [class_Orderings_Oorder(_1298711), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1298711, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1298711, _1298713), _1298715)), c_SetInterval_Oord__class_OatLeastAtMost(_1298711, _1298715, _1298717)) = c_Orderings_Obot__class_Obot(tc_fun(_1298711, tc_HOL_Obool)))], (39609 ^ _780478) ^ [_1551390, _1551392, _1551394, _1551396, _1551398, _1551400] : [-(hAPP(c_Set_Ovimage(_1551390, tc_prod(_1551392, _1551394), _1551396), hAPP(hAPP(c_Product__Type_OSigma(_1551392, _1551394), _1551398), hAPP(c_COMBK(tc_fun(_1551394, tc_HOL_Obool), _1551392), _1551400))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1551390, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1551390, _1551392, hAPP(c_Fun_Ocomp(tc_prod(_1551392, _1551394), _1551392, _1551390, c_Product__Type_Ofst(_1551392, _1551394)), _1551396)), _1551398)), hAPP(c_Set_Ovimage(_1551390, _1551394, hAPP(c_Fun_Ocomp(tc_prod(_1551392, _1551394), _1551394, _1551390, c_Product__Type_Osnd(_1551392, _1551394)), _1551396)), _1551400)))], (44263 ^ _780478) ^ [_1666460, _1666462] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1666460), _1666462) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1666460 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 44269 ^ _780478 : [(44272 ^ _780478) ^ [] : [44268 ^ [_1666460, _1666462] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44270 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 44268 ^ [_1666460, _1666462]), hAPP(c_List_Oset(tc_Nat_Onat), _1666462))))]]], (19708 ^ _780478) ^ [_1148298, _1148300, _1148302, _1148304] : [class_Rings_Olinordered__semidom(_1148298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148298), _1148300), _1148302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1148298), c_Groups_Ozero__class_Ozero(_1148298)), _1148300)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1148304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148298), hAPP(hAPP(c_Power_Opower__class_Opower(_1148298), _1148300), _1148304)), hAPP(hAPP(c_Power_Opower__class_Opower(_1148298), _1148302), _1148304))))], (35181 ^ _780478) ^ [_1443616, _1443618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1443616), 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)))), _1443618))), 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)))), _1443616)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443618), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1443616))], (1674 ^ _780478) ^ [_804267, _804269] : [-(class_Groups_Ocomm__monoid__add(_804267)), _804269 = _804267, class_Groups_Ocomm__monoid__add(_804269)], (43055 ^ _780478) ^ [_1639147, _1639149, _1639151] : [-(hAPP(hAPP(c_List_Ozip(_1639147, _1639149), _1639151), c_List_Olist_ONil(_1639149)) = c_List_Olist_ONil(tc_prod(_1639147, _1639149)))], (1884 ^ _780478) ^ [_806892, _806894] : [-(class_Groups_Oone(_806892)), _806894 = _806892, class_Groups_Oone(_806894)], (29005 ^ _780478) ^ [_1317984, _1317986, _1317988] : [hAPP(c_Set_Oimage(_1317986, tc_fun(_1317986, tc_HOL_Obool), _1317984), _1317988) = hAPP(c_Set_OPow(_1317986), _1317988)], (3068 ^ _780478) ^ [_826023, _826025, _826027, _826029] : [-(c_Nitpick_Ocard_H(_826029, _826025) = c_Nitpick_Ocard_H(_826027, _826023)), _826029 = _826027, _826025 = _826023], (10443 ^ _780478) ^ [_962683, _962685, _962687] : [class_Orderings_Olinorder(_962683), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962683), _962685), _962687)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_962683), _962687), _962685) = _962687)], (50002 ^ _780478) ^ [_1791227] : [-(c_Hilbert__Choice_Oinv__into(_1791227, _1791227, c_Orderings_Otop__class_Otop(tc_fun(_1791227, tc_HOL_Obool)), c_Fun_Oid(_1791227)) = c_Fun_Oid(_1791227))], (25166 ^ _780478) ^ [_1248005, _1248007, _1248009, _1248011, _1248013] : [class_Fields_Ofield(_1248005), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248007), _1248009)), -(hAPP(_1248011, _1248013) = c_Groups_Ozero__class_Ozero(_1248005)), 25177 ^ _780478 : [(25184 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248007), _1248013), _1248009))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1248007, _1248005), _1248011), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248007, tc_HOL_Obool)), _1248009), hAPP(hAPP(c_Set_Oinsert(_1248007), _1248013), c_Orderings_Obot__class_Obot(tc_fun(_1248007, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1248007, _1248005), _1248011), _1248009))], (25178 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1248007), _1248013), _1248009)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1248007, _1248005), _1248011), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248007, tc_HOL_Obool)), _1248009), hAPP(hAPP(c_Set_Oinsert(_1248007), _1248013), c_Orderings_Obot__class_Obot(tc_fun(_1248007, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1248005), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1248007, _1248005), _1248011), _1248009)), hAPP(_1248011, _1248013)))]]], (3294 ^ _780478) ^ [_829558, _829560, _829562, _829564] : [-(c_Code__Numeral_Onat__of__aux(_829564, _829560) = c_Code__Numeral_Onat__of__aux(_829562, _829558)), _829564 = _829562, _829560 = _829558], (52019 ^ _780478) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (20072 ^ _780478) ^ [_1154840, _1154842, _1154844, _1154846] : [class_Rings_Oordered__comm__semiring(_1154840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154840), _1154842), _1154844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154840), c_Groups_Ozero__class_Ozero(_1154840)), _1154846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154840), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154840), _1154846), _1154842)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154840), _1154846), _1154844))))], (29291 ^ _780478) ^ [_1324346, _1324348, _1324350] : [class_Divides_Oring__div(_1324346), -(c_Divides_Odiv__class_Omod(_1324346, hAPP(c_Groups_Ouminus__class_Ouminus(_1324346), _1324348), _1324350) = c_Divides_Odiv__class_Omod(_1324346, hAPP(c_Groups_Ouminus__class_Ouminus(_1324346), c_Divides_Odiv__class_Omod(_1324346, _1324348, _1324350)), _1324350))], (10693 ^ _780478) ^ [_967044, _967046, _967048] : [class_Orderings_Olinorder(_967044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967044), _967046), _967048)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_967044), _967048), _967046) = _967046)], (28226 ^ _780478) ^ [_1303010, _1303012, _1303014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303010)), 28232 ^ _780478 : [(28235 ^ _780478) ^ [] : [hBOOL(hAPP(_1303012, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28231 ^ [_1303010, _1303012, _1303014]), _1303010)))], (28233 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1303012, 28231 ^ [_1303010, _1303012, _1303014])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1303014)), 28240 ^ _780478 : [(28241 ^ _780478) ^ [_1303299] : [hBOOL(hAPP(_1303012, _1303299)), -(hBOOL(hAPP(_1303012, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1303299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1303014), _1303010)))))]]], (43393 ^ _780478) ^ [_1646436, _1646438, _1646440, _1646442, _1646444] : [hAPP(hAPP(c_List_Oappend(_1646436), _1646438), hAPP(hAPP(c_List_Olist_OCons(_1646436), _1646440), c_List_Olist_ONil(_1646436))) = hAPP(hAPP(c_List_Oappend(_1646436), _1646442), hAPP(hAPP(c_List_Olist_OCons(_1646436), _1646444), c_List_Olist_ONil(_1646436))), 43396 ^ _780478 : [(43399 ^ _780478) ^ [] : [-(_1646440 = _1646444)], (43397 ^ _780478) ^ [] : [-(_1646438 = _1646442)]]], (20214 ^ _780478) ^ [_1157528, _1157530] : [class_Groups_Olinordered__ab__group__add(_1157528), 20217 ^ _780478 : [(20224 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157528), _1157530), c_Groups_Ozero__class_Ozero(_1157528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157528), _1157530), _1157530)), c_Groups_Ozero__class_Ozero(_1157528))))], (20218 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157528), _1157530), _1157530)), c_Groups_Ozero__class_Ozero(_1157528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157528), _1157530), c_Groups_Ozero__class_Ozero(_1157528))))]]], (28672 ^ _780478) ^ [_1311419, _1311421, _1311423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1311419)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1311421), _1311423)), 28679 ^ _780478 : [(28680 ^ _780478) ^ [_1311615] : [28682 ^ _780478 : [(28688 ^ _780478) ^ [] : [-(_1311615 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 28684 ^ [_1311419, _1311421, _1311423, _1311615]), 28681 ^ [_1311419, _1311421, _1311423, _1311615]))], (28686 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28684 ^ [_1311419, _1311421, _1311423, _1311615]), _1311423)))], (28683 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28681 ^ [_1311419, _1311421, _1311423, _1311615]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1311419))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1311421), _1311615)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1311421), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1311615), _1311419))))]]], (31678 ^ _780478) ^ [_1378076, _1378078, _1378080, _1378082] : [c_Fun_Oinj__on(_1378076, tc_fun(tc_fun(_1378076, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1378076, tc_fun(tc_prod(_1378076, _1378076), tc_HOL_Obool), tc_fun(tc_fun(_1378076, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1378076, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1378076, _1378076), tc_HOL_Obool), tc_fun(tc_fun(_1378076, tc_HOL_Obool), tc_HOL_Obool)), _1378076), c_Equiv__Relations_Oquotient(_1378076)), hAPP(hAPP(c_COMBC(_1378076, tc_fun(_1378076, tc_HOL_Obool), tc_fun(_1378076, tc_HOL_Obool)), c_Set_Oinsert(_1378076)), c_Orderings_Obot__class_Obot(tc_fun(_1378076, tc_HOL_Obool))))), _1378078), _1378080), hBOOL(hAPP(hAPP(c_member(_1378076), _1378082), _1378080)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378076), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1378076, tc_HOL_Obool)), _1378080), hAPP(hAPP(c_Set_Oinsert(_1378076), _1378082), c_Orderings_Obot__class_Obot(tc_fun(_1378076, tc_HOL_Obool))))), _1378078) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1378076, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378076), _1378080), _1378078)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378076), hAPP(hAPP(c_Set_Oinsert(_1378076), _1378082), c_Orderings_Obot__class_Obot(tc_fun(_1378076, tc_HOL_Obool)))), _1378078)))], (30865 ^ _780478) ^ [_1353968, _1353970, _1353972] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1353968, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353968, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1353968, tc_HOL_Obool), tc_HOL_Obool)), _1353970), _1353972))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1353968, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353968, tc_HOL_Obool), _1353970)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1353968, tc_HOL_Obool), _1353972)))))], (2662 ^ _780478) ^ [_819710, _819712, _819714, _819716] : [-(c_Predicate_OPowp(_819716, _819712) = c_Predicate_OPowp(_819714, _819710)), _819716 = _819714, _819712 = _819710], (41281 ^ _780478) ^ [_1591523, _1591525, _1591527, _1591529] : [-(hAPP(hAPP(c_Nat_Ocompow(_1591523, _1591523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1591525), _1591527)), _1591529) = hAPP(c_Fun_Ocomp(_1591523, _1591523, _1591523, hAPP(hAPP(c_Nat_Ocompow(_1591523, _1591523), _1591525), _1591529)), hAPP(hAPP(c_Nat_Ocompow(_1591523, _1591523), _1591527), _1591529)))], (43077 ^ _780478) ^ [_1639531, _1639533] : [hAPP(c_List_Oset(_1639531), _1639533) = c_Orderings_Obot__class_Obot(tc_fun(_1639531, tc_HOL_Obool)), -(_1639533 = c_List_Olist_ONil(_1639531))], (34961 ^ _780478) ^ [] : [-(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))))], (34473 ^ _780478) ^ [_1430607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1430607))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1430607)))], (36345 ^ _780478) ^ [_1471885, _1471887, _1471889, _1471891, _1471893, _1471895] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471885, _1471887, _1471889), _1471891), hAPP(hAPP(c_Product__Type_OPair(_1471885, _1471887), _1471893), _1471895)) = hAPP(hAPP(_1471891, _1471893), _1471895))], (37387 ^ _780478) ^ [_1492137, _1492139] : [c_Code__Numeral_OSuc__code__numeral(_1492137) = c_Code__Numeral_OSuc__code__numeral(_1492139), -(_1492137 = _1492139)], (34699 ^ _780478) ^ [_1434740] : [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), _1434740))), 34702 ^ _780478 : [(34705 ^ _780478) ^ [] : [-(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(_1434740)))))], (34703 ^ _780478) ^ [] : [-(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(_1434740)))))]]], (43047 ^ _780478) ^ [_1639009, _1639011] : [-(c_List_Oremove1(_1639009, _1639011, c_List_Olist_ONil(_1639009)) = c_List_Olist_ONil(_1639009))], (25635 ^ _780478) ^ [_1256148, _1256150] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256148) = _1256150), _1256148 = hAPP(c_Int_Onat, _1256150), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256150))], (45528 ^ _780478) ^ [_1694184, _1694186, _1694188, _1694190] : [_1694190 = c_List_Olist_ONil(_1694186), -(c_List_Olist__all2(_1694184, _1694186, _1694188, c_List_Olist_ONil(_1694184), _1694190))], (41710 ^ _780478) ^ [_1603152, _1603154, _1603156] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1603152)), c_List_Osublist(_1603152, _1603154, _1603156)) = 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(_1603152)), _1603154)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1603156)))))], (502 ^ _780478) ^ [_788043, _788045] : [-(class_Lattices_Oab__semigroup__idem__mult(_788043)), _788045 = _788043, class_Lattices_Oab__semigroup__idem__mult(_788045)], (28550 ^ _780478) ^ [_1309018, _1309020] : [class_Orderings_Olinorder(_1309018), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309018, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1309018), _1309020), c_Orderings_Obot__class_Obot(tc_fun(_1309018, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1309018), _1309020)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1309018), _1309020))], (33620 ^ _780478) ^ [_1414565, _1414567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414565), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414565)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414567)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11243 ^ _780478) ^ [_977154, _977156, _977158] : [class_Orderings_Olinorder(_977154), hBOOL(hAPP(c_Finite__Set_Ofinite(_977154), _977156)), -(_977156 = c_Orderings_Obot__class_Obot(tc_fun(_977154, tc_HOL_Obool))), 11254 ^ _780478 : [(11264 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977154), hAPP(c_Finite__Set_Ofold1(_977154, c_Orderings_Oord__class_Omin(_977154)), _977156)), _977158))), 11265 ^ _780478 : [(11266 ^ _780478) ^ [_977543] : [hBOOL(hAPP(hAPP(c_member(_977154), _977543), _977156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977154), _977543), _977158))]]], (11255 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977154), hAPP(c_Finite__Set_Ofold1(_977154, c_Orderings_Oord__class_Omin(_977154)), _977156)), _977158)), 11259 ^ _780478 : [(11262 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_977154), 11258 ^ [_977154, _977156, _977158]), _977158)))], (11260 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_977154), 11258 ^ [_977154, _977156, _977158]), _977156)))]]]]], (29960 ^ _780478) ^ [_1336440] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336440, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48020 ^ _780478) ^ [_1748406, _1748408, _1748410] : [-(c_List_Olist__ex(_1748406, _1748408, _1748410)), 48021 ^ _780478 : [(48022 ^ _780478) ^ [_1748471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748471), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748406)), _1748410))), hBOOL(hAPP(_1748408, hAPP(hAPP(c_List_Onth(_1748406), _1748410), _1748471)))]]], (30612 ^ _780478) ^ [_1348677, _1348679, _1348681] : [class_Fields_Olinordered__field(_1348677), -(_1348679 = c_Groups_Ozero__class_Ozero(_1348677)), -(hAPP(c_Groups_Oabs__class_Oabs(_1348677), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348677), _1348681), _1348679)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348677), hAPP(c_Groups_Oabs__class_Oabs(_1348677), _1348681)), hAPP(c_Groups_Oabs__class_Oabs(_1348677), _1348679)))], (38929 ^ _780478) ^ [_1532962, _1532964, _1532966, _1532968] : [-(hAPP(c_Set_OCollect(tc_prod(_1532962, _1532964)), hAPP(c_Product__Type_Oprod_Oprod__case(_1532962, _1532964, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1532962, tc_fun(_1532964, tc_HOL_Obool), tc_fun(_1532964, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1532964, tc_HOL_Obool), tc_fun(_1532964, tc_HOL_Obool)), _1532962), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1532964)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532962), c_fconj), _1532966))), _1532968))) = hAPP(hAPP(c_Product__Type_OSigma(_1532962, _1532964), hAPP(c_Set_OCollect(_1532962), _1532966)), hAPP(hAPP(c_COMBB(tc_fun(_1532964, tc_HOL_Obool), tc_fun(_1532964, tc_HOL_Obool), _1532962), c_Set_OCollect(_1532964)), _1532968)))], (33394 ^ _780478) ^ [_1410874, _1410876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1410874)), _1410876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1410874), _1410876)))], (11991 ^ _780478) ^ [_991146, _991148, _991150] : [class_Orderings_Olinorder(_991146), hBOOL(hAPP(c_Finite__Set_Ofinite(_991146), _991148)), -(_991150 = c_Orderings_Obot__class_Obot(tc_fun(_991146, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991146, tc_HOL_Obool)), _991150), _991148)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_991146), c_Big__Operators_Olattice_OSup__fin(_991146, c_Orderings_Oord__class_Omax(_991146), _991150)), c_Big__Operators_Olattice_OSup__fin(_991146, c_Orderings_Oord__class_Omax(_991146), _991148)) = c_Big__Operators_Olattice_OSup__fin(_991146, c_Orderings_Oord__class_Omax(_991146), _991148))], (23323 ^ _780478) ^ [_1214372, _1214374, _1214376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214372), _1214374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214372), _1214376)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214374), _1214376))))], (21748 ^ _780478) ^ [_1184307, _1184309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1184307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1184309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184309), _1184307))))], (41501 ^ _780478) ^ [_1597573, _1597575, _1597577] : [class_Divides_Osemiring__div(_1597573), -(_1597575 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1597573), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1597573), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1597573), _1597575), _1597577)), _1597577)), c_Divides_Odiv__class_Omod(_1597573, _1597575, _1597577)))], (39745 ^ _780478) ^ [_1554377, _1554379, _1554381, _1554383, _1554385] : [hAPP(c_Set_Oimage(_1554377, _1554379, _1554381), c_Orderings_Otop__class_Otop(tc_fun(_1554377, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1554379, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1554379, _1554383, _1554385), c_Orderings_Otop__class_Otop(tc_fun(_1554379, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1554383, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1554377, _1554383, hAPP(c_Fun_Ocomp(_1554379, _1554383, _1554377, _1554385), _1554381)), c_Orderings_Otop__class_Otop(tc_fun(_1554377, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1554383, tc_HOL_Obool)))], (17699 ^ _780478) ^ [_1109994, _1109996, _1109998, _1110000] : [hBOOL(hAPP(hAPP(c_member(_1109994), _1109996), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1109994, tc_HOL_Obool), _1109998))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1109994, tc_HOL_Obool)), _1110000), _1109998)), -(hBOOL(hAPP(hAPP(c_member(_1109994), _1109996), _1110000)))], (38927 ^ _780478) ^ [_1532841, _1532843, _1532845, _1532847] : [-(hAPP(c_Set_OCollect(tc_prod(_1532841, _1532843)), hAPP(c_Product__Type_Oprod_Oprod__case(_1532841, _1532843, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1532841, tc_fun(_1532843, tc_HOL_Obool), tc_fun(_1532843, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1532843, tc_HOL_Obool), tc_fun(_1532843, tc_HOL_Obool)), _1532841), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1532843)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1532841), c_fconj), _1532845))), _1532847))) = hAPP(hAPP(c_Product__Type_OSigma(_1532841, _1532843), hAPP(c_Set_OCollect(_1532841), _1532845)), hAPP(c_COMBK(tc_fun(_1532843, tc_HOL_Obool), _1532841), hAPP(c_Set_OCollect(_1532843), _1532847))))], (31344 ^ _780478) ^ [_1365238, _1365240, _1365242, _1365244, _1365246, _1365248] : [class_Groups_Ocomm__monoid__add(_1365238), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365240), _1365242)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365240, _1365238), _1365244), _1365242) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365246, _1365238), hAPP(hAPP(c_COMBB(tc_fun(_1365240, tc_HOL_Obool), _1365238, _1365246), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365240, _1365238), _1365244)), hAPP(hAPP(c_COMBB(tc_fun(_1365240, tc_HOL_Obool), tc_fun(_1365240, tc_HOL_Obool), _1365246), c_Set_OCollect(_1365240)), hAPP(hAPP(c_COMBB(tc_fun(_1365240, tc_HOL_Obool), tc_fun(_1365240, tc_HOL_Obool), _1365246), hAPP(c_COMBS(_1365240, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1365240), c_fconj), hAPP(hAPP(c_COMBC(_1365240, tc_fun(_1365240, tc_HOL_Obool), tc_HOL_Obool), c_member(_1365240)), _1365242)))), hAPP(c_COMBC(_1365240, _1365246, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1365246, tc_fun(_1365246, tc_HOL_Obool), _1365240), c_fequal), _1365248)))))), hAPP(c_Set_Oimage(_1365240, _1365246, _1365248), _1365242)))], (19418 ^ _780478) ^ [_1143967] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1143967)], (4936 ^ _780478) ^ [_855813, _855815, _855817, _855819, _855821, _855823] : [-(c_Relation_Orel__comp(_855823, _855819, _855815) = c_Relation_Orel__comp(_855821, _855817, _855813)), _855823 = _855821, _855819 = _855817, _855815 = _855813], (31439 ^ _780478) ^ [_1369272, _1369274] : [-(hAPP(c_Set_OPow(_1369272), _1369274) = hAPP(c_Set_OCollect(tc_fun(_1369272, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1369272, tc_HOL_Obool), tc_fun(_1369272, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1369272, tc_HOL_Obool))), _1369274)))], (13831 ^ _780478) ^ [_1027814, _1027816, _1027818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027814), _1027816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027814), _1027818)), _1027816)))], (51155 ^ _780478) ^ [_1817138, _1817140, _1817142, _1817144] : [class_Divides_Osemiring__div(_1817138), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817138), _1817140), _1817142)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817138), _1817144), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817138), _1817142), _1817140)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817138), _1817144), _1817142)), _1817140))], (24703 ^ _780478) ^ [_1239482, _1239484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1239482), _1239484)), -(c_Nat__Transfer_Otsub(_1239484, _1239482) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1239484), _1239482))], (50483 ^ _780478) ^ [_1801860, _1801862, _1801864] : [c_Fun_Obij__betw(_1801860, _1801862, _1801864, c_Orderings_Otop__class_Otop(tc_fun(_1801860, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1801862, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1801860, _1801862, _1801864, c_Orderings_Otop__class_Otop(tc_fun(_1801860, tc_HOL_Obool))))], (43598 ^ _780478) ^ [_1650842, _1650844, _1650846] : [_1650846 = c_List_Olist_ONil(_1650842), -(hAPP(hAPP(c_List_Oappend(_1650842), _1650844), _1650846) = _1650844)], (18095 ^ _780478) ^ [_1117449, _1117451, _1117453, _1117455, _1117457] : [18097 ^ _780478 : [(18100 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1117449), _1117451), hAPP(_1117457, 18096 ^ [_1117449, _1117451, _1117453, _1117455, _1117457])))], (18098 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1117453), 18096 ^ [_1117449, _1117451, _1117453, _1117455, _1117457]), _1117455)))]], -(hBOOL(hAPP(hAPP(c_member(_1117449), _1117451), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117453, tc_fun(_1117449, tc_HOL_Obool)), _1117455), _1117457))))], (40818 ^ _780478) ^ [_1579504, _1579506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1579504)), -(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(_1579504), _1579506))), _1579504)))], (13124 ^ _780478) ^ [_1013135, _1013137, _1013139] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013135, tc_HOL_Obool)), _1013137), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013135, tc_HOL_Obool)), _1013137), _1013139))))], (15840 ^ _780478) ^ [_1067113, _1067115, _1067117] : [class_Lattices_Osemilattice__inf(_1067113), 15843 ^ _780478 : [(15850 ^ _780478) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067113), _1067115), _1067117) = _1067115, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067113), _1067115), _1067117)))], (15844 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067113), _1067115), _1067117)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067113), _1067115), _1067117) = _1067115)]]], (47542 ^ _780478) ^ [_1737443, _1737445, _1737447] : [hBOOL(hAPP(hAPP(c_member(_1737443), _1737445), hAPP(c_List_Oset(_1737443), _1737447))), -(c_List_Oinsert(_1737443, _1737445, _1737447) = _1737447)], (19420 ^ _780478) ^ [_1144002] : [hAPP(c_Nat_OSuc, _1144002) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47639 ^ _780478) ^ [_1739694, _1739696, _1739698, _1739700, _1739702] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1739694, _1739694)), hAPP(hAPP(c_Product__Type_OPair(_1739694, _1739694), _1739696), _1739698)), c_List_Omeasures(_1739694, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1739694, tc_Nat_Onat)), _1739700), _1739702))))), 47640 ^ _780478 : [(47643 ^ _780478) ^ [] : [hAPP(_1739700, _1739696) = hAPP(_1739700, _1739698), hBOOL(hAPP(hAPP(c_member(tc_prod(_1739694, _1739694)), hAPP(hAPP(c_Product__Type_OPair(_1739694, _1739694), _1739696), _1739698)), c_List_Omeasures(_1739694, _1739702)))], (47641 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1739700, _1739696)), hAPP(_1739700, _1739698)))]]], (16016 ^ _780478) ^ [_1070195, _1070197, _1070199, _1070201] : [class_Lattices_Odistrib__lattice(_1070195), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070195), _1070197), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070195), _1070199), _1070201)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070195), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070195), _1070197), _1070199)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070195), _1070197), _1070201)))], (4724 ^ _780478) ^ [_852427, _852429, _852431, _852433, _852435, _852437, _852439, _852441] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_852441, _852437, _852433, _852429) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_852439, _852435, _852431, _852427)), _852441 = _852439, _852437 = _852435, _852433 = _852431, _852429 = _852427], (49377 ^ _780478) ^ [_1777999, _1778001, _1778003, _1778005] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1777999, tc_fun(_1778001, tc_HOL_Obool)), _1778003), _1778005) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1778001, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1778001, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1777999, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1778001, tc_HOL_Obool)), c_HOL_OEx(_1777999)), hAPP(hAPP(c_COMBB(tc_fun(_1777999, tc_HOL_Obool), tc_fun(_1777999, tc_HOL_Obool), tc_fun(_1778001, tc_HOL_Obool)), hAPP(c_COMBS(_1777999, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1777999), c_fconj), hAPP(hAPP(c_COMBC(_1777999, tc_fun(_1777999, tc_HOL_Obool), tc_HOL_Obool), c_member(_1777999)), _1778003)))), hAPP(hAPP(c_COMBC(tc_fun(_1778001, tc_HOL_Obool), tc_fun(_1777999, tc_fun(_1778001, tc_HOL_Obool)), tc_fun(_1777999, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778001, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1777999, tc_fun(_1778001, tc_HOL_Obool)), tc_fun(_1777999, tc_HOL_Obool)), tc_fun(_1778001, tc_HOL_Obool)), c_COMBB(tc_fun(_1778001, tc_HOL_Obool), tc_HOL_Obool, _1777999)), c_fequal)), _1778005))))))], (31809 ^ _780478) ^ [_1381335] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1381335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1381335), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32180 ^ _780478) ^ [_1388343, _1388345, _1388347, _1388349] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388343), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388343), _1388345), _1388347)), hAPP(c_Int_Onumber__class_Onumber__of(_1388343), _1388349)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388343), _1388345), hAPP(c_Int_Onumber__class_Onumber__of(_1388343), _1388349))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388343), _1388347), hAPP(c_Int_Onumber__class_Onumber__of(_1388343), _1388349)))), class_Int_Onumber(_1388343), class_Rings_Oring(_1388343)], (39390 ^ _780478) ^ [_1545625, _1545627] : [c_Wellfounded_Owf(_1545625, _1545627), -(c_Wellfounded_Oacyclic(_1545625, _1545627))], (47009 ^ _780478) ^ [_1726148, _1726150, _1726152, _1726154, _1726156] : [c_List_Olist__all2(_1726148, _1726150, _1726152, _1726154, _1726156), -(c_List_Olist__all2(_1726148, _1726150, _1726152, hAPP(c_List_Orev(_1726148), _1726154), hAPP(c_List_Orev(_1726150), _1726156)))], (49167 ^ _780478) ^ [_1773493, _1773495, _1773497, _1773499] : [c_Relation_Otrans(_1773493, _1773495), c_Relation_Otrans(_1773497, _1773499), -(c_Relation_Otrans(tc_prod(_1773493, _1773497), c_Wellfounded_Olex__prod(_1773493, _1773497, _1773495, _1773499)))], (4444 ^ _780478) ^ [_847861, _847863, _847865, _847867, _847869, _847871, _847873, _847875, _847877, _847879] : [-(c_Option_Ooption_Ooption__case(_847879, _847875, _847871, _847867, _847863) = c_Option_Ooption_Ooption__case(_847877, _847873, _847869, _847865, _847861)), _847879 = _847877, _847875 = _847873, _847871 = _847869, _847867 = _847865, _847863 = _847861], (52329 ^ _780478) ^ [_1833458, _1833460, _1833462, _1833464] : [-(hAPP(hAPP(c_COMBK(_1833458, _1833460), _1833462), _1833464) = _1833462)], (8314 ^ _780478) ^ [_922999, _923001, _923003, _923005, _923007, _923009, _923011] : [c_Finite__Set_Ofun__left__comm(_922999, _923001, _923003), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922999, _923001, _923003, _923005, _923007), _923009)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922999, _923001, _923003, _923005, _923007), _923011)), -(_923011 = _923009)], (23409 ^ _780478) ^ [] : [-(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))], (44785 ^ _780478) ^ [_1677727, _1677729, _1677731, _1677733, _1677735] : [c_Fun_Oinj__on(_1677727, _1677729, _1677731, c_Orderings_Otop__class_Otop(tc_fun(_1677727, tc_HOL_Obool))), 44788 ^ _780478 : [(44795 ^ _780478) ^ [] : [_1677733 = _1677735, -(hAPP(hAPP(c_List_Omap(_1677727, _1677729), _1677731), _1677733) = hAPP(hAPP(c_List_Omap(_1677727, _1677729), _1677731), _1677735))], (44789 ^ _780478) ^ [] : [hAPP(hAPP(c_List_Omap(_1677727, _1677729), _1677731), _1677733) = hAPP(hAPP(c_List_Omap(_1677727, _1677729), _1677731), _1677735), -(_1677733 = _1677735)]]], (51859 ^ _780478) ^ [_1828868, _1828870] : [-(class_Enum_Oenum(tc_fun(_1828868, _1828870))), class_Enum_Oenum(_1828868), class_Enum_Oenum(_1828870)], (7834 ^ _780478) ^ [_913291, _913293, _913295, _913297] : [hBOOL(hAPP(hAPP(c_member(_913291), _913293), _913295)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_913291, tc_Nat_Onat), _913297), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913291, tc_HOL_Obool)), _913295), hAPP(hAPP(c_Set_Oinsert(_913291), _913293), c_Orderings_Obot__class_Obot(tc_fun(_913291, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_913291, tc_Nat_Onat), _913297), _913295)), hAPP(_913297, _913293)))], (3716 ^ _780478) ^ [_836105, _836107, _836109, _836111, _836113, _836115] : [-(c_List_Oinsert(_836115, _836111, _836107) = c_List_Oinsert(_836113, _836109, _836105)), _836115 = _836113, _836111 = _836109, _836107 = _836105], (14927 ^ _780478) ^ [_1048675, _1048677, _1048679, _1048681] : [hBOOL(hAPP(hAPP(c_member(_1048675), _1048677), c_SetInterval_Oord_OgreaterThan(_1048675, _1048679, _1048681))), -(hBOOL(hAPP(hAPP(_1048679, _1048681), _1048677)))], (46157 ^ _780478) ^ [_1708535, _1708537] : [46159 ^ _780478 : [(46162 ^ _780478) ^ [] : [46158 ^ [_1708535, _1708537] = c_List_Olist_ONil(_1708535)], (46160 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1708535)), 46158 ^ [_1708535, _1708537]), hAPP(c_List_Oset(tc_List_Olist(_1708535)), _1708537))))]], -(c_List_Otranspose(_1708535, _1708537) = c_List_Olist_ONil(tc_List_Olist(_1708535)))], (17903 ^ _780478) ^ [_1114028, _1114030] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114028), _1114030))), 17906 ^ _780478 : [(17913 ^ _780478) ^ [] : [_1114028 = _1114030, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114028), hAPP(c_Nat_OSuc, _1114030))))], (17907 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114028), hAPP(c_Nat_OSuc, _1114030))), -(_1114028 = _1114030)]]], (51933 ^ _780478) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (17428 ^ _780478) ^ [_1103236, _1103238, _1103240, _1103242, _1103244] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103236, tc_HOL_Obool)), _1103238), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103240, tc_fun(_1103236, tc_HOL_Obool)), _1103242), _1103244)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103240, tc_fun(_1103236, tc_HOL_Obool)), _1103242), hAPP(hAPP(c_COMBB(tc_fun(_1103236, tc_HOL_Obool), tc_fun(_1103236, tc_HOL_Obool), _1103240), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103236, tc_HOL_Obool)), _1103238)), _1103244)))], (38955 ^ _780478) ^ [_1533587, _1533589, _1533591, _1533593, _1533595, _1533597] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1533587, _1533589), hAPP(hAPP(c_Set_Oinsert(_1533587), _1533591), _1533593)), hAPP(c_COMBK(tc_fun(_1533589, tc_HOL_Obool), _1533587), hAPP(hAPP(c_Set_Oinsert(_1533589), _1533595), _1533597))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1533587, _1533589)), hAPP(hAPP(c_Product__Type_OPair(_1533587, _1533589), _1533591), _1533595)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1533587, _1533589), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1533587, _1533589), _1533593), hAPP(c_COMBK(tc_fun(_1533589, tc_HOL_Obool), _1533587), hAPP(hAPP(c_Set_Oinsert(_1533589), _1533595), _1533597)))), hAPP(hAPP(c_Product__Type_OSigma(_1533587, _1533589), hAPP(hAPP(c_Set_Oinsert(_1533587), _1533591), _1533593)), hAPP(c_COMBK(tc_fun(_1533589, tc_HOL_Obool), _1533587), _1533597)))))], (7465 ^ _780478) ^ [_905813, _905815, _905817, _905819, _905821, _905823] : [c_Fun_Oinj__on(_905813, _905815, _905817, _905819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905813, tc_HOL_Obool)), _905821), _905819)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905813, tc_HOL_Obool)), _905823), _905819)), -(hAPP(c_Set_Oimage(_905813, _905815, _905817), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905813, tc_HOL_Obool)), _905821), _905823)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_905815, tc_HOL_Obool)), hAPP(c_Set_Oimage(_905813, _905815, _905817), _905821)), hAPP(c_Set_Oimage(_905813, _905815, _905817), _905823)))], (34755 ^ _780478) ^ [] : [-(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))))], (31950 ^ _780478) ^ [_1384018, _1384020, _1384022, _1384024] : [class_Lattices_Osemilattice__inf(_1384018), hBOOL(hAPP(c_Finite__Set_Ofinite(_1384018), _1384020)), 31960 ^ _780478 : [(31963 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384018), _1384022), 31959 ^ [_1384018, _1384020, _1384022, _1384024]))], (31961 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1384018), 31959 ^ [_1384018, _1384020, _1384022, _1384024]), _1384020)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384018), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1384018), _1384022), _1384024)), hAPP(hAPP(c_Finite__Set_Ofold(_1384018, _1384018, c_Lattices_Osemilattice__inf__class_Oinf(_1384018)), _1384024), _1384020))))], (22696 ^ _780478) ^ [_1202976, _1202978] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202976)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202978)), _1202976 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1202978 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49242 ^ _780478) ^ [_1775329, _1775331] : [c_Relation_Otrans(_1775329, _1775331), -(c_Transitive__Closure_Otrancl(_1775329, _1775331) = _1775331)], (36310 ^ _780478) ^ [_1471070, _1471072, _1471074, _1471076, _1471078, _1471080] : [-(hAPP(hAPP(c_Product__Type_OPair(_1471070, _1471072), _1471074), _1471076) = hAPP(hAPP(c_Product__Type_OPair(_1471070, _1471072), _1471078), _1471080)), _1471074 = _1471078, _1471076 = _1471080], (4424 ^ _780478) ^ [_847563, _847565, _847567, _847569] : [-(c_Lazy__Sequence_Osmall__lazy_H(_847569, _847565) = c_Lazy__Sequence_Osmall__lazy_H(_847567, _847563)), _847569 = _847567, _847565 = _847563], (39670 ^ _780478) ^ [_1552857, _1552859, _1552861, _1552863, _1552865, _1552867, _1552869, _1552871, _1552873, _1552875, _1552877] : [hAPP(_1552857, hAPP(_1552859, _1552861)) = hAPP(_1552863, hAPP(_1552865, _1552867)), -(hAPP(hAPP(c_Fun_Ocomp(_1552869, _1552871, _1552873, _1552857), _1552859), _1552861) = hAPP(hAPP(c_Fun_Ocomp(_1552875, _1552871, _1552877, _1552863), _1552865), _1552867))], (48113 ^ _780478) ^ [_1750147, _1750149, _1750151] : [hBOOL(hAPP(hAPP(c_member(_1750147), _1750149), hAPP(c_List_Oset(_1750147), _1750151))), 48118 ^ _780478 : [(48121 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1750147), _1750149), hAPP(c_List_Oset(_1750147), 48116 ^ [_1750147, _1750149, _1750151])))], (48119 ^ _780478) ^ [] : [-(_1750151 = hAPP(hAPP(c_List_Oappend(_1750147), 48116 ^ [_1750147, _1750149, _1750151]), hAPP(hAPP(c_List_Olist_OCons(_1750147), _1750149), 48117 ^ [_1750147, _1750149, _1750151])))]]], (14429 ^ _780478) ^ [_1037942, _1037944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037942), _1037944)), _1037942 = _1037944], (29512 ^ _780478) ^ [_1328489, _1328491, _1328493, _1328495] : [class_Divides_Osemiring__div(_1328489), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328489), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328489), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328489), _1328491), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1328489), _1328493), _1328491))), c_Divides_Odiv__class_Omod(_1328489, _1328493, _1328491))), _1328495) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328489), _1328493), _1328495))], (6524 ^ _780478) ^ [_886961, _886963, _886965] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886961, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886961, tc_HOL_Obool)), _886963), _886965)), _886965) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_886961, tc_HOL_Obool)), _886963), _886965))], (43849 ^ _780478) ^ [_1657377, _1657379] : [hBOOL(hAPP(c_List_Odistinct(_1657377), hAPP(c_List_Orotate1(_1657377), _1657379))), -(hBOOL(hAPP(c_List_Odistinct(_1657377), _1657379)))], (29618 ^ _780478) ^ [_1330448, _1330450, _1330452, _1330454] : [_1330448 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1330450), _1330452)), _1330454), -(_1330450 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330448, _1330450) = _1330454), 29625 ^ _780478 : [(29628 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330454)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330454), _1330450))], (29626 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330450)))]], 29633 ^ _780478 : [(29636 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1330450), _1330454)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1330454), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (29634 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330450))]]], (42284 ^ _780478) ^ [_1620388, _1620390, _1620392] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1620388, tc_HOL_Obool)), hAPP(c_List_Oset(_1620388), c_List_Osublist(_1620388, _1620390, _1620392))), hAPP(c_List_Oset(_1620388), _1620390))))], (47258 ^ _780478) ^ [_1731309] : [-(c_List_Oreturn__list(_1731309) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1731309))], (4656 ^ _780478) ^ [_851357, _851359, _851361, _851363] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_851363, _851359) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_851361, _851357)), _851363 = _851361, _851359 = _851357], (12734 ^ _780478) ^ [_1005809, _1005811, _1005813] : [class_Lattices_Olattice(_1005809), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005809), _1005811), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005809), _1005811), _1005813)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005809), _1005811), _1005813))], (23909 ^ _780478) ^ [_1225023, _1225025, _1225027] : [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), _1225023), _1225025)), _1225027)), 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)), _1225027)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225025), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34545 ^ _780478) ^ [_1431840, _1431842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1431840)), c_Int_OBit0(_1431842))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431840), _1431842)))], (45436 ^ _780478) ^ [_1692289, _1692291, _1692293, _1692295, _1692297, _1692299, _1692301] : [c_List_Olist__all2(_1692289, _1692297, hAPP(hAPP(c_COMBC(_1692289, tc_fun(_1692297, _1692291), tc_fun(_1692297, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1692291, tc_HOL_Obool), tc_fun(tc_fun(_1692297, _1692291), tc_fun(_1692297, tc_HOL_Obool)), _1692289), c_COMBB(_1692291, tc_HOL_Obool, _1692297)), _1692293)), _1692299), _1692295, _1692301), -(c_List_Olist__all2(_1692289, _1692291, _1692293, _1692295, hAPP(hAPP(c_List_Omap(_1692297, _1692291), _1692299), _1692301)))], (41136 ^ _780478) ^ [_1587879, _1587881] : [-(c_Relation_Oirrefl(_1587879, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1587879, _1587879), tc_HOL_Obool)), _1587881), c_Relation_OId(_1587879))))], (30634 ^ _780478) ^ [_1349093, _1349095, _1349097] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349093, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1349093, tc_HOL_Obool), _1349095)), _1349097) = c_Orderings_Obot__class_Obot(tc_fun(_1349093, tc_HOL_Obool)), 30637 ^ _780478 : [(30638 ^ _780478) ^ [_1349228] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1349093, tc_HOL_Obool)), _1349228), _1349095)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349093, tc_HOL_Obool)), _1349228), _1349097) = c_Orderings_Obot__class_Obot(tc_fun(_1349093, tc_HOL_Obool)))]]], (15419 ^ _780478) ^ [_1058278, _1058280, _1058282, _1058284] : [class_Rings_Olinordered__semidom(_1058278), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1058278), c_Groups_Oone__class_Oone(_1058278)), _1058280)), 15426 ^ _780478 : [(15433 ^ _780478) ^ [] : [_1058282 = _1058284, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1058278), _1058280), _1058282) = hAPP(hAPP(c_Power_Opower__class_Opower(_1058278), _1058280), _1058284))], (15427 ^ _780478) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1058278), _1058280), _1058282) = hAPP(hAPP(c_Power_Opower__class_Opower(_1058278), _1058280), _1058284), -(_1058282 = _1058284)]]], (31074 ^ _780478) ^ [_1358485, _1358487, _1358489, _1358491, _1358493, _1358495] : [-(_1358485 = c_Orderings_Obot__class_Obot(tc_fun(_1358487, tc_HOL_Obool))), 31080 ^ _780478 : [(31083 ^ _780478) ^ [] : [c_Fun_Oinj__on(_1358489, _1358491, _1358493, hAPP(_1358495, 31079 ^ [_1358485, _1358487, _1358489, _1358491, _1358493, _1358495]))], (31081 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358487), 31079 ^ [_1358485, _1358487, _1358489, _1358491, _1358493, _1358495]), _1358485)))]], -(c_Fun_Oinj__on(_1358489, _1358491, _1358493, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1358487, tc_fun(_1358489, tc_HOL_Obool)), _1358485), _1358495)))], (48437 ^ _780478) ^ [_1757139, _1757141] : [-(c_List_Osplice(_1757139, _1757141, c_List_Olist_ONil(_1757139)) = _1757141)], (52039 ^ _780478) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (14423 ^ _780478) ^ [_1037854, _1037856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037854), _1037856)), _1037856 = _1037854], (37772 ^ _780478) ^ [_1501573, _1501575, _1501577, _1501579] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1501573, _1501573)), hAPP(hAPP(c_Product__Type_OPair(_1501573, _1501573), _1501575), _1501577)), c_Relation_OId__on(_1501573, _1501579))), 37775 ^ _780478 : [(37778 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501573), _1501575), _1501579)))], (37776 ^ _780478) ^ [] : [-(_1501575 = _1501577)]]], (23144 ^ _780478) ^ [_1211322, _1211324] : [-(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), _1211322))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211324))))], (18584 ^ _780478) ^ [_1129020] : [class_Complete__Lattice_Ocomplete__lattice(_1129020), -(c_Complete__Lattice_OInf__class_OInf(_1129020, c_Orderings_Otop__class_Otop(tc_fun(_1129020, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1129020))], (5026 ^ _780478) ^ [_857170, _857172, _857174, _857176] : [-(c_Quickcheck_Obeyond(_857176, _857172) = c_Quickcheck_Obeyond(_857174, _857170)), _857176 = _857174, _857172 = _857170], (45147 ^ _780478) ^ [_1685512, _1685514] : [_1685512 = _1685514, -(hAPP(c_Code__Numeral_Onat__of, _1685512) = hAPP(c_Code__Numeral_Onat__of, _1685514))], (31304 ^ _780478) ^ [_1363615, _1363617] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1363615, tc_HOL_Obool)), _1363617) = hAPP(c_Set_OCollect(_1363615), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1363615), c_fNot), hAPP(hAPP(c_COMBC(_1363615, tc_fun(_1363615, tc_HOL_Obool), tc_HOL_Obool), c_member(_1363615)), _1363617))))], (18614 ^ _780478) ^ [_1129773, _1129775, _1129777, _1129779, _1129781] : [-(_1129773 = c_Orderings_Obot__class_Obot(tc_fun(_1129775, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129775, tc_fun(_1129777, tc_HOL_Obool)), _1129773), hAPP(hAPP(c_COMBB(tc_fun(_1129777, tc_HOL_Obool), tc_fun(_1129777, tc_HOL_Obool), _1129775), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129777, tc_HOL_Obool)), _1129779)), _1129781)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129777, tc_HOL_Obool)), _1129779), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129775, tc_fun(_1129777, tc_HOL_Obool)), _1129773), _1129781)))], (43867 ^ _780478) ^ [_1657746, _1657748, _1657750, _1657752] : [-(hAPP(hAPP(c_List_Otake(_1657746), _1657748), hAPP(hAPP(c_List_Odrop(_1657746), _1657750), _1657752)) = hAPP(hAPP(c_List_Odrop(_1657746), _1657750), hAPP(hAPP(c_List_Otake(_1657746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657748), _1657750)), _1657752)))], (49349 ^ _780478) ^ [_1777471, _1777473, _1777475] : [c_List_Olist__ex(_1777471, _1777475, _1777473), 49353 ^ _780478 : [(49356 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1777475, 49352 ^ [_1777471, _1777473, _1777475])))], (49354 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777471), 49352 ^ [_1777471, _1777473, _1777475]), hAPP(c_List_Oset(_1777471), _1777473))))]]], (43169 ^ _780478) ^ [_1641180, _1641182, _1641184] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641180), tc_List_Olist(_1641180))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641180), tc_List_Olist(_1641180)), _1641182), c_List_Olist_ONil(_1641180))), c_List_Olistrel1(_1641180, _1641184)))], (47469 ^ _780478) ^ [_1735850, _1735852, _1735854, _1735856] : [47471 ^ _780478 : [(47476 ^ _780478) ^ [] : [hBOOL(hAPP(_1735856, hAPP(hAPP(c_List_Onth(_1735852), _1735854), 47470 ^ [_1735850, _1735852, _1735854, _1735856])))], (47474 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47470 ^ [_1735850, _1735852, _1735854, _1735856]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735852)), _1735854))))], (47472 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47470 ^ [_1735850, _1735852, _1735854, _1735856]), _1735850)))]], 47479 ^ _780478 : [(47482 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1735856, hAPP(hAPP(c_List_Onth(_1735852), _1735854), _1735850))))], (47480 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1735850), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735852)), _1735854))))]], -(c_List_OtakeWhile(_1735852, _1735856, _1735854) = hAPP(hAPP(c_List_Otake(_1735852), _1735850), _1735854))], (37481 ^ _780478) ^ [_1495001, _1495003, _1495005, _1495007, _1495009, _1495011, _1495013] : [hBOOL(hAPP(_1495001, _1495003)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1495005, _1495005)), hAPP(hAPP(c_Product__Type_OPair(_1495005, _1495005), _1495007), _1495009)), hAPP(_1495011, _1495003))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1495013, _1495005), tc_prod(_1495013, _1495005))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1495013, _1495005), tc_prod(_1495013, _1495005)), hAPP(hAPP(c_Product__Type_OPair(_1495013, _1495005), _1495003), _1495007)), hAPP(hAPP(c_Product__Type_OPair(_1495013, _1495005), _1495003), _1495009))), c_Recdef_Osame__fst(_1495013, _1495005, _1495001, _1495011))))], (39031 ^ _780478) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (43654 ^ _780478) ^ [_1652061, _1652063, _1652065, _1652067] : [-(hBOOL(hAPP(hAPP(c_member(_1652061), _1652063), hAPP(c_List_Oset(_1652061), _1652065)))), -(c_List_Oremove1(_1652061, _1652063, hAPP(hAPP(c_List_Oappend(_1652061), _1652065), _1652067)) = hAPP(hAPP(c_List_Oappend(_1652061), _1652065), c_List_Oremove1(_1652061, _1652063, _1652067)))], (23941 ^ _780478) ^ [_1225611, _1225613, _1225615, _1225617, _1225619, _1225621] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225611), _1225613)), _1225615) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1225617), _1225619)), _1225621), 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), _1225617), _1225619)), _1225621))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225621), _1225617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225617), _1225611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225613), _1225619)))], (8446 ^ _780478) ^ [_925596, _925598, _925600, _925602, _925604] : [class_Groups_Ocomm__monoid__add(_925596), hBOOL(hAPP(c_Finite__Set_Ofinite(_925598), _925600)), hBOOL(hAPP(hAPP(c_member(_925598), _925602), _925600)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_925598, _925596), _925604), _925600) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925596), hAPP(_925604, _925602)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_925598, _925596), _925604), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925598, tc_HOL_Obool)), _925600), hAPP(hAPP(c_Set_Oinsert(_925598), _925602), c_Orderings_Obot__class_Obot(tc_fun(_925598, tc_HOL_Obool)))))))], (13574 ^ _780478) ^ [_1022662, _1022664, _1022666, _1022668, _1022670] : [c_Fun_Oinj__on(_1022662, _1022664, _1022666, c_Orderings_Otop__class_Otop(tc_fun(_1022662, tc_HOL_Obool))), 13577 ^ _780478 : [(13584 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022662, tc_HOL_Obool)), _1022668), _1022670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022664, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1022662, _1022664, _1022666), _1022668)), hAPP(c_Set_Oimage(_1022662, _1022664, _1022666), _1022670))))], (13578 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022664, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1022662, _1022664, _1022666), _1022668)), hAPP(c_Set_Oimage(_1022662, _1022664, _1022666), _1022670))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022662, tc_HOL_Obool)), _1022668), _1022670)))]]], (18031 ^ _780478) ^ [_1116064] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1116064)), _1116064))], (22975 ^ _780478) ^ [_1208067, _1208069, _1208071] : [class_Rings_Oring__1(_1208067), hBOOL(hAPP(hAPP(c_member(_1208067), _1208069), c_Int_Oring__1__class_OInts(_1208067))), -(hBOOL(hAPP(hAPP(c_member(_1208067), hAPP(hAPP(c_Power_Opower__class_Opower(_1208067), _1208069), _1208071)), c_Int_Oring__1__class_OInts(_1208067))))], (13930 ^ _780478) ^ [_1029519, _1029521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029519), _1029521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1029521), _1029519)), -(_1029519 = _1029521)], (11397 ^ _780478) ^ [_980163, _980165, _980167] : [class_Orderings_Olinorder(_980163), hBOOL(hAPP(c_Finite__Set_Ofinite(_980163), _980165)), hBOOL(hAPP(hAPP(c_member(_980163), _980167), _980165)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_980163), _980167), c_Big__Operators_Olinorder__class_OMax(_980163, _980165)) = c_Big__Operators_Olinorder__class_OMax(_980163, _980165))], (34347 ^ _780478) ^ [_1428324, _1428326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1428324), 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)))), _1428326)), 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)))), _1428324)) = 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), _1428326), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1428324))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (52099 ^ _780478) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (40622 ^ _780478) ^ [_1575508, _1575510, _1575512, _1575514, _1575516] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575508, _1575508)), hAPP(hAPP(c_Product__Type_OPair(_1575508, _1575508), _1575510), _1575512)), c_Transitive__Closure_Ortrancl(_1575508, _1575514))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575508, _1575508)), hAPP(hAPP(c_Product__Type_OPair(_1575508, _1575508), _1575512), _1575516)), _1575514)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575508, _1575508)), hAPP(hAPP(c_Product__Type_OPair(_1575508, _1575508), _1575510), _1575516)), c_Transitive__Closure_Otrancl(_1575508, _1575514))))], (22239 ^ _780478) ^ [_1193909, _1193911] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1193909), _1193911)), -(hAPP(c_Finite__Set_Ocard(_1193909), _1193911) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1193909, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1193909), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1193911))], (38273 ^ _780478) ^ [_1515671, _1515673, _1515675] : [c_Wellfounded_Owf(_1515671, _1515673), -(c_Wellfounded_Owf(_1515671, c_Wellfounded_Omlex__prod(_1515671, _1515675, _1515673)))], (41083 ^ _780478) ^ [_1586489, _1586491, _1586493, _1586495, _1586497, _1586499] : [c_Relation_Osingle__valued(_1586489, _1586491, _1586493), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586489, _1586491)), hAPP(hAPP(c_Product__Type_OPair(_1586489, _1586491), _1586495), _1586497)), _1586493)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586489, _1586491)), hAPP(hAPP(c_Product__Type_OPair(_1586489, _1586491), _1586495), _1586499)), _1586493)), -(_1586497 = _1586499)], (24773 ^ _780478) ^ [_1240760, _1240762] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_1240760, _1240762)) = 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), _1240760)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1240762))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18294 ^ _780478) ^ [_1122710, _1122712, _1122714, _1122716, _1122718] : [class_Complete__Lattice_Ocomplete__lattice(_1122710), 18297 ^ _780478 : [(18298 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122710), _1122712), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1122714, _1122710), _1122716), _1122718))), 18301 ^ _780478 : [(18302 ^ _780478) ^ [_1122891] : [hBOOL(hAPP(hAPP(c_member(_1122714), _1122891), _1122716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122710), _1122712), hAPP(_1122718, _1122891))))]]], (18308 ^ _780478) ^ [] : [18310 ^ _780478 : [(18313 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122710), _1122712), hAPP(_1122718, 18309 ^ [_1122710, _1122712, _1122714, _1122716, _1122718])))], (18311 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1122714), 18309 ^ [_1122710, _1122712, _1122714, _1122716, _1122718]), _1122716)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1122710), _1122712), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1122714, _1122710), _1122716), _1122718))))]]], (29409 ^ _780478) ^ [_1326605, _1326607, _1326609, _1326611] : [class_Divides_Osemiring__div(_1326605), -(c_Divides_Odiv__class_Omod(_1326605, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1326605), _1326607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326605), _1326609), _1326611)), _1326609) = c_Divides_Odiv__class_Omod(_1326605, _1326607, _1326609))], (48381 ^ _780478) ^ [_1755689, _1755691, _1755693, _1755695, _1755697] : [_1755689 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1755691, _1755693, _1755695, _1755697), _1755689) = c_Lazy__Sequence_Ohit__bound(_1755693))], (9908 ^ _780478) ^ [_952355, _952357, _952359, _952361, _952363] : [class_Rings_Osemiring(_952355), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952355), _952357), _952359)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952355), _952361), _952359)), _952363)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_952355), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_952355), _952357), _952361)), _952359)), _952363))], (41595 ^ _780478) ^ [_1600007, _1600009, _1600011, _1600013] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600007, _1600009)), _1600011), hAPP(c_Relation_Oconverse(_1600009, _1600007), _1600013))), 41600 ^ _780478 : [(41603 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600009, _1600007)), hAPP(hAPP(c_Product__Type_OPair(_1600009, _1600007), 41598 ^ [_1600007, _1600009, _1600011, _1600013]), 41599 ^ [_1600007, _1600009, _1600011, _1600013])), _1600013)))], (41601 ^ _780478) ^ [] : [-(_1600011 = hAPP(hAPP(c_Product__Type_OPair(_1600007, _1600009), 41599 ^ [_1600007, _1600009, _1600011, _1600013]), 41598 ^ [_1600007, _1600009, _1600011, _1600013]))]]], (31033 ^ _780478) ^ [_1357678, _1357680] : [-(_1357678 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1357680, _1357678) = c_Nitpick_Onat__gcd(_1357678, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357680, _1357678)))], (31334 ^ _780478) ^ [_1364829, _1364831, _1364833, _1364835, _1364837] : [class_Groups_Ocomm__monoid__add(_1364829), hBOOL(hAPP(c_Finite__Set_Ofinite(_1364831), _1364833)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364831, _1364829), _1364835), hAPP(c_Set_OCollect(_1364831), hAPP(hAPP(c_COMBS(_1364831, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1364831), c_fconj), hAPP(hAPP(c_COMBC(_1364831, tc_fun(_1364831, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364831)), _1364833))), hAPP(hAPP(c_COMBC(_1364831, tc_fun(_1364831, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364831)), _1364837)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1364831, _1364829), hAPP(hAPP(c_COMBC(_1364831, _1364829, _1364829), hAPP(hAPP(c_COMBS(_1364831, _1364829, tc_fun(_1364829, _1364829)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1364829, tc_fun(_1364829, _1364829)), _1364831), c_If(_1364829)), hAPP(hAPP(c_COMBC(_1364831, tc_fun(_1364831, tc_HOL_Obool), tc_HOL_Obool), c_member(_1364831)), _1364837))), _1364835)), c_Groups_Ozero__class_Ozero(_1364829))), _1364833))], (14517 ^ _780478) ^ [_1039845, _1039847, _1039849] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039845), _1039847)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039849), _1039847)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1039845), _1039849)), _1039847))], (18510 ^ _780478) ^ [_1127299, _1127301, _1127303, _1127305, _1127307] : [-(_1127299 = c_Orderings_Obot__class_Obot(tc_fun(_1127301, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127303, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127301, tc_fun(_1127303, tc_HOL_Obool)), _1127299), _1127305)), _1127307) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127301, tc_fun(_1127303, tc_HOL_Obool)), _1127299), hAPP(hAPP(c_COMBC(_1127301, tc_fun(_1127303, tc_HOL_Obool), tc_fun(_1127303, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1127303, tc_HOL_Obool), tc_fun(tc_fun(_1127303, tc_HOL_Obool), tc_fun(_1127303, tc_HOL_Obool)), _1127301), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1127303, tc_HOL_Obool))), _1127305)), _1127307)))], (52349 ^ _780478) ^ [] : [hBOOL(c_fFalse)], (43538 ^ _780478) ^ [_1649793, _1649795, _1649797] : [-(c_List_Olist_ONil(_1649793) = hAPP(hAPP(c_List_Oappend(_1649793), _1649795), _1649797)), _1649795 = c_List_Olist_ONil(_1649793), _1649797 = c_List_Olist_ONil(_1649793)], (52147 ^ _780478) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (39638 ^ _780478) ^ [_1552114, _1552116, _1552118, _1552120, _1552122, _1552124, _1552126] : [-(hAPP(c_Fun_Ocomp(_1552114, _1552116, _1552118, _1552120), c_Fun_Ofun__upd(_1552118, _1552114, _1552122, _1552124, _1552126)) = c_Fun_Ofun__upd(_1552118, _1552116, hAPP(c_Fun_Ocomp(_1552114, _1552116, _1552118, _1552120), _1552122), _1552124, hAPP(_1552120, _1552126)))], (32494 ^ _780478) ^ [_1394058, _1394060, _1394062] : [class_Int_Onumber__ring(_1394058), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394058), hAPP(c_Groups_Ouminus__class_Ouminus(_1394058), hAPP(c_Int_Onumber__class_Onumber__of(_1394058), _1394060))), _1394062) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394058), hAPP(c_Int_Onumber__class_Onumber__of(_1394058), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1394060))), _1394062))], (45097 ^ _780478) ^ [_1684464] : [-(_1684464 = 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)), _1684464)))], (26162 ^ _780478) ^ [_1265564, _1265566, _1265568] : [class_Fields_Ofield__inverse__zero(_1265564), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1265564), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265564), _1265566), _1265568)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265564), _1265566), hAPP(c_Groups_Ouminus__class_Ouminus(_1265564), _1265568)))], (51985 ^ _780478) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (14671 ^ _780478) ^ [_1042846, _1042848, _1042850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042846), _1042848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042850), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042848), _1042850)), _1042846))))], (41920 ^ _780478) ^ [_1609986, _1609988, _1609990, _1609992, _1609994, _1609996] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609986), tc_List_Olist(_1609986))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609986), tc_List_Olist(_1609986)), hAPP(hAPP(c_List_Olist_OCons(_1609986), _1609988), _1609990)), hAPP(hAPP(c_List_Olist_OCons(_1609986), _1609992), _1609994))), c_List_Olistrel1(_1609986, _1609996)))), 41921 ^ _780478 : [(41928 ^ _780478) ^ [] : [_1609988 = _1609992, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609986), tc_List_Olist(_1609986))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609986), tc_List_Olist(_1609986)), _1609990), _1609994)), c_List_Olistrel1(_1609986, _1609996)))], (41922 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609986, _1609986)), hAPP(hAPP(c_Product__Type_OPair(_1609986, _1609986), _1609988), _1609992)), _1609996)), _1609990 = _1609994]]], (2550 ^ _780478) ^ [_818010, _818012, _818014, _818016] : [-(c_Wellfounded_Omin__ext(_818016, _818012) = c_Wellfounded_Omin__ext(_818014, _818010)), _818016 = _818014, _818012 = _818010], (20944 ^ _780478) ^ [_1170413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1170413), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1170413 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11809 ^ _780478) ^ [_987803, _987805, _987807] : [class_Orderings_Olinorder(_987803), hBOOL(hAPP(c_Finite__Set_Ofinite(_987803), _987805)), hBOOL(hAPP(hAPP(c_member(_987803), _987807), _987805)), 11820 ^ _780478 : [(11827 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987803, tc_HOL_Obool)), _987805), hAPP(hAPP(c_Set_Oinsert(_987803), _987807), c_Orderings_Obot__class_Obot(tc_fun(_987803, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_987803, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_987803, c_Orderings_Oord__class_Omax(_987803), _987805) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_987803), _987807), c_Big__Operators_Olattice_OSup__fin(_987803, c_Orderings_Oord__class_Omax(_987803), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987803, tc_HOL_Obool)), _987805), hAPP(hAPP(c_Set_Oinsert(_987803), _987807), c_Orderings_Obot__class_Obot(tc_fun(_987803, tc_HOL_Obool)))))))], (11821 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_987803, tc_HOL_Obool)), _987805), hAPP(hAPP(c_Set_Oinsert(_987803), _987807), c_Orderings_Obot__class_Obot(tc_fun(_987803, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_987803, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_987803, c_Orderings_Oord__class_Omax(_987803), _987805) = _987807)]]], (22351 ^ _780478) ^ [] : [-(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)))], (33724 ^ _780478) ^ [_1416818, _1416820] : [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(_1416818))), 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)), _1416820)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416818)), hAPP(c_Nat_OSuc, _1416820))))], (11973 ^ _780478) ^ [_990814, _990816, _990818] : [class_Orderings_Olinorder(_990814), hBOOL(hAPP(c_Finite__Set_Ofinite(_990814), _990816)), -(_990818 = c_Orderings_Obot__class_Obot(tc_fun(_990814, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_990814, tc_HOL_Obool)), _990818), _990816)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_990814), c_Big__Operators_Olattice_OInf__fin(_990814, c_Orderings_Oord__class_Omin(_990814), _990818)), c_Big__Operators_Olattice_OInf__fin(_990814, c_Orderings_Oord__class_Omin(_990814), _990816)) = c_Big__Operators_Olattice_OInf__fin(_990814, c_Orderings_Oord__class_Omin(_990814), _990816))], (11507 ^ _780478) ^ [_982138, _982140, _982142] : [class_Orderings_Olinorder(_982138), hBOOL(hAPP(c_Finite__Set_Ofinite(_982138), _982140)), -(_982140 = c_Orderings_Obot__class_Obot(tc_fun(_982138, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_982138, hAPP(hAPP(c_Set_Oinsert(_982138), _982142), _982140)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_982138), _982142), c_Big__Operators_Olinorder__class_OMin(_982138, _982140)))], (39755 ^ _780478) ^ [_1554636, _1554638, _1554640, _1554642, _1554644, _1554646] : [c_Fun_Oinj__on(_1554636, _1554638, _1554640, _1554642), 39758 ^ _780478 : [(39765 ^ _780478) ^ [] : [c_Fun_Oinj__on(_1554636, _1554644, hAPP(c_Fun_Ocomp(_1554638, _1554644, _1554636, _1554646), _1554640), _1554642), -(c_Fun_Oinj__on(_1554638, _1554644, _1554646, hAPP(c_Set_Oimage(_1554636, _1554638, _1554640), _1554642)))], (39759 ^ _780478) ^ [] : [c_Fun_Oinj__on(_1554638, _1554644, _1554646, hAPP(c_Set_Oimage(_1554636, _1554638, _1554640), _1554642)), -(c_Fun_Oinj__on(_1554636, _1554644, hAPP(c_Fun_Ocomp(_1554638, _1554644, _1554636, _1554646), _1554640), _1554642))]]], (46334 ^ _780478) ^ [_1713077, _1713079, _1713081, _1713083] : [c_List_Oupt(_1713077, _1713079) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1713081), _1713083), 46337 ^ _780478 : [(46342 ^ _780478) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713077), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1713079) = _1713083)], (46340 ^ _780478) ^ [] : [-(_1713077 = _1713081)], (46338 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713077), _1713079)))]]], (50769 ^ _780478) ^ [_1807378, _1807380, _1807382, _1807384, _1807386] : [hBOOL(hAPP(hAPP(c_member(_1807378), _1807380), _1807382)), -(hAPP(c_Quotient_OBabs(_1807378, _1807384, _1807382, _1807386), _1807380) = hAPP(_1807386, _1807380))], (14036 ^ _780478) ^ [_1031425, _1031427] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1031425), _1031427) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 14039 ^ _780478 : [(14042 ^ _780478) ^ [] : [-(_1031427 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (14040 ^ _780478) ^ [] : [-(_1031425 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (42726 ^ _780478) ^ [_1632121, _1632123, _1632125, _1632127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632121), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632123)), _1632125))), -(hAPP(hAPP(c_List_Onth(_1632123), hAPP(hAPP(c_List_Olist__update(_1632123, _1632125), _1632121), _1632127)), _1632121) = _1632127)], (10783 ^ _780478) ^ [_968574, _968576, _968578, _968580] : [class_Orderings_Olinorder(_968574), 10786 ^ _780478 : [(10787 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968574), hAPP(hAPP(c_Orderings_Oord__class_Omin(_968574), _968576), _968578)), _968580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968574), _968576), _968580))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968574), _968578), _968580)))], (10797 ^ _780478) ^ [] : [10798 ^ _780478 : [(10801 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968574), _968578), _968580))], (10799 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968574), _968576), _968580))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_968574), hAPP(hAPP(c_Orderings_Oord__class_Omin(_968574), _968576), _968578)), _968580)))]]], (15481 ^ _780478) ^ [_1059508, _1059510, _1059512, _1059514] : [c_Fun_Oinj__on(_1059508, _1059510, _1059512, c_Orderings_Otop__class_Otop(tc_fun(_1059508, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1059508, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1059508, _1059510, _1059512), hAPP(hAPP(c_Set_Oinsert(_1059510), _1059514), c_Orderings_Obot__class_Obot(tc_fun(_1059510, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1059508), c_HOL_OThe(_1059508, hAPP(hAPP(c_COMBC(_1059508, _1059510, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1059510, tc_fun(_1059510, tc_HOL_Obool), _1059508), c_fequal), _1059512)), _1059514))), c_Orderings_Obot__class_Obot(tc_fun(_1059508, tc_HOL_Obool))))))], (52137 ^ _780478) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (13268 ^ _780478) ^ [_1016312, _1016314, _1016316] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1016312), _1016314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016312, tc_HOL_Obool)), _1016316), _1016314)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1016312), _1016314)), hAPP(c_Finite__Set_Ocard(_1016312), _1016316))), -(_1016316 = _1016314)], (52059 ^ _780478) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (47927 ^ _780478) ^ [_1746671, _1746673] : [class_Enum_Oenum(_1746671), 47930 ^ _780478 : [(47938 ^ _780478) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746671), _1746673)), 47941 ^ _780478 : [(47942 ^ _780478) ^ [_1746889] : [-(hBOOL(hAPP(_1746673, _1746889)))]]], (47931 ^ _780478) ^ [] : [hBOOL(hAPP(_1746673, 47932 ^ [_1746671, _1746673])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1746671), _1746673)))]]], (43947 ^ _780478) ^ [_1659605, _1659607, _1659609, _1659611] : [-(hAPP(hAPP(c_List_Odrop(_1659605), _1659607), hAPP(hAPP(c_List_Olist_OCons(_1659605), _1659609), _1659611)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1659605), hAPP(hAPP(c_List_Olist_OCons(_1659605), _1659609), _1659611), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1659605), tc_List_Olist(_1659605)), c_List_Odrop(_1659605)), _1659611), _1659607))], (6320 ^ _780478) ^ [_882340, _882342, _882344, _882346, _882348] : [c_Finite__Set_Ofolding__one__idem(_882340, _882342, _882344), hBOOL(hAPP(c_Finite__Set_Ofinite(_882340), _882346)), hBOOL(hAPP(hAPP(c_member(_882340), _882348), _882346)), -(hAPP(hAPP(_882342, _882348), hAPP(_882344, _882346)) = hAPP(_882344, _882346))], (10081 ^ _780478) ^ [_955842, _955844] : [class_Groups_Olinordered__ab__group__add(_955842), hBOOL(hAPP(c_Finite__Set_Ofinite(_955842), _955844)), -(_955844 = c_Orderings_Obot__class_Obot(tc_fun(_955842, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_955842), c_Big__Operators_Olinorder__class_OMax(_955842, _955844)) = c_Big__Operators_Olinorder__class_OMin(_955842, hAPP(c_Set_Oimage(_955842, _955842, c_Groups_Ouminus__class_Ouminus(_955842)), _955844)))], (30254 ^ _780478) ^ [_1341774, _1341776, _1341778, _1341780] : [class_Groups_Oordered__ab__group__add__abs(_1341774), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341774), c_Groups_Ozero__class_Ozero(_1341774)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1341776, _1341774), hAPP(hAPP(c_COMBB(_1341774, _1341774, _1341776), c_Groups_Oabs__class_Oabs(_1341774)), _1341778)), _1341780))))], (31893 ^ _780478) ^ [_1382728, _1382730, _1382732, _1382734, _1382736] : [c_Com_Ocom_OCond(_1382728, _1382730, _1382732) = c_Com_Ocom_OWhile(_1382734, _1382736)], (13710 ^ _780478) ^ [_1025443, _1025445, _1025447] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1025443), _1025445)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025443, tc_HOL_Obool)), _1025445), _1025447) = hAPP(hAPP(c_Finite__Set_Ofold(_1025443, tc_fun(_1025443, tc_HOL_Obool), c_Set_Oinsert(_1025443)), _1025447), _1025445))], (3556 ^ _780478) ^ [_833571, _833573, _833575, _833577, _833579, _833581, _833583, _833585] : [-(c_List_Olinorder__class_Osort__key(_833585, _833581, _833577, _833573) = c_List_Olinorder__class_Osort__key(_833583, _833579, _833575, _833571)), _833585 = _833583, _833581 = _833579, _833577 = _833575, _833573 = _833571], (49149 ^ _780478) ^ [_1772970, _1772972, _1772974, _1772976] : [-(hAPP(c_Relation_OImage(_1772970, _1772972, hAPP(c_Set_OCollect(tc_prod(_1772970, _1772972)), hAPP(c_Product__Type_Oprod_Oprod__case(_1772970, _1772972, tc_HOL_Obool), _1772974))), _1772976) = hAPP(c_Set_OCollect(_1772972), hAPP(hAPP(c_COMBB(tc_fun(_1772970, tc_HOL_Obool), tc_HOL_Obool, _1772972), c_HOL_OEx(_1772970)), hAPP(hAPP(c_COMBB(tc_fun(_1772970, tc_HOL_Obool), tc_fun(_1772970, tc_HOL_Obool), _1772972), hAPP(c_COMBS(_1772970, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1772970), c_fconj), hAPP(hAPP(c_COMBC(_1772970, tc_fun(_1772970, tc_HOL_Obool), tc_HOL_Obool), c_member(_1772970)), _1772976)))), hAPP(c_COMBC(_1772970, _1772972, tc_HOL_Obool), _1772974)))))], (18578 ^ _780478) ^ [_1128927] : [class_Complete__Lattice_Ocomplete__lattice(_1128927), -(c_Complete__Lattice_OInf__class_OInf(_1128927, c_Orderings_Obot__class_Obot(tc_fun(_1128927, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1128927))], (48669 ^ _780478) ^ [_1762205, _1762207, _1762209] : [_1762207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1762205) = c_List_Oreplicate(_1762205, _1762207, _1762209))], (34139 ^ _780478) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (142 ^ _780478) ^ [_782811, _782813, _782815, _782817, _782819, _782821] : [-(c_Finite__Set_Ofolding__one(_782819, _782815, _782811)), c_Finite__Set_Ofolding__one(_782821, _782817, _782813), _782821 = _782819, _782817 = _782815, _782813 = _782811], (33608 ^ _780478) ^ [_1414308, _1414310] : [class_Int_Onumber__ring(_1414308), -(hAPP(c_Int_Onumber__class_Onumber__of(_1414308), c_Int_Osucc(_1414310)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414308), c_Groups_Oone__class_Oone(_1414308)), hAPP(c_Int_Onumber__class_Onumber__of(_1414308), _1414310)))], (22763 ^ _780478) ^ [_1204239, _1204241] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1204239), _1204241)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1204239)), _1204241))], (41344 ^ _780478) ^ [_1593255] : [-(c_Nat_Ofunpow(_1593255) = c_Nat_Ocompow(_1593255, _1593255))], (10993 ^ _780478) ^ [_972244, _972246, _972248] : [class_Groups_Ogroup__add(_972244), -(hAPP(c_Groups_Ouminus__class_Ouminus(_972244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972244), _972246), _972248)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972244), hAPP(c_Groups_Ouminus__class_Ouminus(_972244), _972248)), hAPP(c_Groups_Ouminus__class_Ouminus(_972244), _972246)))], (46066 ^ _780478) ^ [_1706463] : [-(c_List_Otranspose(_1706463, c_List_Olist_ONil(tc_List_Olist(_1706463))) = c_List_Olist_ONil(tc_List_Olist(_1706463)))], (31724 ^ _780478) ^ [_1379604, _1379606, _1379608, _1379610, _1379612] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1379604, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379606, _1379604, _1379608), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1379606, tc_HOL_Obool)), _1379610), _1379612))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1379604, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1379606, _1379604, _1379608), _1379610)), hAPP(c_Relation_OImage(_1379606, _1379604, _1379608), _1379612)))))], (26096 ^ _780478) ^ [_1264227, _1264229, _1264231, _1264233] : [class_Fields_Olinordered__field(_1264227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264227), c_Groups_Ozero__class_Ozero(_1264227)), _1264229)), 26103 ^ _780478 : [(26110 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264227), _1264231), _1264229)), _1264233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264227), _1264231), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264227), _1264233), _1264229))))], (26104 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264227), _1264231), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264227), _1264233), _1264229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1264227), _1264231), _1264229)), _1264233)))]]], (27547 ^ _780478) ^ [_1289794, _1289796, _1289798] : [class_Rings_Oring__1(_1289794), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289794), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1289796), _1289798)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1289794), hAPP(c_Int_Oring__1__class_Oof__int(_1289794), _1289796)), hAPP(c_Int_Oring__1__class_Oof__int(_1289794), _1289798)))], (34267 ^ _780478) ^ [_1426747, _1426749] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426747))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426749)) = 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)))), _1426747), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1426749)))], (39963 ^ _780478) ^ [_1559443, _1559445, _1559447, _1559449, _1559451, _1559453, _1559455, _1559457] : [c_Finite__Set_Ofolding__image(_1559443, _1559445, _1559447, _1559449, _1559451), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559445), _1559453)), -(hAPP(hAPP(_1559451, hAPP(hAPP(c_COMBS(_1559445, _1559443, _1559443), hAPP(hAPP(c_COMBB(_1559443, tc_fun(_1559443, _1559443), _1559445), _1559447), _1559455)), _1559457)), _1559453) = hAPP(hAPP(_1559447, hAPP(hAPP(_1559451, _1559455), _1559453)), hAPP(hAPP(_1559451, _1559457), _1559453)))], (44747 ^ _780478) ^ [_1676551, _1676553, _1676555, _1676557, _1676559, _1676561, _1676563] : [hAPP(hAPP(c_List_Omap(_1676551, _1676553), _1676555), _1676557) = hAPP(hAPP(c_List_Omap(_1676559, _1676553), _1676561), _1676563), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676551)), _1676557) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676559)), _1676563))], (17857 ^ _780478) ^ [_1113368, _1113370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113368), hAPP(c_Nat_OSuc, _1113370))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113368), _1113370))), -(_1113368 = _1113370)], (33494 ^ _780478) ^ [_1412488, _1412490] : [class_Int_Onumber__ring(_1412488), class_Rings_Olinordered__idom(_1412488), 33501 ^ _780478 : [(33508 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1412490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412488), c_Groups_Ozero__class_Ozero(_1412488)), hAPP(c_Int_Onumber__class_Onumber__of(_1412488), _1412490))))], (33502 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412488), c_Groups_Ozero__class_Ozero(_1412488)), hAPP(c_Int_Onumber__class_Onumber__of(_1412488), _1412490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1412490)))]]], (30723 ^ _780478) ^ [_1351146, _1351148, _1351150, _1351152] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1351146, tc_HOL_Obool), hAPP(c_Set_Oimage(_1351148, tc_fun(_1351146, tc_HOL_Obool), _1351150), _1351152)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1351148, tc_fun(_1351146, tc_HOL_Obool)), _1351152), _1351150))], (26952 ^ _780478) ^ [_1279844, _1279846, _1279848, _1279850, _1279852] : [class_Fields_Ofield(_1279844), -(_1279846 = c_Groups_Ozero__class_Ozero(_1279844)), -(_1279848 = c_Groups_Ozero__class_Ozero(_1279844)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1279844), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279844), _1279850), _1279846)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279844), _1279852), _1279848)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279844), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1279844), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279844), _1279850), _1279848)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279844), _1279852), _1279846))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279844), _1279846), _1279848)))], (254 ^ _780478) ^ [_784443, _784445] : [-(class_Fields_Ofield__inverse__zero(_784443)), _784445 = _784443, class_Fields_Ofield__inverse__zero(_784445)], (46044 ^ _780478) ^ [_1706110, _1706112, _1706114, _1706116] : [-(hAPP(c_List_Ofilter(_1706110, _1706112), c_List_Oremove1(_1706110, _1706114, _1706116)) = c_List_Oremove1(_1706110, _1706114, hAPP(c_List_Ofilter(_1706110, _1706112), _1706116)))], (51789 ^ _780478) ^ [_1827949, _1827951] : [class_Lattices_Odistrib__lattice(_1827949), -(class_Lattices_Odistrib__lattice(tc_fun(_1827951, _1827949)))], (48030 ^ _780478) ^ [_1748644, _1748646, _1748648] : [hBOOL(hAPP(hAPP(c_member(_1748644), _1748646), hAPP(c_List_Oset(_1748644), _1748648))), -(_1748648 = hAPP(hAPP(c_List_Oappend(_1748644), 48033 ^ [_1748644, _1748646, _1748648]), hAPP(hAPP(c_List_Olist_OCons(_1748644), _1748646), 48034 ^ [_1748644, _1748646, _1748648])))], (44125 ^ _780478) ^ [_1663593, _1663595, _1663597] : [hBOOL(hAPP(c_List_Odistinct(_1663593), hAPP(c_List_Orotate(_1663593, _1663595), _1663597))), -(hBOOL(hAPP(c_List_Odistinct(_1663593), _1663597)))], (35834 ^ _780478) ^ [_1460734] : [class_Rings_Osemiring__1(_1460734), -(hBOOL(hAPP(hAPP(c_member(_1460734), c_Groups_Ozero__class_Ozero(_1460734)), c_Nat_Osemiring__1__class_ONats(_1460734))))], (46300 ^ _780478) ^ [_1712425] : [-(c_List_Oupt(_1712425, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (13320 ^ _780478) ^ [_1017490, _1017492, _1017494] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1017490), _1017492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1017490, tc_HOL_Obool)), _1017494), _1017492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1017490), _1017494)), hAPP(c_Finite__Set_Ocard(_1017490), _1017492))))], (11421 ^ _780478) ^ [_980621, _980623, _980625] : [class_Orderings_Olinorder(_980621), hBOOL(hAPP(c_Finite__Set_Ofinite(_980621), _980623)), hBOOL(hAPP(hAPP(c_member(_980621), _980625), _980623)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_980621), _980625), c_Big__Operators_Olinorder__class_OMin(_980621, _980623)) = c_Big__Operators_Olinorder__class_OMin(_980621, _980623))], (3606 ^ _780478) ^ [_834410, _834412, _834414, _834416, _834418, _834420] : [-(c_List_Oremove1(_834420, _834416, _834412) = c_List_Oremove1(_834418, _834414, _834410)), _834420 = _834418, _834416 = _834414, _834412 = _834410], (50731 ^ _780478) ^ [_1806713, _1806715, _1806717] : [hBOOL(hAPP(c_Quotient_ORespects(_1806713, _1806715), _1806717)), -(hBOOL(hAPP(hAPP(_1806715, _1806717), _1806717)))], (29351 ^ _780478) ^ [_1325438, _1325440, _1325442, _1325444] : [class_Divides_Osemiring__div(_1325438), -(c_Divides_Odiv__class_Omod(_1325438, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325438), _1325440), _1325442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325438), _1325444), _1325442)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325438), c_Divides_Odiv__class_Omod(_1325438, _1325440, _1325444)), _1325442))], (33296 ^ _780478) ^ [_1409442, _1409444] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1409442), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409444)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409442)) = 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), _1409444), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1409442)))), 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)))], (44761 ^ _780478) ^ [_1676985, _1676987, _1676989, _1676991, _1676993] : [class_Groups_Oab__group__add(_1676985), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676985), hAPP(hAPP(c_List_Omap(_1676987, _1676985), hAPP(hAPP(c_COMBS(_1676987, _1676985, _1676985), hAPP(hAPP(c_COMBB(_1676985, tc_fun(_1676985, _1676985), _1676987), c_Groups_Ominus__class_Ominus(_1676985)), _1676989)), _1676991)), _1676993)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1676985), hAPP(c_List_Omonoid__add__class_Olistsum(_1676985), hAPP(hAPP(c_List_Omap(_1676987, _1676985), _1676989), _1676993))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676985), hAPP(hAPP(c_List_Omap(_1676987, _1676985), _1676991), _1676993))))], (34399 ^ _780478) ^ [_1429270, _1429272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429270), _1429272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1429270)), c_Int_OBit0(_1429272))))], (16234 ^ _780478) ^ [_1075082, _1075084, _1075086, _1075088] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075082, tc_HOL_Obool)), _1075084), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075082, tc_HOL_Obool)), _1075086), _1075088)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075082, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075082, tc_HOL_Obool)), _1075084), _1075086)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075082, tc_HOL_Obool)), _1075084), _1075088)))], (31795 ^ _780478) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (46200 ^ _780478) ^ [_1710353, _1710355, _1710357, _1710359, _1710361, _1710363] : [-(c_List_Ofoldr(_1710353, _1710355, _1710357, hAPP(hAPP(c_List_Olist_OCons(_1710353), _1710359), _1710361), _1710363) = hAPP(hAPP(_1710357, _1710359), c_List_Ofoldr(_1710353, _1710355, _1710357, _1710361, _1710363)))], (48143 ^ _780478) ^ [_1750958, _1750960, _1750962] : [-(hBOOL(hAPP(hAPP(c_member(_1750958), _1750960), hAPP(c_List_Oset(_1750958), _1750962)))), 48144 ^ _780478 : [(48145 ^ _780478) ^ [_1751047, _1751049] : [_1750962 = hAPP(hAPP(c_List_Oappend(_1750958), _1751049), hAPP(hAPP(c_List_Olist_OCons(_1750958), _1750960), _1751047)), -(hBOOL(hAPP(hAPP(c_member(_1750958), _1750960), hAPP(c_List_Oset(_1750958), _1751047))))]]], (31108 ^ _780478) ^ [_1359274, _1359276] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1359274))), -(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)), _1359274))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1359276)))) = 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)), _1359274))), 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, _1359276))))))], (30805 ^ _780478) ^ [_1352747] : [class_Complete__Lattice_Ocomplete__lattice(_1352747), -(c_Complete__Lattice_OSup__class_OSup(_1352747, c_Orderings_Obot__class_Obot(tc_fun(_1352747, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1352747))], (330 ^ _780478) ^ [_785465, _785467, _785469, _785471, _785473, _785475, _785477, _785479] : [-(c_Finite__Set_Ofolding(_785477, _785473, _785469, _785465)), c_Finite__Set_Ofolding(_785479, _785475, _785471, _785467), _785479 = _785477, _785475 = _785473, _785471 = _785469, _785467 = _785465], (40843 ^ _780478) ^ [_1580190, _1580192] : [c_Wellfounded_Oacyclic(_1580190, _1580192), -(c_Wellfounded_Oacyclic(_1580190, hAPP(c_Relation_Oconverse(_1580190, _1580190), _1580192)))], (33748 ^ _780478) ^ [_1417356, _1417358, _1417360, _1417362, _1417364] : [-(hAPP(c_Nat_Onat_Onat__rec(_1417356, _1417358, _1417360), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417362)), _1417364)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1417356), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417362))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417356, _1417356), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1417356, tc_fun(_1417356, _1417356)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417356, tc_fun(_1417356, _1417356)), tc_Int_Oint), c_If(_1417356)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1417356, _1417358, _1417360), _1417364))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417356, _1417356), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1417356, _1417356), tc_Int_Oint), _1417360), 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)), _1417364))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1417356, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1417356, _1417358, _1417360)), 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)), _1417364))))))], (40410 ^ _780478) ^ [_1570112, _1570114] : [-(hAPP(c_Relation_ODomain(_1570112, _1570112), c_Transitive__Closure_Otrancl(_1570112, _1570114)) = hAPP(c_Relation_ODomain(_1570112, _1570112), _1570114))], (19538 ^ _780478) ^ [_1145671] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1145671), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1145671)], (43213 ^ _780478) ^ [_1642152, _1642154, _1642156, _1642158] : [-(_1642152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1642154), _1642152), hAPP(hAPP(c_List_Olist_OCons(_1642154), _1642156), _1642158)) = hAPP(hAPP(c_List_Olist_OCons(_1642154), _1642156), hAPP(hAPP(c_List_Otake(_1642154), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1642152), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1642158)))], (52297 ^ _780478) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (13890 ^ _780478) ^ [_1028799, _1028801, _1028803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028801), _1028803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028799), _1028801)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028799), _1028803))))], (40883 ^ _780478) ^ [_1581213, _1581215, _1581217, _1581219, _1581221] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581215, _1581213)), hAPP(hAPP(c_Product__Type_OPair(_1581215, _1581213), _1581219), _1581217)), _1581221)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581213, _1581215)), hAPP(hAPP(c_Product__Type_OPair(_1581213, _1581215), _1581217), _1581219)), hAPP(c_Relation_Oconverse(_1581215, _1581213), _1581221))))], (23453 ^ _780478) ^ [_1216499, _1216501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216501), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1216499), _1216501)))], (18608 ^ _780478) ^ [_1129604, _1129606, _1129608, _1129610, _1129612] : [_1129604 = c_Orderings_Obot__class_Obot(tc_fun(_1129606, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1129606, tc_fun(_1129608, tc_HOL_Obool)), _1129604), hAPP(hAPP(c_COMBB(tc_fun(_1129608, tc_HOL_Obool), tc_fun(_1129608, tc_HOL_Obool), _1129606), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1129608, tc_HOL_Obool)), _1129610)), _1129612)) = c_Orderings_Otop__class_Otop(tc_fun(_1129608, tc_HOL_Obool)))], (11701 ^ _780478) ^ [_985706, _985708, _985710] : [class_Orderings_Olinorder(_985706), hBOOL(hAPP(c_Finite__Set_Ofinite(_985706), _985708)), -(hBOOL(hAPP(hAPP(c_member(_985706), _985710), _985708))), -(c_Big__Operators_Olinorder__class_OMin(_985706, hAPP(hAPP(c_Set_Oinsert(_985706), _985710), _985708)) = hAPP(hAPP(c_Finite__Set_Ofold(_985706, _985706, c_Orderings_Oord__class_Omin(_985706)), _985710), _985708))], (41664 ^ _780478) ^ [_1601609, _1601611, _1601613] : [-(c_Product__Type_Ointernal__split(_1601609, _1601611, _1601613) = c_Product__Type_Oprod_Oprod__case(_1601609, _1601611, _1601613))], (5955 ^ _780478) ^ [_875165, _875167, _875169] : [hBOOL(hAPP(hAPP(c_member(_875165), _875167), _875169)), -(hBOOL(hAPP(_875169, _875167)))], (37453 ^ _780478) ^ [_1494257, _1494259, _1494261, _1494263, _1494265, _1494267, _1494269, _1494271] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1494257, _1494259), tc_prod(_1494257, _1494259))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1494257, _1494259), tc_prod(_1494257, _1494259)), hAPP(hAPP(c_Product__Type_OPair(_1494257, _1494259), _1494261), _1494263)), hAPP(hAPP(c_Product__Type_OPair(_1494257, _1494259), _1494265), _1494267))), c_Wellfounded_Olex__prod(_1494257, _1494259, _1494269, _1494271))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494257, _1494257)), hAPP(hAPP(c_Product__Type_OPair(_1494257, _1494257), _1494261), _1494265)), _1494269))), 37460 ^ _780478 : [(37463 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494259, _1494259)), hAPP(hAPP(c_Product__Type_OPair(_1494259, _1494259), _1494263), _1494267)), _1494271)))], (37461 ^ _780478) ^ [] : [-(_1494261 = _1494265)]]], (38422 ^ _780478) ^ [_1518952, _1518954, _1518956, _1518958] : [c_FunDef_Oreduction__pair(_1518952, _1518954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518952, _1518952), tc_HOL_Obool)), _1518956), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1518952, _1518952), tc_HOL_Obool), tc_fun(tc_prod(_1518952, _1518952), tc_HOL_Obool)), _1518954))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1518952, _1518952), tc_HOL_Obool)), _1518958), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1518952, _1518952), tc_HOL_Obool), tc_fun(tc_prod(_1518952, _1518952), tc_HOL_Obool)), _1518954))), c_Wellfounded_Owf(_1518952, _1518958), -(c_Wellfounded_Owf(_1518952, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518952, _1518952), tc_HOL_Obool)), _1518956), _1518958)))], (35413 ^ _780478) ^ [_1447676] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1447676), hAPP(c_Int_Onumber__class_Onumber__of(_1447676), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1447676)), class_Int_Onumber__ring(_1447676), class_Rings_Olinordered__idom(_1447676)], (29325 ^ _780478) ^ [_1324919, _1324921, _1324923] : [class_Divides_Osemiring__div(_1324919), -(c_Divides_Odiv__class_Omod(_1324919, c_Divides_Odiv__class_Omod(_1324919, _1324921, _1324923), _1324923) = c_Divides_Odiv__class_Omod(_1324919, _1324921, _1324923))], (37233 ^ _780478) ^ [_1488904, _1488906, _1488908, _1488910, _1488912] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1488904, _1488906, _1488908), _1488910), _1488912) = hAPP(hAPP(_1488910, hAPP(c_Product__Type_Ofst(_1488904, _1488906), _1488912)), hAPP(c_Product__Type_Osnd(_1488904, _1488906), _1488912)))], (15165 ^ _780478) ^ [_1053511, _1053513, _1053515] : [class_Lattices_Olattice(_1053511), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053511), _1053513)), -(_1053515 = c_Orderings_Obot__class_Obot(tc_fun(_1053511, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1053511, tc_HOL_Obool)), _1053515), _1053513)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1053511), c_Big__Operators_Olattice__class_OSup__fin(_1053511, _1053515)), c_Big__Operators_Olattice__class_OSup__fin(_1053511, _1053513)) = c_Big__Operators_Olattice__class_OSup__fin(_1053511, _1053513))], (14337 ^ _780478) ^ [_1036460, _1036462, _1036464, _1036466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036460), _1036462)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036464), _1036462) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1036460), _1036466), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1036464), _1036466)))], (51919 ^ _780478) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (37465 ^ _780478) ^ [_1494582, _1494584, _1494586, _1494588, _1494590, _1494592, _1494594, _1494596] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1494582, _1494584), tc_prod(_1494582, _1494584))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1494582, _1494584), tc_prod(_1494582, _1494584)), hAPP(hAPP(c_Product__Type_OPair(_1494582, _1494584), _1494586), _1494588)), hAPP(hAPP(c_Product__Type_OPair(_1494582, _1494584), _1494590), _1494592))), c_Wellfounded_Olex__prod(_1494582, _1494584, _1494594, _1494596)))), 37466 ^ _780478 : [(37469 ^ _780478) ^ [] : [_1494586 = _1494590, hBOOL(hAPP(hAPP(c_member(tc_prod(_1494584, _1494584)), hAPP(hAPP(c_Product__Type_OPair(_1494584, _1494584), _1494588), _1494592)), _1494596))], (37467 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494582, _1494582)), hAPP(hAPP(c_Product__Type_OPair(_1494582, _1494582), _1494586), _1494590)), _1494594))]]], (3112 ^ _780478) ^ [_826691, _826693, _826695, _826697, _826699, _826701, _826703, _826705] : [-(c_Nat_Onat_Onat__case(_826705, _826701, _826697, _826693) = c_Nat_Onat_Onat__case(_826703, _826699, _826695, _826691)), _826705 = _826703, _826701 = _826699, _826697 = _826695, _826693 = _826691], (14435 ^ _780478) ^ [_1038030, _1038032, _1038034] : [14436 ^ _780478 : [(14439 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1038034, _1038032), _1038030))], (14437 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038030), _1038032)))]], 14442 ^ _780478 : [(14445 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1038034, _1038032), _1038030))], (14443 ^ _780478) ^ [] : [-(_1038030 = _1038032)]], 14448 ^ _780478 : [(14451 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1038034, _1038032), _1038030))], (14449 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1038032), _1038030)))]], -(hBOOL(hAPP(hAPP(_1038034, _1038032), _1038030)))], (40794 ^ _780478) ^ [_1579201, _1579203, _1579205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1579201), _1579203)), -(c_Random_Ominus__shift(_1579205, _1579201, _1579203) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1579205), _1579201)), _1579203))], (23385 ^ _780478) ^ [_1215378, _1215380, _1215382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215378), _1215380)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215380), _1215382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215378), _1215382)))], (51165 ^ _780478) ^ [_1817351, _1817353, _1817355] : [class_Divides_Osemiring__div(_1817351), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1817351), _1817353), _1817355)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1817351), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1817351), _1817355), _1817353)), _1817353) = _1817355)], (52247 ^ _780478) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52159 ^ _780478) ^ [_1831634, _1831636] : [-(class_Finite__Set_Ofinite(tc_sum(_1831634, _1831636))), class_Finite__Set_Ofinite(_1831634), class_Finite__Set_Ofinite(_1831636)], (39129 ^ _780478) ^ [_1539406, _1539408, _1539410, _1539412, _1539414, _1539416] : [hAPP(c_Set_Oimage(_1539406, _1539408, _1539410), c_Orderings_Otop__class_Otop(tc_fun(_1539406, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1539408, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1539412, _1539414, _1539416), c_Orderings_Otop__class_Otop(tc_fun(_1539412, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1539414, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1539406, _1539412), tc_prod(_1539408, _1539414), c_Product__Type_Omap__pair(_1539406, _1539408, _1539412, _1539414, _1539410, _1539416)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1539406, _1539412), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1539408, _1539414), tc_HOL_Obool)))], (38303 ^ _780478) ^ [_1516197, _1516199, _1516201, _1516203] : [c_Wellfounded_Owf(_1516197, _1516199), hBOOL(hAPP(hAPP(c_member(tc_prod(_1516197, _1516197)), hAPP(hAPP(c_Product__Type_OPair(_1516197, _1516197), _1516201), _1516203)), _1516199)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1516197, _1516197)), hAPP(hAPP(c_Product__Type_OPair(_1516197, _1516197), _1516203), _1516201)), _1516199))], (13152 ^ _780478) ^ [_1013731, _1013733, _1013735, _1013737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013731, tc_HOL_Obool)), _1013733), _1013735)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013731, tc_HOL_Obool)), _1013737), _1013735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013731, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013731, tc_HOL_Obool)), _1013733), _1013737)), _1013735)))], (26622 ^ _780478) ^ [_1273689, _1273691, _1273693] : [class_Fields_Olinordered__field(_1273689), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273689), _1273691), c_Groups_Ozero__class_Ozero(_1273689))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273689), c_Groups_Ozero__class_Ozero(_1273689)), _1273693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273689), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273689), _1273691), _1273693)), c_Groups_Ozero__class_Ozero(_1273689))))], (33370 ^ _780478) ^ [_1410558] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410558), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1410558)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1410558)))], (4786 ^ _780478) ^ [_853420, _853422, _853424, _853426, _853428, _853430, _853432, _853434] : [-(c_Random__Sequence_Obind(_853434, _853430, _853426, _853422) = c_Random__Sequence_Obind(_853432, _853428, _853424, _853420)), _853434 = _853432, _853430 = _853428, _853426 = _853424, _853422 = _853420], (24479 ^ _780478) ^ [_1235273, _1235275, _1235277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1235273), _1235275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235273), _1235277)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1235275), _1235277))))], (34597 ^ _780478) ^ [_1432797, _1432799] : [class_Int_Onumber__ring(_1432797), class_Int_Oring__char__0(_1432797), 34604 ^ _780478 : [(34611 ^ _780478) ^ [] : [c_Int_Oiszero(_1432797, hAPP(c_Int_Onumber__class_Onumber__of(_1432797), _1432799)), -(c_Int_Oiszero(_1432797, hAPP(c_Int_Onumber__class_Onumber__of(_1432797), c_Int_OBit0(_1432799))))], (34605 ^ _780478) ^ [] : [c_Int_Oiszero(_1432797, hAPP(c_Int_Onumber__class_Onumber__of(_1432797), c_Int_OBit0(_1432799))), -(c_Int_Oiszero(_1432797, hAPP(c_Int_Onumber__class_Onumber__of(_1432797), _1432799)))]]], (24071 ^ _780478) ^ [_1228105, _1228107, _1228109, _1228111] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1228105, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228105, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24072 ^ [_1228105, _1228107, _1228109, _1228111])), _1228107)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228105, 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), 24072 ^ [_1228105, _1228107, _1228109, _1228111]), _1228109))), _1228111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1228105, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228105, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1228107)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228105, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1228111))))], (8700 ^ _780478) ^ [_931051, _931053, _931055] : [class_Orderings_Olinorder(_931051), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931051), _931053), _931055))), -(_931053 = _931055), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931051), _931055), _931053)))], (6616 ^ _780478) ^ [_889018, _889020, _889022, _889024] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889018, tc_HOL_Obool)), _889020), hAPP(hAPP(c_Set_Oinsert(_889018), _889022), _889024)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889018, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889018, tc_HOL_Obool)), _889020), _889024)), hAPP(hAPP(c_Set_Oinsert(_889018), _889022), c_Orderings_Obot__class_Obot(tc_fun(_889018, tc_HOL_Obool)))))], (29075 ^ _780478) ^ [_1319852, _1319854] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1319852), hAPP(c_Nat_OSuc, _1319854)) = 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), _1319852), _1319854)))], (51947 ^ _780478) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (25737 ^ _780478) ^ [_1257948, _1257950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257950)), 25744 ^ _780478 : [(25751 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257948), _1257950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1257948)), hAPP(c_Int_Onat, _1257950))))], (25745 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1257948)), hAPP(c_Int_Onat, _1257950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257948), _1257950)))]]], (7042 ^ _780478) ^ [_898048, _898050, _898052, _898054, _898056] : [class_Orderings_Oord(_898048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898050, _898048)), _898052), _898054)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898048), hAPP(_898052, _898056)), hAPP(_898054, _898056))))], (45246 ^ _780478) ^ [_1687296, _1687298, _1687300, _1687302, _1687304] : [c_List_Opartition(_1687296, _1687298, _1687300) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1687296), tc_List_Olist(_1687296)), _1687302), _1687304), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1687296, tc_HOL_Obool)), hAPP(c_List_Oset(_1687296), _1687302)), hAPP(c_List_Oset(_1687296), _1687304)) = hAPP(c_List_Oset(_1687296), _1687300))], (42798 ^ _780478) ^ [_1633909, _1633911, _1633913, _1633915] : [hBOOL(hAPP(c_List_Odistinct(_1633909), _1633911)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1633909, _1633913)), hAPP(hAPP(c_List_Ozip(_1633909, _1633913), _1633911), _1633915))))], (46579 ^ _780478) ^ [_1717533, _1717535] : [class_Orderings_Olinorder(_1717533), c_List_Olinorder__class_Osorted(_1717533, _1717535), -(c_List_Olinorder__class_Osorted(_1717533, c_List_Oremdups(_1717533, _1717535)))], (16338 ^ _780478) ^ [_1077612, _1077614, _1077616, _1077618] : [-(hBOOL(hAPP(hAPP(c_member(_1077612), _1077614), _1077616))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077612, tc_HOL_Obool)), _1077616), hAPP(hAPP(c_Set_Oinsert(_1077612), _1077614), _1077618)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077612, tc_HOL_Obool)), _1077616), _1077618))], (6164 ^ _780478) ^ [_879014, _879016, _879018] : [c_Orderings_Obot__class_Obot(tc_fun(_879014, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_879014), _879016), _879018)], (28388 ^ _780478) ^ [] : [-(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)))], (34579 ^ _780478) ^ [_1432476, _1432478] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1432476))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1432478))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432476)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432478)))], (14733 ^ _780478) ^ [_1044149, _1044151, _1044153, _1044155] : [class_Groups_Ocomm__monoid__mult(_1044149), hBOOL(hAPP(c_Finite__Set_Ofinite(_1044151), _1044153)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1044151, _1044149), _1044155), _1044153) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1044149, _1044151, c_Groups_Otimes__class_Otimes(_1044149)), _1044155), c_Groups_Oone__class_Oone(_1044149)), _1044153))], (38519 ^ _780478) ^ [_1521210, _1521212] : [-(hAPP(c_Relation_ORange(_1521210, _1521210), c_Relation_OId__on(_1521210, _1521212)) = _1521212)], (36906 ^ _780478) ^ [_1482521, _1482523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1482523)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1482521, _1482523) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1482521, _1482523)))], (27529 ^ _780478) ^ [_1289437, _1289439, _1289441] : [class_Rings_Oring__1(_1289437), -(hAPP(c_Int_Oring__1__class_Oof__int(_1289437), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1289439), _1289441)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1289437), hAPP(c_Int_Oring__1__class_Oof__int(_1289437), _1289439)), hAPP(c_Int_Oring__1__class_Oof__int(_1289437), _1289441)))], (42810 ^ _780478) ^ [_1634169, _1634171, _1634173] : [hBOOL(hAPP(c_List_Odistinct(_1634169), hAPP(hAPP(c_List_Olist_OCons(_1634169), _1634171), _1634173))), 42813 ^ _780478 : [(42816 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1634169), _1634173)))], (42814 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1634169), _1634171), hAPP(c_List_Oset(_1634169), _1634173)))]]], (41023 ^ _780478) ^ [_1585371, _1585373] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585371, _1585371)), hAPP(hAPP(c_Product__Type_OPair(_1585371, _1585371), _1585373), _1585373)), c_Relation_OId(_1585371))))], (37439 ^ _780478) ^ [_1493903, _1493905, _1493907] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1493903, tc_HOL_Obool), tc_fun(_1493903, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1493903, tc_HOL_Obool), tc_fun(_1493903, tc_HOL_Obool)), _1493905), _1493907)), c_Wellfounded_Ofinite__psubset(_1493903)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1493903, tc_HOL_Obool)), _1493905), _1493907)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1493903), _1493907))], (45970 ^ _780478) ^ [_1703815, _1703817, _1703819] : [45972 ^ _780478 : [(45975 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1703815), tc_List_Olist(_1703815), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1703815), tc_fun(tc_List_Olist(_1703815), tc_Nat_Onat), tc_fun(tc_List_Olist(_1703815), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1703815), tc_Nat_Onat), tc_fun(tc_List_Olist(_1703815), tc_HOL_Obool)), tc_List_Olist(_1703815)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1703815))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1703815)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1703815))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1703815)))), 45971 ^ [_1703815, _1703817, _1703819]))], (45973 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1703815), tc_List_Olist(_1703815))), 45971 ^ [_1703815, _1703817, _1703819]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1703815), tc_List_Olist(_1703815))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1703815), tc_List_Olist(_1703815)), _1703817), _1703819)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1703815))), _1703817) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1703815))), _1703819), 45980 ^ _780478 : [(45987 ^ _780478) ^ [] : [_1703817 = _1703819, -(c_List_Oconcat(_1703815, _1703817) = c_List_Oconcat(_1703815, _1703819))], (45981 ^ _780478) ^ [] : [c_List_Oconcat(_1703815, _1703817) = c_List_Oconcat(_1703815, _1703819), -(_1703817 = _1703819)]]], (39203 ^ _780478) ^ [_1541503, _1541505, _1541507] : [c_Relation_Orefl__on(_1541503, _1541505, _1541507), 39206 ^ _780478 : [(39209 ^ _780478) ^ [_1541685] : [hBOOL(hAPP(hAPP(c_member(_1541503), _1541685), _1541505)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1541503, _1541503)), hAPP(hAPP(c_Product__Type_OPair(_1541503, _1541503), _1541685), _1541685)), _1541507)))], (39207 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541503, _1541503), tc_HOL_Obool)), _1541507), hAPP(hAPP(c_Product__Type_OSigma(_1541503, _1541503), _1541505), hAPP(c_COMBK(tc_fun(_1541503, tc_HOL_Obool), _1541503), _1541505)))))]]], (47332 ^ _780478) ^ [_1732999, _1733001, _1733003] : [-(hAPP(hAPP(c_List_Oappend(_1732999), c_List_OtakeWhile(_1732999, _1733001, _1733003)), c_List_OdropWhile(_1732999, _1733001, _1733003)) = _1733003)], (45043 ^ _780478) ^ [_1683245, _1683247, _1683249, _1683251] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683245)), _1683247) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683249)), _1683251), -(hAPP(hAPP(c_List_Omap(tc_prod(_1683245, _1683249), _1683249), c_Product__Type_Osnd(_1683245, _1683249)), hAPP(hAPP(c_List_Ozip(_1683245, _1683249), _1683247), _1683251)) = _1683251)], (41346 ^ _780478) ^ [_1593283, _1593285, _1593287, _1593289, _1593291] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593283, _1593283)), hAPP(hAPP(c_Product__Type_OPair(_1593283, _1593283), _1593285), _1593287)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1593283, _1593283), tc_HOL_Obool), _1593289), _1593291))), 41351 ^ _780478 : [(41354 ^ _780478) ^ [] : [-(_1593285 = _1593287)], (41352 ^ _780478) ^ [] : [-(_1593289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41357 ^ _780478 : [(41362 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593283, _1593283)), hAPP(hAPP(c_Product__Type_OPair(_1593283, _1593283), 41355 ^ [_1593283, _1593285, _1593287, _1593289, _1593291]), _1593287)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1593283, _1593283), tc_HOL_Obool), 41356 ^ [_1593283, _1593285, _1593287, _1593289, _1593291]), _1593291))))], (41360 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593283, _1593283)), hAPP(hAPP(c_Product__Type_OPair(_1593283, _1593283), _1593285), 41355 ^ [_1593283, _1593285, _1593287, _1593289, _1593291])), _1593291)))], (41358 ^ _780478) ^ [] : [-(_1593289 = hAPP(c_Nat_OSuc, 41356 ^ [_1593283, _1593285, _1593287, _1593289, _1593291]))]]], (42330 ^ _780478) ^ [_1621414, _1621416] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1621414), hAPP(c_List_Oset(_1621414), _1621416))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621414)), _1621416))))], (12892 ^ _780478) ^ [_1008917, _1008919, _1008921, _1008923] : [class_Lattices_Osemilattice__sup(_1008917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008917), _1008919), _1008921)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008917), _1008919), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1008917), _1008923), _1008921))))], (12976 ^ _780478) ^ [_1010410, _1010412, _1010414, _1010416] : [class_Lattices_Osemilattice__sup(_1010410), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010410), _1010412), _1010414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010410), _1010412), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010410), _1010414), _1010416))))], (18630 ^ _780478) ^ [_1130088, _1130090, _1130092, _1130094, _1130096] : [_1130088 = c_Orderings_Obot__class_Obot(tc_fun(_1130090, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130092, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130090, tc_fun(_1130092, tc_HOL_Obool)), _1130088), _1130094)), _1130096) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130092, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1130092, tc_HOL_Obool))), _1130096))], (9945 ^ _780478) ^ [_953238, _953240, _953242] : [class_Orderings_Olinorder(_953238), hBOOL(hAPP(c_Finite__Set_Ofinite(_953238), _953240)), hBOOL(hAPP(hAPP(c_member(_953238), _953242), _953240)), 9956 ^ _780478 : [(9963 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953238, tc_HOL_Obool)), _953240), hAPP(hAPP(c_Set_Oinsert(_953238), _953242), c_Orderings_Obot__class_Obot(tc_fun(_953238, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_953238, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_953238, _953240) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_953238), _953242), c_Big__Operators_Olinorder__class_OMin(_953238, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953238, tc_HOL_Obool)), _953240), hAPP(hAPP(c_Set_Oinsert(_953238), _953242), c_Orderings_Obot__class_Obot(tc_fun(_953238, tc_HOL_Obool)))))))], (9957 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_953238, tc_HOL_Obool)), _953240), hAPP(hAPP(c_Set_Oinsert(_953238), _953242), c_Orderings_Obot__class_Obot(tc_fun(_953238, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_953238, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_953238, _953240) = _953242)]]], (38319 ^ _780478) ^ [_1516529] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1516529)))], (6866 ^ _780478) ^ [_894098, _894100, _894102, _894104, _894106, _894108, _894110] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_894098, _894100, _894102, _894104, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894098, tc_HOL_Obool)), _894106), hAPP(hAPP(c_Set_Oinsert(_894098), _894108), c_Orderings_Obot__class_Obot(tc_fun(_894098, tc_HOL_Obool))))), _894110)), hBOOL(hAPP(hAPP(c_member(_894098), _894108), _894106)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_894098, _894100, _894102, _894104, _894106), hAPP(hAPP(_894102, _894108), _894110))))], (51951 ^ _780478) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (7649 ^ _780478) ^ [_909302, _909304, _909306, _909308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909302, tc_HOL_Obool)), _909304), _909306)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909302, tc_HOL_Obool)), _909304), hAPP(hAPP(c_Set_Oinsert(_909302), _909308), _909306))))], (17546 ^ _780478) ^ [_1106471, _1106473, _1106475, _1106477, _1106479] : [_1106471 = c_Orderings_Obot__class_Obot(tc_fun(_1106473, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106475, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106473, tc_fun(_1106475, tc_HOL_Obool)), _1106471), _1106477)), _1106479) = _1106479)], (19028 ^ _780478) ^ [_1137721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1137721)))], (43205 ^ _780478) ^ [_1641976] : [-(c_List_Olists(_1641976, c_Orderings_Obot__class_Obot(tc_fun(_1641976, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1641976)), c_List_Olist_ONil(_1641976)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1641976), tc_HOL_Obool))))], (12576 ^ _780478) ^ [_1002536, _1002538, _1002540] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002536, tc_HOL_Obool)), _1002538), _1002540) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002536, tc_HOL_Obool)), _1002540), _1002538))], (52071 ^ _780478) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (27984 ^ _780478) ^ [_1298052, _1298054] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1298052), _1298054) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1298052, _1298054))], (5450 ^ _780478) ^ [_863824, _863826] : [_863826 = _863824, -(c_Groups_Oplus__class_Oplus(_863826) = c_Groups_Oplus__class_Oplus(_863824))], (23569 ^ _780478) ^ [_1218493, _1218495, _1218497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218493), _1218495)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1218495), _1218497)) = 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, _1218493), _1218495)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1218495), _1218497))))], (12902 ^ _780478) ^ [_1009096, _1009098, _1009100] : [class_Lattices_Osemilattice__sup(_1009096), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009096), _1009098), _1009100)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1009096), _1009098), _1009100) = _1009100)], (5652 ^ _780478) ^ [_867007, _867009] : [_867009 = _867007, -(c_Finite__Set_Ofinite(_867009) = c_Finite__Set_Ofinite(_867007))], (34617 ^ _780478) ^ [_1433090] : [-(c_Int_Osucc(c_Int_OBit0(_1433090)) = c_Int_OBit1(_1433090))], (52085 ^ _780478) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (46318 ^ _780478) ^ [_1712769, _1712771] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1712769, _1712771))))], (44833 ^ _780478) ^ [_1678758, _1678760, _1678762, _1678764, _1678766] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1678758), tc_List_Olist(_1678760), tc_List_Olist(_1678762), hAPP(c_List_Omap(_1678758, _1678760), _1678764)), hAPP(c_List_Omap(_1678762, _1678758), _1678766)) = hAPP(c_List_Omap(_1678762, _1678760), hAPP(c_Fun_Ocomp(_1678758, _1678760, _1678762, _1678764), _1678766)))], (36748 ^ _780478) ^ [_1479394, _1479396, _1479398, _1479400, _1479402] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1479394, _1479396), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1479398), _1479400))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1479396)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479402), _1479394), _1479396), 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), _1479402), _1479398)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479402), _1479400)), _1479396))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1479402), _1479400), _1479396)))))], (1364 ^ _780478) ^ [_800392, _800394] : [-(class_Lattices_Obounded__lattice__top(_800392)), _800394 = _800392, class_Lattices_Obounded__lattice__top(_800394)], (50271 ^ _780478) ^ [_1797380, _1797382, _1797384, _1797386] : [c_Fun_Obij__betw(_1797380, _1797382, _1797384, c_Orderings_Otop__class_Otop(tc_fun(_1797380, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1797382, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1797380, _1797382, _1797384), hAPP(c_Set_OCollect(_1797380), _1797386)) = hAPP(c_Set_OCollect(_1797382), hAPP(hAPP(c_COMBB(_1797380, tc_HOL_Obool, _1797382), _1797386), c_Hilbert__Choice_Oinv__into(_1797380, _1797382, c_Orderings_Otop__class_Otop(tc_fun(_1797380, tc_HOL_Obool)), _1797384))))], (11017 ^ _780478) ^ [_972750, _972752, _972754] : [class_Rings_Oring(_972750), -(hAPP(c_Groups_Ouminus__class_Ouminus(_972750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972750), _972752), _972754)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_972750), hAPP(c_Groups_Ouminus__class_Ouminus(_972750), _972752)), _972754))], (29043 ^ _780478) ^ [_1318905] : [-(hAPP(c_Set_OPow(_1318905), c_Orderings_Otop__class_Otop(tc_fun(_1318905, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1318905, tc_HOL_Obool), tc_HOL_Obool)))], (49982 ^ _780478) ^ [_1790762, _1790764, _1790766] : [c_Fun_Oinj__on(_1790762, _1790764, _1790766, c_Orderings_Otop__class_Otop(tc_fun(_1790762, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1790764, _1790762, _1790762, c_Hilbert__Choice_Oinv__into(_1790762, _1790764, c_Orderings_Otop__class_Otop(tc_fun(_1790762, tc_HOL_Obool)), _1790766)), _1790766) = c_Fun_Oid(_1790762))], (42618 ^ _780478) ^ [_1629740, _1629742, _1629744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1629740), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1629742))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1629742), _1629740), _1629744)) = 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), _1629742)), _1629744)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1629742), _1629740)))], (51493 ^ _780478) ^ [_1823151, _1823153] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823151, _1823153) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823151), _1823153))], (33208 ^ _780478) ^ [_1407878, _1407880] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407878)))), 33211 ^ _780478 : [(33218 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407880)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407878), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407880)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407878), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407880))))], (33212 ^ _780478) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1407880))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407878), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407880)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407878))]]], (31803 ^ _780478) ^ [_1381237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1381237)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1381237))], (49533 ^ _780478) ^ [_1782317, _1782319, _1782321, _1782323] : [-(c_Wellfounded_Omax__extp(_1782317, _1782319, _1782321, _1782323)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1782317), _1782321)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1782317), _1782323)), -(_1782323 = c_Orderings_Obot__class_Obot(tc_fun(_1782317, tc_HOL_Obool))), 49547 ^ _780478 : [(49550 ^ _780478) ^ [_1782662] : [hBOOL(hAPP(hAPP(c_member(_1782317), _1782662), _1782323)), hBOOL(hAPP(hAPP(_1782319, 49546 ^ [_1782317, _1782319, _1782321, _1782323]), _1782662))], (49548 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1782317), 49546 ^ [_1782317, _1782319, _1782321, _1782323]), _1782321)))]]], (21133 ^ _780478) ^ [_1173260, _1173262] : [-(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), _1173260), _1173262)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173262))], (22859 ^ _780478) ^ [_1205950, _1205952, _1205954] : [class_Rings_Olinordered__semidom(_1205950), 22862 ^ _780478 : [(22869 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205952), _1205954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205950), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205950), _1205952)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205950), _1205954))))], (22863 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205950), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205950), _1205952)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205950), _1205954))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1205952), _1205954)))]]], (35351 ^ _780478) ^ [_1446771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1446771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1446771)))], (29604 ^ _780478) ^ [_1330179, _1330181] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1330179), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1330181), _1330179)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1330181), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330181, _1330179)))], (25835 ^ _780478) ^ [_1259441, _1259443] : [hBOOL(hAPP(_1259441, hAPP(c_Int_Onat, _1259443))), 25838 ^ _780478 : [(25845 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1259443), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1259441, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25839 ^ _780478) ^ [_1259541] : [_1259443 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1259541), -(hBOOL(hAPP(_1259441, _1259541)))]]], (41744 ^ _780478) ^ [_1604163, _1604165, _1604167, _1604169, _1604171, _1604173] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604163), tc_List_Olist(_1604163))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604163), tc_List_Olist(_1604163)), hAPP(hAPP(c_List_Olist_OCons(_1604163), _1604165), _1604167)), hAPP(hAPP(c_List_Olist_OCons(_1604163), _1604169), _1604171))), c_List_Olex(_1604163, _1604173))), 41749 ^ _780478 : [(41752 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604163)), _1604167) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1604163)), _1604171))], (41750 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604163, _1604163)), hAPP(hAPP(c_Product__Type_OPair(_1604163, _1604163), _1604165), _1604169)), _1604173)))]], 41753 ^ _780478 : [(41756 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604163), tc_List_Olist(_1604163))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604163), tc_List_Olist(_1604163)), _1604167), _1604171)), c_List_Olex(_1604163, _1604173))))], (41754 ^ _780478) ^ [] : [-(_1604165 = _1604169)]]], (4434 ^ _780478) ^ [_847712, _847714, _847716, _847718] : [-(c_Wellfounded_Oaccp(_847718, _847714) = c_Wellfounded_Oaccp(_847716, _847712)), _847718 = _847716, _847714 = _847712], (35589 ^ _780478) ^ [_1450511, _1450513] : [-(c_Divides_Odivmod__int__rel(_1450511, _1450513) = 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, _1450511))), 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), _1450513)))))), 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)), _1450513))), 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)), _1450513))))), 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)), _1450513)))), 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), _1450513))), 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))))))))], (42083 ^ _780478) ^ [_1615045, _1615047, _1615049] : [c_Equiv__Relations_Oequiv(_1615045, _1615047, _1615049), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1615045), c_List_Olists(_1615045, _1615047), c_List_Olistrel(_1615045, _1615049)))], (32980 ^ _780478) ^ [_1403603, _1403605, _1403607, _1403609] : [c_Equiv__Relations_Oequiv(_1403603, _1403605, _1403607), hBOOL(hAPP(hAPP(c_member(_1403603), _1403609), _1403605)), -(hBOOL(hAPP(hAPP(c_member(_1403603), _1403609), hAPP(c_Relation_OImage(_1403603, _1403603, _1403607), hAPP(hAPP(c_Set_Oinsert(_1403603), _1403609), c_Orderings_Obot__class_Obot(tc_fun(_1403603, tc_HOL_Obool)))))))], (51199 ^ _780478) ^ [_1818062, _1818064, _1818066] : [class_Rings_Ocomm__semiring__1(_1818062), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818062), _1818064), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1818062), _1818064), _1818066))))], (31785 ^ _780478) ^ [_1381000] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1381000)))], (11869 ^ _780478) ^ [_989089, _989091] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_989089, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_989089, tc_HOL_Obool)), _989091)) = _989091)], (6484 ^ _780478) ^ [_886194, _886196, _886198, _886200, _886202, _886204, _886206, _886208] : [c_Finite__Set_Ofolding__image__simple__idem(_886194, _886196, _886198, _886200, _886202, _886204), hBOOL(hAPP(c_Finite__Set_Ofinite(_886196), _886206)), hBOOL(hAPP(hAPP(c_member(_886196), _886208), _886206)), -(hAPP(hAPP(_886198, hAPP(_886202, _886208)), hAPP(_886204, _886206)) = hAPP(_886204, _886206))], (36090 ^ _780478) ^ [_1466404, _1466406, _1466408, _1466410, _1466412] : [c_Equiv__Relations_Oequiv(_1466404, _1466406, _1466408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466404, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1466404, _1466404, _1466408), hAPP(hAPP(c_Set_Oinsert(_1466404), _1466410), c_Orderings_Obot__class_Obot(tc_fun(_1466404, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1466404, _1466404, _1466408), hAPP(hAPP(c_Set_Oinsert(_1466404), _1466412), c_Orderings_Obot__class_Obot(tc_fun(_1466404, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1466404), _1466410), _1466406)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1466404, _1466404)), hAPP(hAPP(c_Product__Type_OPair(_1466404, _1466404), _1466412), _1466410)), _1466408)))], (38482 ^ _780478) ^ [_1520482, _1520484] : [c_Wellfounded_Owf(_1520482, _1520484), -(c_Wellfounded_Owf(tc_List_Olist(_1520482), c_List_Olex(_1520482, _1520484)))], (13496 ^ _780478) ^ [_1021148] : [class_Lattices_Oboolean__algebra(_1021148), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1021148), c_Orderings_Otop__class_Otop(_1021148)) = c_Orderings_Obot__class_Obot(_1021148))], (45692 ^ _780478) ^ [_1697956, _1697958, _1697960, _1697962] : [45694 ^ _780478 : [(45697 ^ _780478) ^ [] : [hBOOL(hAPP(_1697960, hAPP(hAPP(c_List_Onth(_1697956), _1697958), 45693 ^ [_1697956, _1697958, _1697960, _1697962])))], (45695 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45693 ^ [_1697956, _1697958, _1697960, _1697962]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697956)), _1697958))))]], hBOOL(hAPP(hAPP(c_member(_1697956), _1697962), hAPP(c_List_Oset(_1697956), _1697958))), -(hBOOL(hAPP(_1697960, _1697962)))], (2742 ^ _780478) ^ [_820988, _820990, _820992, _820994, _820996, _820998] : [-(c_Com_Ocom_OCond(_820998, _820994, _820990) = c_Com_Ocom_OCond(_820996, _820992, _820988)), _820998 = _820996, _820994 = _820992, _820990 = _820988], (19630 ^ _780478) ^ [_1147029, _1147031, _1147033] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147029), _1147031) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1147033), _1147031), -(_1147029 = _1147033), -(_1147031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40209 ^ _780478) ^ [_1565119, _1565121, _1565123, _1565125, _1565127, _1565129, _1565131, _1565133] : [class_Groups_Ocomm__monoid__mult(_1565119), c_Fun_Oinj__on(_1565121, _1565123, _1565125, _1565127), _1565129 = hAPP(c_Set_Oimage(_1565121, _1565123, _1565125), _1565127), 40223 ^ _780478 : [(40226 ^ _780478) ^ [] : [hAPP(_1565131, 40222 ^ [_1565119, _1565121, _1565123, _1565125, _1565127, _1565129, _1565131, _1565133]) = hAPP(hAPP(c_Fun_Ocomp(_1565123, _1565119, _1565121, _1565133), _1565125), 40222 ^ [_1565119, _1565121, _1565123, _1565125, _1565127, _1565129, _1565131, _1565133])], (40224 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1565121), 40222 ^ [_1565119, _1565121, _1565123, _1565125, _1565127, _1565129, _1565131, _1565133]), _1565127)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1565123, _1565119), _1565133), _1565129) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1565121, _1565119), _1565131), _1565127))], (16176 ^ _780478) ^ [_1073456, _1073458, _1073460] : [-(hAPP(c_Set_Ovimage(_1073456, _1073458, _1073460), c_Orderings_Otop__class_Otop(tc_fun(_1073458, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1073456, tc_HOL_Obool)))], (15918 ^ _780478) ^ [_1068429, _1068431, _1068433, _1068435] : [class_Lattices_Osemilattice__inf(_1068429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068429), _1068431), _1068433)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068429), _1068431), _1068435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068429), _1068431), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1068429), _1068433), _1068435))))], (45905 ^ _780478) ^ [_1702061, _1702063] : [45907 ^ _780478 : [(45910 ^ _780478) ^ [] : [45906 ^ [_1702061, _1702063] = c_List_Olist_ONil(_1702061)], (45908 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1702061)), 45906 ^ [_1702061, _1702063]), hAPP(c_List_Oset(tc_List_Olist(_1702061)), _1702063))))]], -(c_List_Oconcat(_1702061, _1702063) = c_List_Olist_ONil(_1702061))], (3536 ^ _780478) ^ [_833265, _833267, _833269, _833271, _833273, _833275] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_833275, _833271, _833267) = c_SetInterval_Oord__class_OgreaterThanLessThan(_833273, _833269, _833265)), _833275 = _833273, _833271 = _833269, _833267 = _833265], (13837 ^ _780478) ^ [_1027921, _1027923] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1027921), _1027923))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1027923), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1027921), _1027923)) = _1027921)], (45276 ^ _780478) ^ [_1688022, _1688024, _1688026] : [45278 ^ _780478 : [(45281 ^ _780478) ^ [] : [hBOOL(hAPP(_1688024, 45277 ^ [_1688022, _1688024, _1688026]))], (45279 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1688022), 45277 ^ [_1688022, _1688024, _1688026]), hAPP(c_List_Oset(_1688022), _1688026))))]], -(hBOOL(hAPP(c_List_Olistsp(_1688022, _1688024), _1688026)))], (33350 ^ _780478) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (52319 ^ _780478) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (38178 ^ _780478) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (10335 ^ _780478) ^ [_960780, _960782, _960784] : [class_Orderings_Olinorder(_960780), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_960780), _960782), _960784) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_960780), _960784), _960782))], (41457 ^ _780478) ^ [_1596545, _1596547, _1596549, _1596551] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596545, _1596545)), hAPP(hAPP(c_Product__Type_OPair(_1596545, _1596545), _1596547), _1596549)), c_Transitive__Closure_Otrancl(_1596545, _1596551))), 41461 ^ _780478 : [(41464 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596545, _1596545)), hAPP(hAPP(c_Product__Type_OPair(_1596545, _1596545), 41460 ^ [_1596545, _1596547, _1596549, _1596551]), _1596549)), c_Transitive__Closure_Ortrancl(_1596545, _1596551))))], (41462 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596545, _1596545)), hAPP(hAPP(c_Product__Type_OPair(_1596545, _1596545), _1596547), 41460 ^ [_1596545, _1596547, _1596549, _1596551])), _1596551)))]]], (21876 ^ _780478) ^ [_1186636, _1186638, _1186640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186636), _1186638)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1186640), _1186638))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1186638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1186636), _1186640)))], (34715 ^ _780478) ^ [_1435088, _1435090] : [class_Int_Onumber__ring(_1435088), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1435088), hAPP(c_Int_Onumber__class_Onumber__of(_1435088), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1435090) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1435088), _1435090), _1435090))], (30691 ^ _780478) ^ [_1350423, _1350425, _1350427] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350423, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1350423, tc_HOL_Obool), tc_HOL_Obool)), _1350425), _1350427)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350423, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350423, tc_HOL_Obool), _1350425)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350423, tc_HOL_Obool), _1350427)))], (35293 ^ _780478) ^ [_1445832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1445832), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1445832)), c_Int_OMin)))], (4532 ^ _780478) ^ [_849285, _849287, _849289, _849291, _849293, _849295, _849297, _849299, _849301, _849303] : [-(c_Nitpick_Opair__box_Opair__box__case(_849303, _849299, _849295, _849291, _849287) = c_Nitpick_Opair__box_Opair__box__case(_849301, _849297, _849293, _849289, _849285)), _849303 = _849301, _849299 = _849297, _849295 = _849293, _849291 = _849289, _849287 = _849285], (33680 ^ _780478) ^ [_1415677, _1415679, _1415681, _1415683] : [-(c_Nat_Onat_Onat__case(_1415677, _1415679, _1415681, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415683)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1415677), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415683))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1415677, _1415677), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1415677, tc_fun(_1415677, _1415677)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1415677, tc_fun(_1415677, _1415677)), tc_Int_Oint), c_If(_1415677)), c_Nat__Numeral_Oneg)), _1415679)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1415677, tc_Int_Oint), _1415681), c_Int_Onat))))], (48399 ^ _780478) ^ [_1755981, _1755983, _1755985, _1755987, _1755989] : [-(_1755981 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1755983, _1755985, _1755987, _1755989), _1755981) = hAPP(c_Lazy__Sequence_Obind(_1755983, _1755985, hAPP(_1755987, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1755981), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1755983, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1755985)), _1755989), _1755981)))], (36162 ^ _780478) ^ [_1468042, _1468044] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1468042), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36165 ^ _780478 : [(36174 ^ _780478) ^ [] : [-(c_Nitpick_Onorm__frac(_1468044, _1468042) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1468044), _1468042)), 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), _1468044))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1468042)))), -(_1468044 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1468042 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36166 ^ _780478) ^ [] : [36167 ^ _780478 : [(36170 ^ _780478) ^ [] : [_1468042 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36168 ^ _780478) ^ [] : [_1468044 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1468044, _1468042) = 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)))]]], (28516 ^ _780478) ^ [_1308347, _1308349, _1308351] : [class_Orderings_Oorder(_1308347), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308347, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1308347, _1308349, _1308351)), hAPP(c_SetInterval_Oord__class_OatLeast(_1308347), _1308351)) = c_Orderings_Obot__class_Obot(tc_fun(_1308347, tc_HOL_Obool)))], (16208 ^ _780478) ^ [_1074206, _1074208, _1074210, _1074212, _1074214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1074206, tc_HOL_Obool)), _1074208), _1074210)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1074206, tc_HOL_Obool)), _1074212), _1074214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1074206, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074206, tc_HOL_Obool)), _1074208), _1074212)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074206, tc_HOL_Obool)), _1074210), _1074214))))], (48423 ^ _780478) ^ [_1756715, _1756717, _1756719, _1756721, _1756723, _1756725, _1756727] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1756715, _1756717, _1756719, _1756721), _1756723), _1756725), _1756727) = c_New__DSequence_Opos__bind(_1756715, _1756717, hAPP(hAPP(hAPP(_1756719, _1756723), _1756725), _1756727), hAPP(hAPP(c_COMBC(_1756715, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1756717))), hAPP(hAPP(c_COMBC(_1756715, 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(_1756717)))), hAPP(hAPP(c_COMBC(_1756715, 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(_1756717))))), _1756721), _1756723)), _1756725)), _1756727)))], (15793 ^ _780478) ^ [_1066210, _1066212, _1066214, _1066216] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1066210), _1066212)), 15796 ^ _780478 : [(15797 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1066214), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1066210, tc_fun(_1066214, tc_HOL_Obool)), _1066212), _1066216))), 15800 ^ _780478 : [(15801 ^ _780478) ^ [_1066394] : [hBOOL(hAPP(hAPP(c_member(_1066210), _1066394), _1066212)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1066214), hAPP(_1066216, _1066394))))]]], (15807 ^ _780478) ^ [] : [15809 ^ _780478 : [(15812 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1066214), hAPP(_1066216, 15808 ^ [_1066210, _1066212, _1066214, _1066216])))], (15810 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1066210), 15808 ^ [_1066210, _1066212, _1066214, _1066216]), _1066212)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1066214), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1066210, tc_fun(_1066214, tc_HOL_Obool)), _1066212), _1066216))))]]], (39851 ^ _780478) ^ [_1556813, _1556815, _1556817, _1556819, _1556821] : [class_Groups_Ocomm__monoid__mult(_1556813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556815), _1556817)), c_Fun_Oinj__on(_1556815, _1556815, _1556819, _1556817), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1556815, _1556813), _1556821), hAPP(c_Set_Oimage(_1556815, _1556815, _1556819), _1556817)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1556815, _1556813), hAPP(c_Fun_Ocomp(_1556815, _1556813, _1556815, _1556821), _1556819)), _1556817))], (29035 ^ _780478) ^ [_1318678, _1318680, _1318682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318678, tc_HOL_Obool)), _1318680), _1318682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1318678, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1318678), _1318680)), hAPP(c_Set_OPow(_1318678), _1318682))))], (4900 ^ _780478) ^ [_855179, _855181, _855183, _855185] : [-(c_Complete__Lattice_OInf__class_OInf(_855185, _855181) = c_Complete__Lattice_OInf__class_OInf(_855183, _855179)), _855185 = _855183, _855181 = _855179], (2200 ^ _780478) ^ [_812635, _812637, _812639, _812641] : [-(c_Int_Onat__aux(_812641, _812637) = c_Int_Onat__aux(_812639, _812635)), _812641 = _812639, _812637 = _812635], (33352 ^ _780478) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18035 ^ _780478) ^ [_1116152, _1116154] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1116152)), hAPP(c_Nat_OSuc, _1116154)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116152), _1116154))], (40023 ^ _780478) ^ [_1560853, _1560855, _1560857, _1560859] : [c_Finite__Set_Ofolding(_1560853, _1560855, _1560857, _1560859), -(hAPP(_1560859, c_Orderings_Obot__class_Obot(tc_fun(_1560853, tc_HOL_Obool))) = c_Fun_Oid(_1560855))], (49088 ^ _780478) ^ [_1771365, _1771367, _1771369] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1771365), _1771367, _1771369)), -(c_List_Olist__ex(tc_Int_Oint, _1771365, c_List_Oupto(_1771367, _1771369)))], (43903 ^ _780478) ^ [_1658560, _1658562, _1658564, _1658566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1658560), _1658562)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1658564, tc_HOL_Obool)), hAPP(c_List_Oset(_1658564), hAPP(hAPP(c_List_Odrop(_1658564), _1658562), _1658566))), hAPP(c_List_Oset(_1658564), hAPP(hAPP(c_List_Odrop(_1658564), _1658560), _1658566)))))], (42961 ^ _780478) ^ [_1637571, _1637573, _1637575] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637571), tc_List_Olist(_1637571))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637571), tc_List_Olist(_1637571)), _1637573), c_List_Olist_ONil(_1637571))), c_List_Olistrel(_1637571, _1637575))), -(_1637573 = c_List_Olist_ONil(_1637571))], (48123 ^ _780478) ^ [_1750402, _1750404, _1750406] : [-(hBOOL(hAPP(hAPP(c_member(_1750402), _1750404), hAPP(c_List_Oset(_1750402), _1750406)))), 48124 ^ _780478 : [(48125 ^ _780478) ^ [_1750491] : [48126 ^ _780478 : [(48127 ^ _780478) ^ [_1750564] : [_1750406 = hAPP(hAPP(c_List_Oappend(_1750402), _1750491), hAPP(hAPP(c_List_Olist_OCons(_1750402), _1750404), _1750564))]], -(hBOOL(hAPP(hAPP(c_member(_1750402), _1750404), hAPP(c_List_Oset(_1750402), _1750491))))]]], (39510 ^ _780478) ^ [_1548173] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1548173, tc_HOL_Obool) = c_Set_OBall(_1548173))], (20604 ^ _780478) ^ [_1164692] : [class_Rings_Olinordered__semidom(_1164692), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164692), c_Groups_Ozero__class_Ozero(_1164692)), c_Groups_Oone__class_Oone(_1164692))))], (48800 ^ _780478) ^ [_1764791, _1764793, _1764795, _1764797, _1764799] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1764791, _1764793, _1764795) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1764791, _1764797, _1764799), 48803 ^ _780478 : [(48806 ^ _780478) ^ [] : [-(_1764795 = _1764799)], (48804 ^ _780478) ^ [] : [-(_1764793 = _1764797)]]], (47460 ^ _780478) ^ [_1735729, _1735731, _1735733] : [47462 ^ _780478 : [(47465 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1735731, 47461 ^ [_1735729, _1735731, _1735733])))], (47463 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735729), 47461 ^ [_1735729, _1735731, _1735733]), hAPP(c_List_Oset(_1735729), c_List_OdropWhile(_1735729, _1735731, _1735733)))))]], -(c_List_OtakeWhile(_1735729, _1735731, _1735733) = hAPP(c_List_Ofilter(_1735729, _1735731), _1735733))], (36222 ^ _780478) ^ [_1469137, _1469139, _1469141, _1469143, _1469145, _1469147, _1469149] : [hBOOL(hAPP(hAPP(c_member(_1469137), _1469139), hAPP(hAPP(_1469141, _1469143), _1469145))), -(hBOOL(hAPP(hAPP(c_member(_1469137), _1469139), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1469147, _1469149, tc_fun(_1469137, tc_HOL_Obool)), _1469141), hAPP(hAPP(c_Product__Type_OPair(_1469147, _1469149), _1469143), _1469145)))))], (14002 ^ _780478) ^ [_1030850, _1030852, _1030854] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030850), _1030852) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1030850), _1030854), -(_1030852 = _1030854)], (14521 ^ _780478) ^ [_1039959, _1039961, _1039963] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039959), _1039961)), _1039963) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039959), _1039963)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1039961), _1039963)))], (43616 ^ _780478) ^ [_1651157, _1651159, _1651161] : [_1651157 = _1651159, -(_1651157 = hAPP(hAPP(c_List_Oappend(_1651161), c_List_Olist_ONil(_1651161)), _1651159))], (36698 ^ _780478) ^ [_1478112, _1478114] : [-(_1478112 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36701 ^ _780478 : [(36708 ^ _780478) ^ [] : [-(_1478114 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1478112, _1478114) = 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, _1478114))), 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, _1478112)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1478114))), c_Divides_Opdivmod(_1478112, _1478114)), 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), _1478114))))), c_Divides_Opdivmod(_1478112, _1478114)))))], (36702 ^ _780478) ^ [] : [_1478114 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1478112, _1478114) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1478112))]]], (21025 ^ _780478) ^ [_1171622, _1171624] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1171622), _1171624) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 21026 ^ _780478 : [(21033 ^ _780478) ^ [] : [_1171622 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1171624 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21027 ^ _780478) ^ [] : [_1171622 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1171624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (20100 ^ _780478) ^ [_1155378, _1155380, _1155382, _1155384] : [class_Rings_Oordered__ring(_1155378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155378), _1155380), _1155382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155378), _1155384), c_Groups_Ozero__class_Ozero(_1155378))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155378), _1155384), _1155382)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155378), _1155384), _1155380))))], (31821 ^ _780478) ^ [_1381511] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1381511)), -(hAPP(c_Int_Onat, _1381511) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31087 ^ _780478) ^ [_1358777, _1358779, _1358781, _1358783, _1358785, _1358787, _1358789, _1358791] : [c_Finite__Set_Ofolding__image__simple(_1358777, _1358779, _1358781, _1358783, _1358785, _1358787), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358779), _1358789)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358779), _1358791)), 31101 ^ _780478 : [(31104 ^ _780478) ^ [] : [hAPP(_1358785, 31100 ^ [_1358777, _1358779, _1358781, _1358783, _1358785, _1358787, _1358789, _1358791]) = _1358783], (31102 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358779), 31100 ^ [_1358777, _1358779, _1358781, _1358783, _1358785, _1358787, _1358789, _1358791]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1358779, tc_HOL_Obool)), _1358789), _1358791))))]], -(hAPP(_1358787, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1358779, tc_HOL_Obool)), _1358789), _1358791)) = hAPP(hAPP(_1358781, hAPP(_1358787, _1358789)), hAPP(_1358787, _1358791)))], (19558 ^ _780478) ^ [_1145957] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1145957), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1145957)], (23447 ^ _780478) ^ [_1216399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1216399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1216399)))], (51455 ^ _780478) ^ [_1822538, _1822540] : [51456 ^ _780478 : [(51459 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822540), _1822538))], (51457 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822538), _1822540)))]], -(c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1822538, _1822540) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (4322 ^ _780478) ^ [_845848, _845850, _845852, _845854, _845856, _845858, _845860, _845862, _845864, _845866] : [-(c_Predicate_Opred__comp(_845866, _845862, _845858, _845854, _845850) = c_Predicate_Opred__comp(_845864, _845860, _845856, _845852, _845848)), _845866 = _845864, _845862 = _845860, _845858 = _845856, _845854 = _845852, _845850 = _845848], (30679 ^ _780478) ^ [_1350160, _1350162, _1350164] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350160, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1350160, tc_HOL_Obool)), _1350162), _1350164)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1350160, tc_HOL_Obool)), _1350162), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1350160, tc_HOL_Obool), _1350164)))], (49076 ^ _780478) ^ [_1771166, _1771168, _1771170] : [c_List_Oall__interval__int(_1771166, _1771168, _1771170), -(c_List_Olist__all(tc_Int_Oint, _1771166, c_List_Oupto(_1771168, _1771170)))], (14249 ^ _780478) ^ [_1035158, _1035160, _1035162, _1035164] : [class_Groups_Ocomm__monoid__mult(_1035158), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035160), _1035162))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1035160, _1035158), _1035164), _1035162) = c_Groups_Oone__class_Oone(_1035158))], (50331 ^ _780478) ^ [_1798868, _1798870, _1798872, _1798874, _1798876, _1798878, _1798880, _1798882] : [c_Fun_Obij__betw(_1798868, _1798870, _1798872, _1798874, _1798876), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1798868, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1798878, _1798868, _1798880), _1798882)), _1798874)), 50338 ^ _780478 : [(50345 ^ _780478) ^ [] : [c_Fun_Obij__betw(_1798878, _1798870, hAPP(c_Fun_Ocomp(_1798868, _1798870, _1798878, _1798872), _1798880), _1798882, _1798876), -(c_Fun_Obij__betw(_1798878, _1798868, _1798880, _1798882, _1798874))], (50339 ^ _780478) ^ [] : [c_Fun_Obij__betw(_1798878, _1798868, _1798880, _1798882, _1798874), -(c_Fun_Obij__betw(_1798878, _1798870, hAPP(c_Fun_Ocomp(_1798868, _1798870, _1798878, _1798872), _1798880), _1798882, _1798876))]]], (36234 ^ _780478) ^ [_1469437, _1469439, _1469441, _1469443, _1469445] : [hBOOL(hAPP(hAPP(_1469437, _1469439), _1469441)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1469443, _1469445, tc_HOL_Obool), _1469437), hAPP(hAPP(c_Product__Type_OPair(_1469443, _1469445), _1469439), _1469441))))], (22594 ^ _780478) ^ [_1201222, _1201224, _1201226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1201222), _1201224)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201226), _1201222)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1201226), _1201224))))], (19556 ^ _780478) ^ [_1145931] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145931) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14749 ^ _780478) ^ [_1044521, _1044523, _1044525] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044521), _1044523)), hBOOL(hAPP(hAPP(c_member(_1044521), _1044525), _1044523)), -(hAPP(c_Finite__Set_Ocard(_1044521), _1044523) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1044521), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1044521, tc_HOL_Obool)), _1044523), hAPP(hAPP(c_Set_Oinsert(_1044521), _1044525), c_Orderings_Obot__class_Obot(tc_fun(_1044521, tc_HOL_Obool)))))))], (23201 ^ _780478) ^ [_1212340] : [-(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), _1212340))))], (44472 ^ _780478) ^ [_1670944, _1670946, _1670948] : [class_Orderings_Olinorder(_1670944), -(hBOOL(hAPP(hAPP(c_member(_1670944), _1670946), hAPP(c_List_Oset(_1670944), _1670948)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1670944, _1670944, c_COMBI(_1670944), _1670946, _1670948) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1670944, _1670944, c_COMBI(_1670944)), _1670946), _1670948))], (51419 ^ _780478) ^ [_1821890, _1821892] : [51420 ^ _780478 : [(51423 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821892), _1821890))], (51421 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821890), _1821892)))]], -(c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821890, _1821892))], (43897 ^ _780478) ^ [_1658463, _1658465] : [_1658465 = c_List_Olist_ONil(_1658463), -(hAPP(c_List_Orotate1(_1658463), _1658465) = c_List_Olist_ONil(_1658463))], (37790 ^ _780478) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (23155 ^ _780478) ^ [_1211529, _1211531] : [23156 ^ _780478 : [(23157 ^ _780478) ^ [_1211582] : [_1211531 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1211529), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211582))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211529), _1211531)))], (38210 ^ _780478) ^ [_1514531, _1514533] : [c_Wellfounded_Owf(_1514531, _1514533), -(c_Wellfounded_Owf(_1514531, hAPP(hAPP(c_Relation_Orel__comp(_1514531, _1514531, _1514531), _1514533), _1514533)))], (27621 ^ _780478) ^ [_1291093, _1291095, _1291097, _1291099] : [class_Rings_Oring__1(_1291093), -(hAPP(c_Int_Oring__1__class_Oof__int(_1291093), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1291095, tc_Int_Oint), _1291097), _1291099)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1291095, _1291093), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1291093, _1291095), c_Int_Oring__1__class_Oof__int(_1291093)), _1291097)), _1291099))], (38384 ^ _780478) ^ [_1517959, _1517961, _1517963] : [c_Wellfounded_Owf(_1517959, _1517961), c_Wellfounded_Owf(_1517959, _1517963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1517959, _1517959), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1517959, _1517959, _1517959), _1517961), _1517963)), _1517961)), -(c_Wellfounded_Owf(_1517959, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1517959, _1517959), tc_HOL_Obool)), _1517961), _1517963)))], (30965 ^ _780478) ^ [_1355915, _1355917] : [-(c_Nitpick_Onat__lcm(_1355915, _1355917) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1355915), _1355917)), c_Nitpick_Onat__gcd(_1355915, _1355917)))], (34879 ^ _780478) ^ [_1437933, _1437935, _1437937] : [class_Rings_Olinordered__semidom(_1437933), hAPP(hAPP(c_Power_Opower__class_Opower(_1437933), _1437935), 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(_1437933), _1437937), 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(_1437933), c_Groups_Ozero__class_Ozero(_1437933)), _1437935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1437933), c_Groups_Ozero__class_Ozero(_1437933)), _1437937)), -(_1437935 = _1437937)], (26794 ^ _780478) ^ [_1276867, _1276869, _1276871, _1276873] : [class_Fields_Olinordered__field(_1276867), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276867), c_Groups_Ozero__class_Ozero(_1276867)), _1276869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276867), _1276871), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276867), _1276873), _1276869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276867), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276867), _1276871), _1276869)), _1276873)))], (50000 ^ _780478) ^ [_1791159, _1791161, _1791163, _1791165] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1791159, _1791161, c_Orderings_Otop__class_Otop(tc_fun(_1791159, tc_HOL_Obool)), _1791163), _1791165) = c_Hilbert__Choice_OEps(_1791159, hAPP(hAPP(c_COMBC(_1791159, _1791161, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1791161, tc_fun(_1791161, tc_HOL_Obool), _1791159), c_fequal), _1791163)), _1791165)))], (12161 ^ _780478) ^ [_994244, _994246] : [class_Orderings_Olinorder(_994244), hBOOL(hAPP(c_Finite__Set_Ofinite(_994244), _994246)), -(_994246 = c_Orderings_Obot__class_Obot(tc_fun(_994244, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_994244), hAPP(hAPP(c_Orderings_Oord__class_Omax(_994244), 12174 ^ [_994244, _994246]), 12175 ^ [_994244, _994246])), hAPP(hAPP(c_Set_Oinsert(_994244), 12174 ^ [_994244, _994246]), hAPP(hAPP(c_Set_Oinsert(_994244), 12175 ^ [_994244, _994246]), c_Orderings_Obot__class_Obot(tc_fun(_994244, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_994244), c_Big__Operators_Olattice_OSup__fin(_994244, c_Orderings_Oord__class_Omax(_994244), _994246)), _994246)))], (24085 ^ _780478) ^ [_1228715, _1228717, _1228719] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1228715, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228715, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24086 ^ [_1228715, _1228717, _1228719])), _1228717)), _1228719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1228715, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1228715, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1228717)), _1228719)))], (938 ^ _780478) ^ [_794549, _794551, _794553, _794555] : [-(c_Wellfounded_Owf(_794553, _794549)), c_Wellfounded_Owf(_794555, _794551), _794555 = _794553, _794551 = _794549], (14203 ^ _780478) ^ [_1034387, _1034389] : [class_Rings_Ocomm__semiring__1(_1034387), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034387), _1034389), _1034389) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034387), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034387), c_Groups_Oone__class_Oone(_1034387)), c_Groups_Oone__class_Oone(_1034387))), _1034389))], (44877 ^ _780478) ^ [_1679798, _1679800, _1679802, _1679804, _1679806, _1679808] : [-(hBOOL(hAPP(hAPP(c_member(_1679798), _1679800), hAPP(c_List_Oset(_1679798), _1679802)))), -(hAPP(hAPP(c_List_Omap(_1679798, _1679804), c_Fun_Ofun__upd(_1679798, _1679804, _1679806, _1679800, _1679808)), _1679802) = hAPP(hAPP(c_List_Omap(_1679798, _1679804), _1679806), _1679802))], (39457 ^ _780478) ^ [_1546560] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1546560), c_Int_OInteg)), -(_1546560 = hAPP(c_Int_ORep__Integ, 39460 ^ [_1546560]))], (45313 ^ _780478) ^ [_1688804, _1688806, _1688808] : [-(c_List_Olistsp(_1688804, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1688804, tc_HOL_Obool)), _1688806), _1688808)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1688804), tc_HOL_Obool)), c_List_Olistsp(_1688804, _1688806)), c_List_Olistsp(_1688804, _1688808)))], (34791 ^ _780478) ^ [_1436348] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1436348), 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), _1436348), _1436348))], (38646 ^ _780478) ^ [_1524510, _1524512, _1524514, _1524516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1524510, _1524512), tc_HOL_Obool)), _1524514), _1524516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524510, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1524510, _1524512), _1524514)), hAPP(c_Relation_ODomain(_1524510, _1524512), _1524516))))], (12359 ^ _780478) ^ [_998519, _998521, _998523, _998525] : [c_Fun_Oinj__on(_998519, _998521, _998523, c_Orderings_Otop__class_Otop(tc_fun(_998519, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998521, tc_HOL_Obool)), hAPP(c_Set_Oimage(_998519, _998521, _998523), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_998519, tc_HOL_Obool)), _998525))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_998521, tc_HOL_Obool)), hAPP(c_Set_Oimage(_998519, _998521, _998523), _998525)))))], (18189 ^ _780478) ^ [_1120620, _1120622] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1120620)), hAPP(c_Nat_OSuc, _1120622)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1120620), _1120622)))], (12023 ^ _780478) ^ [_991713, _991715, _991717] : [class_Orderings_Olinorder(_991713), hBOOL(hAPP(c_Finite__Set_Ofinite(_991713), _991715)), hBOOL(hAPP(hAPP(c_member(_991713), _991717), _991715)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_991713), _991717), c_Big__Operators_Olattice_OInf__fin(_991713, c_Orderings_Oord__class_Omin(_991713), _991715)) = _991717)], (49115 ^ _780478) ^ [_1771850, _1771852, _1771854, _1771856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1771850), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1771852, _1771854, _1771850, _1771856) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1771852)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1771852)))], (34809 ^ _780478) ^ [_1436667, _1436669] : [class_Rings_Olinordered__idom(_1436667), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1436667), hAPP(c_Groups_Oabs__class_Oabs(_1436667), _1436669)), 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(_1436667), _1436669), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (44773 ^ _780478) ^ [_1677341, _1677343, _1677345, _1677347, _1677349] : [class_Rings_Osemiring__0(_1677341), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1677341), hAPP(hAPP(c_List_Omap(_1677343, _1677341), hAPP(hAPP(c_COMBB(_1677341, _1677341, _1677343), hAPP(c_Groups_Otimes__class_Otimes(_1677341), _1677345)), _1677347)), _1677349)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1677341), _1677345), hAPP(c_List_Omonoid__add__class_Olistsum(_1677341), hAPP(hAPP(c_List_Omap(_1677343, _1677341), _1677347), _1677349))))], (18780 ^ _780478) ^ [_1133174, _1133176, _1133178] : [class_Lattices_Olattice(_1133174), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133174), _1133176)), -(_1133176 = c_Orderings_Obot__class_Obot(tc_fun(_1133174, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1133174, hAPP(hAPP(c_Set_Oinsert(_1133174), _1133178), _1133176)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1133174), _1133178), c_Big__Operators_Olattice__class_OInf__fin(_1133174, _1133176)))], (2526 ^ _780478) ^ [_817624, _817626, _817628, _817630, _817632, _817634, _817636, _817638] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_817638, _817634, _817630, _817626) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_817636, _817632, _817628, _817624)), _817638 = _817636, _817634 = _817632, _817630 = _817628, _817626 = _817624], (36469 ^ _780478) ^ [_1474381, _1474383] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1474381, _1474381)), hAPP(hAPP(c_Product__Type_OPair(_1474381, _1474381), 36470 ^ [_1474381, _1474383]), 36470 ^ [_1474381, _1474383])), _1474383)), -(c_Nitpick_Orefl_H(_1474381, _1474383))], (31431 ^ _780478) ^ [_1368835, _1368837] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1368835), _1368837)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1368835, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1368835, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1368835, tc_HOL_Obool), tc_fun(_1368835, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1368835, tc_HOL_Obool))), _1368837)))))], (34277 ^ _780478) ^ [_1426992, _1426994] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1426992), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426994)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1426992), 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)))), _1426994)))], (7740 ^ _780478) ^ [_911250, _911252, _911254, _911256, _911258, _911260] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911250, _911252, _911254, _911256, _911258), _911260)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_911250), _911258)))], (6206 ^ _780478) ^ [_879898, _879900] : [-(c_Set_Othe__elem(_879898, hAPP(hAPP(c_Set_Oinsert(_879898), _879900), c_Orderings_Obot__class_Obot(tc_fun(_879898, tc_HOL_Obool)))) = _879900)], (45167 ^ _780478) ^ [_1685827, _1685829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1685827), _1685829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1685827)), hAPP(c_Code__Numeral_Onat__of, _1685829))))], (50562 ^ _780478) ^ [_1803210] : [-(c_Fun_Obij__betw(_1803210, _1803210, c_Fun_Oid(_1803210), c_Orderings_Otop__class_Otop(tc_fun(_1803210, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1803210, tc_HOL_Obool))))], (34557 ^ _780478) ^ [_1432063, _1432065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1432063)), c_Int_OBit0(_1432065))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432063), _1432065)))], (46487 ^ _780478) ^ [_1716102, _1716104, _1716106] : [class_Orderings_Olinorder(_1716102), c_List_Olinorder__class_Osorted(_1716102, _1716104), -(c_List_Olinorder__class_Osorted(_1716102, c_List_Oremove1(_1716102, _1716106, _1716104)))], (20846 ^ _780478) ^ [_1168823, _1168825, _1168827] : [class_Groups_Ocomm__monoid__add(_1168823), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168825, _1168823), _1168827), c_Orderings_Obot__class_Obot(tc_fun(_1168825, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1168823))], (41162 ^ _780478) ^ [_1588493, _1588495, _1588497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588493, _1588493), tc_HOL_Obool)), c_Relation_OId(_1588493)), _1588495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588493, _1588493), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1588493, _1588493, _1588493), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1588493, _1588493), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588493, _1588497)), _1588495)), _1588497)), _1588495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1588493, _1588493), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588493, _1588497)), _1588495)))], (29069 ^ _780478) ^ [_1319701, _1319703, _1319705] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1319701, tc_HOL_Obool)), _1319705), hAPP(c_Set_OPow(_1319701), _1319703))), -(hBOOL(hAPP(c_Predicate_OPowp(_1319701, hAPP(hAPP(c_COMBC(_1319701, tc_fun(_1319701, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319701)), _1319703)), _1319705)))], (48689 ^ _780478) ^ [_1762568, _1762570, _1762572, _1762574] : [hBOOL(hAPP(hAPP(c_member(_1762568), _1762570), hAPP(c_List_Oset(_1762568), c_List_Oreplicate(_1762568, _1762572, _1762574)))), 48692 ^ _780478 : [(48695 ^ _780478) ^ [] : [_1762572 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48693 ^ _780478) ^ [] : [-(_1762570 = _1762574)]]], (21298 ^ _780478) ^ [_1176054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176054)), -(_1176054 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1176054), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (2308 ^ _780478) ^ [_814247, _814249] : [_814249 = _814247, -(c_Int_Osucc(_814249) = c_Int_Osucc(_814247))], (30779 ^ _780478) ^ [_1352260, _1352262, _1352264] : [class_Rings_Olinordered__idom(_1352260), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1352260), c_Groups_Ozero__class_Ozero(_1352260)), hAPP(hAPP(c_Power_Opower__class_Opower(_1352260), hAPP(c_Groups_Oabs__class_Oabs(_1352260), _1352262)), _1352264))))], (41342 ^ _780478) ^ [_1593184, _1593186] : [-(c_Transitive__Closure_Ortrancl(_1593184, _1593186) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1593184, _1593184), 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(_1593184, _1593184), tc_HOL_Obool), tc_fun(tc_prod(_1593184, _1593184), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1593184, _1593184), tc_HOL_Obool)), _1593186)))], (13360 ^ _780478) ^ [_1018391, _1018393] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018391, tc_HOL_Obool)), _1018393), c_Orderings_Otop__class_Otop(tc_fun(_1018391, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1018391, tc_HOL_Obool)))], (6760 ^ _780478) ^ [_892373, _892375, _892377, _892379, _892381] : [-(hAPP(c_Fun_Ofun__upd(_892373, _892375, _892377, _892379, _892381), _892379) = _892381)], (13074 ^ _780478) ^ [_1012136, _1012138, _1012140] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012136, tc_HOL_Obool)), _1012138), _1012140) = c_Orderings_Obot__class_Obot(tc_fun(_1012136, tc_HOL_Obool)), 13077 ^ _780478 : [(13080 ^ _780478) ^ [] : [-(_1012140 = c_Orderings_Obot__class_Obot(tc_fun(_1012136, tc_HOL_Obool)))], (13078 ^ _780478) ^ [] : [-(_1012138 = c_Orderings_Obot__class_Obot(tc_fun(_1012136, tc_HOL_Obool)))]]], (6538 ^ _780478) ^ [_887260, _887262, _887264, _887266] : [hBOOL(hAPP(hAPP(c_member(_887260), _887262), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887260, tc_HOL_Obool)), _887264), _887266))), -(hBOOL(hAPP(hAPP(c_member(_887260), _887262), _887264)))], (40837 ^ _780478) ^ [_1580105, _1580107] : [c_Wellfounded_Oacyclic(_1580105, hAPP(c_Relation_Oconverse(_1580105, _1580105), _1580107)), -(c_Wellfounded_Oacyclic(_1580105, _1580107))], (21079 ^ _780478) ^ [_1172430, _1172432] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1172430), _1172432))), -(hAPP(c_Finite__Set_Ocard(_1172430), _1172432) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37871 ^ _780478) ^ [_1504415] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1504415)) = _1504415)], (23263 ^ _780478) ^ [_1213425, _1213427] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213425) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213427), -(_1213425 = _1213427)], (33260 ^ _780478) ^ [_1408876, _1408878] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408876)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408876)), _1408878) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408876)), _1408878)))], (43057 ^ _780478) ^ [_1639190] : [class_Groups_Omonoid__add(_1639190), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1639190), c_List_Olist_ONil(_1639190)) = c_Groups_Ozero__class_Ozero(_1639190))], (32500 ^ _780478) ^ [_1394203, _1394205, _1394207] : [class_Int_Onumber__ring(_1394203), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1394203), hAPP(c_Int_Onumber__class_Onumber__of(_1394203), _1394205)), hAPP(c_Int_Onumber__class_Onumber__of(_1394203), _1394207)) = hAPP(c_Int_Onumber__class_Onumber__of(_1394203), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1394205), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1394207))))], (24789 ^ _780478) ^ [_1241081] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1241081), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1241081)], (9322 ^ _780478) ^ [_940007, _940009, _940011, _940013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_940007, tc_HOL_Obool)), _940009), _940011)), hBOOL(hAPP(hAPP(c_member(_940007), _940013), _940009)), -(hBOOL(hAPP(hAPP(c_member(_940007), _940013), _940011)))], (48083 ^ _780478) ^ [_1749665, _1749667, _1749669] : [c_List_Olist__ex(_1749665, _1749667, hAPP(c_List_Orev(_1749665), _1749669)), -(c_List_Olist__ex(_1749665, _1749667, _1749669))], (44817 ^ _780478) ^ [_1678365, _1678367, _1678369, _1678371] : [-(hAPP(c_List_Oset(_1678365), hAPP(hAPP(c_List_Omap(_1678367, _1678365), _1678369), _1678371)) = hAPP(c_Set_Oimage(_1678367, _1678365, _1678369), hAPP(c_List_Oset(_1678367), _1678371)))], (41473 ^ _780478) ^ [_1596947, _1596949, _1596951, _1596953] : [41475 ^ _780478 : [(41480 ^ _780478) ^ [] : [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(_1596951, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 41474 ^ [_1596947, _1596949, _1596951, _1596953]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1596951, 41474 ^ [_1596947, _1596949, _1596951, _1596953])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (41478 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41474 ^ [_1596947, _1596949, _1596951, _1596953]), _1596949)))], (41476 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1596947), 41474 ^ [_1596947, _1596949, _1596951, _1596953])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1596947), _1596949)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1596951, _1596947)), _1596953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1596953), hAPP(_1596951, _1596949))), 41494 ^ _780478 : [(41499 ^ _780478) ^ [] : [-(hAPP(_1596951, 41493 ^ [_1596947, _1596949, _1596951, _1596953]) = _1596953)], (41497 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41493 ^ [_1596947, _1596949, _1596951, _1596953]), _1596949)))], (41495 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1596947), 41493 ^ [_1596947, _1596949, _1596951, _1596953])))]]], (46507 ^ _780478) ^ [_1716378, _1716380, _1716382] : [class_Orderings_Olinorder(_1716378), 46510 ^ _780478 : [(46517 ^ _780478) ^ [] : [c_List_Olinorder__class_Osorted(_1716378, _1716382), -(c_List_Olinorder__class_Osorted(_1716378, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1716378, _1716378, c_COMBI(_1716378)), _1716380), _1716382)))], (46511 ^ _780478) ^ [] : [c_List_Olinorder__class_Osorted(_1716378, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1716378, _1716378, c_COMBI(_1716378)), _1716380), _1716382)), -(c_List_Olinorder__class_Osorted(_1716378, _1716382))]]], (32294 ^ _780478) ^ [_1390640, _1390642, _1390644] : [class_Int_Onumber__ring(_1390640), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390640), hAPP(c_Int_Onumber__class_Onumber__of(_1390640), _1390642)), hAPP(c_Int_Onumber__class_Onumber__of(_1390640), _1390644)) = hAPP(c_Int_Onumber__class_Onumber__of(_1390640), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390642), _1390644)))], (16198 ^ _780478) ^ [_1073987, _1073989, _1073991, _1073993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073987, tc_HOL_Obool)), _1073989), _1073991)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073987, tc_HOL_Obool)), _1073989), _1073993)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073987, tc_HOL_Obool)), _1073989), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073987, tc_HOL_Obool)), _1073991), _1073993))))], (8550 ^ _780478) ^ [_928144, _928146, _928148, _928150, _928152, _928154, _928156, _928158] : [class_Groups_Ocomm__monoid__add(_928144), c_Fun_Oinj__on(_928146, _928148, _928150, _928152), _928154 = hAPP(c_Set_Oimage(_928146, _928148, _928150), _928152), 8564 ^ _780478 : [(8567 ^ _780478) ^ [] : [hAPP(_928156, 8563 ^ [_928144, _928146, _928148, _928150, _928152, _928154, _928156, _928158]) = hAPP(_928158, hAPP(_928150, 8563 ^ [_928144, _928146, _928148, _928150, _928152, _928154, _928156, _928158]))], (8565 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928146), 8563 ^ [_928144, _928146, _928148, _928150, _928152, _928154, _928156, _928158]), _928152)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_928148, _928144), _928158), _928154) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_928146, _928144), _928156), _928152))], (6308 ^ _780478) ^ [_882124, _882126, _882128] : [_882126 = _882128, -(hBOOL(hAPP(hAPP(c_member(_882124), _882126), hAPP(c_fequal, _882128))))], (23269 ^ _780478) ^ [_1213531, _1213533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1213531), _1213533)), -(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)), _1213531)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213533))))], (26150 ^ _780478) ^ [_1265258, _1265260, _1265262, _1265264, _1265266] : [class_Fields_Ofield__inverse__zero(_1265258), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265258), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265258), _1265260), _1265262)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265258), _1265264), _1265266)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265258), _1265260), _1265264)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265258), _1265262), _1265266)))], (12572 ^ _780478) ^ [_1002454, _1002456] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002454, tc_HOL_Obool)), _1002456), c_Orderings_Otop__class_Otop(tc_fun(_1002454, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1002454, tc_HOL_Obool)))], (18085 ^ _780478) ^ [_1117206, _1117208, _1117210, _1117212, _1117214] : [hBOOL(hAPP(hAPP(c_member(_1117206), _1117208), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1117210, tc_fun(_1117206, tc_HOL_Obool)), _1117212), _1117214))), 18088 ^ _780478 : [(18089 ^ _780478) ^ [_1117330] : [hBOOL(hAPP(hAPP(c_member(_1117210), _1117330), _1117212)), -(hBOOL(hAPP(hAPP(c_member(_1117206), _1117208), hAPP(_1117214, _1117330))))]]], (19154 ^ _780478) ^ [_1140037, _1140039] : [class_Groups_Ocomm__monoid__add(_1140037), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1140037), c_Groups_Ozero__class_Ozero(_1140037)), _1140039) = _1140039)], (50686 ^ _780478) ^ [_1805795, _1805797, _1805799, _1805801, _1805803] : [50688 ^ _780478 : [(50691 ^ _780478) ^ [] : [c_Relation_Orefl__on(_1805799, hAPP(_1805801, 50687 ^ [_1805795, _1805797, _1805799, _1805801, _1805803]), hAPP(_1805803, 50687 ^ [_1805795, _1805797, _1805799, _1805801, _1805803]))], (50689 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805795), 50687 ^ [_1805795, _1805797, _1805799, _1805801, _1805803]), _1805797)))]], -(c_Relation_Orefl__on(_1805799, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1805795, tc_fun(_1805799, tc_HOL_Obool)), _1805797), _1805801), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1805795, tc_fun(tc_prod(_1805799, _1805799), tc_HOL_Obool)), _1805797), _1805803)))], (31837 ^ _780478) ^ [_1381717, _1381719, _1381721] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_1381717, _1381719, _1381721)) = 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), _1381719)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1381721))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24255 ^ _780478) ^ [_1231798, _1231800, _1231802] : [class_Divides_Osemiring__div(_1231798), -(_1231800 = c_Groups_Ozero__class_Ozero(_1231798)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231798), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231798), _1231800), _1231802)), _1231800) = _1231802)], (29285 ^ _780478) ^ [_1324237, _1324239, _1324241] : [class_Divides_Osemiring__div(_1324237), -(c_Divides_Odiv__class_Omod(_1324237, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1324237), _1324239), _1324241), _1324241) = c_Divides_Odiv__class_Omod(_1324237, _1324239, _1324241))], (44245 ^ _780478) ^ [_1666139] : [class_Groups_Omonoid__add(_1666139), -(c_List_Omonoid__add__class_Olistsum(_1666139) = c_List_Ofoldl(_1666139, _1666139, c_Groups_Oplus__class_Oplus(_1666139), c_Groups_Ozero__class_Ozero(_1666139)))], (42150 ^ _780478) ^ [_1616821, _1616823, _1616825, _1616827] : [42153 ^ _780478 : [(42158 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616821, _1616821)), hAPP(hAPP(c_Product__Type_OPair(_1616821, _1616821), 42152 ^ [_1616821, _1616823, _1616825, _1616827]), 42151 ^ [_1616821, _1616823, _1616825, _1616827])), _1616823))], (42156 ^ _780478) ^ [] : [42151 ^ [_1616821, _1616823, _1616825, _1616827] = 42152 ^ [_1616821, _1616823, _1616825, _1616827]], (42154 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616821, _1616821)), hAPP(hAPP(c_Product__Type_OPair(_1616821, _1616821), 42151 ^ [_1616821, _1616823, _1616825, _1616827]), 42152 ^ [_1616821, _1616823, _1616825, _1616827])), _1616823))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616821), tc_List_Olist(_1616821))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616821), tc_List_Olist(_1616821)), _1616825), _1616827)), c_List_Olexord(_1616821, _1616823)))), -(_1616825 = _1616827), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616821), tc_List_Olist(_1616821))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616821), tc_List_Olist(_1616821)), _1616827), _1616825)), c_List_Olexord(_1616821, _1616823))))], (31174 ^ _780478) ^ [_1360679] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1360679, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1360679), hAPP(c_COMBK(tc_HOL_Obool, _1360679), c_fFalse)))], (3264 ^ _780478) ^ [_829103, _829105, _829107, _829109, _829111, _829113] : [-(c_List_Olist_Olist__size(_829113, _829109, _829105) = c_List_Olist_Olist__size(_829111, _829107, _829103)), _829113 = _829111, _829109 = _829107, _829105 = _829103], (44031 ^ _780478) ^ [_1661692, _1661694, _1661696, _1661698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1661692), _1661694)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661696)), _1661698))), -(hAPP(hAPP(c_List_Otake(_1661696), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1661692), _1661694)), _1661698) = hAPP(hAPP(c_List_Oappend(_1661696), hAPP(hAPP(c_List_Otake(_1661696), _1661692), _1661698)), hAPP(hAPP(c_List_Otake(_1661696), _1661694), hAPP(hAPP(c_List_Odrop(_1661696), _1661692), _1661698))))], (19296 ^ _780478) ^ [_1142175, _1142177] : [class_Groups_Ogroup__add(_1142175), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142175), _1142177), _1142177) = c_Groups_Ozero__class_Ozero(_1142175))], (5714 ^ _780478) ^ [_867938, _867940, _867942, _867944, _867946, _867948] : [-(c_COMBB(_867948, _867944, _867940) = c_COMBB(_867946, _867942, _867938)), _867948 = _867946, _867944 = _867942, _867940 = _867938], (39701 ^ _780478) ^ [_1553500, _1553502] : [39702 ^ _780478 : [(39703 ^ _780478) ^ [_1553546] : [hBOOL(hAPP(_1553500, _1553546))]], -(hBOOL(hAPP(_1553500, c_Hilbert__Choice_OEps(_1553502, _1553500))))], (52267 ^ _780478) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (21358 ^ _780478) ^ [_1177065, _1177067, _1177069, _1177071] : [class_Groups_Oordered__comm__monoid__add(_1177065), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177065), c_Groups_Ozero__class_Ozero(_1177065)), _1177067)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177065), _1177069), _1177071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177065), _1177069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177065), _1177067), _1177071))))], (33042 ^ _780478) ^ [_1404947, _1404949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404947)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404949))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1404947), _1404949)))], (9716 ^ _780478) ^ [_948049, _948051, _948053, _948055, _948057, _948059] : [class_Rings_Oring(_948049), 9719 ^ _780478 : [(9726 ^ _780478) ^ [] : [_948055 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948049), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_948049), _948057), _948051)), _948053)), _948059), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948049), _948051), _948053)), _948055) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948049), _948057), _948053)), _948059))], (9720 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948049), _948051), _948053)), _948055) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948049), _948057), _948053)), _948059), -(_948055 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_948049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_948049), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_948049), _948057), _948051)), _948053)), _948059))]]], (22725 ^ _780478) ^ [_1203515, _1203517] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203515)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203515), _1203517)))], (24781 ^ _780478) ^ [_1240922, _1240924] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1240922), _1240924)), _1240922)))], (48842 ^ _780478) ^ [_1765679, _1765681, _1765683] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1765679, _1765681), _1765683) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1765679, tc_Lazy__Sequence_Olazy__sequence(_1765679)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1765679, tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1765679, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_Nat_Onat)), _1765679), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1765679), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1765679)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1765679, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765679), tc_Nat_Onat)), _1765679), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1765679))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1765679), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1765681))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1765679, _1765681))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1765679), _1765683)))], (16392 ^ _780478) ^ [_1078968, _1078970, _1078972] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078968, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1078968, tc_HOL_Obool)), _1078970), _1078972)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1078968, tc_HOL_Obool)), _1078970), _1078972)) = _1078970)], (5616 ^ _780478) ^ [_866467, _866469] : [_866469 = _866467, -(tc_Lazy__Sequence_Olazy__sequence(_866469) = tc_Lazy__Sequence_Olazy__sequence(_866467))], (48893 ^ _780478) ^ [_1766945, _1766947, _1766949] : [hBOOL(hAPP(hAPP(c_List_Omember(_1766945), _1766947), _1766949)), -(hBOOL(hAPP(hAPP(c_member(_1766945), _1766949), hAPP(c_List_Oset(_1766945), _1766947))))], (45203 ^ _780478) ^ [_1686455, _1686457] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1686455), _1686457) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686455)), hAPP(c_Code__Numeral_Onat__of, _1686457))))], (8182 ^ _780478) ^ [_920394, _920396, _920398, _920400] : [class_Groups_Ocancel__semigroup__add(_920394), 8185 ^ _780478 : [(8192 ^ _780478) ^ [] : [_920398 = _920400, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920394), _920396), _920398) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920394), _920396), _920400))], (8186 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920394), _920396), _920398) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920394), _920396), _920400), -(_920398 = _920400)]]], (30930 ^ _780478) ^ [_1355152, _1355154, _1355156] : [30932 ^ _780478 : [(30935 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1355152, tc_HOL_Obool)), 30931 ^ [_1355152, _1355154, _1355156]), _1355156))], (30933 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1355152, tc_HOL_Obool)), 30931 ^ [_1355152, _1355154, _1355156]), _1355154)))]], -(_1355154 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1355152, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1355152, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1355152, tc_HOL_Obool), _1355154)), _1355156)))], (15641 ^ _780478) ^ [_1062979, _1062981, _1062983, _1062985, _1062987, _1062989] : [hAPP(_1062979, _1062981) = _1062983, hBOOL(hAPP(hAPP(c_member(_1062985), _1062983), _1062987)), -(hBOOL(hAPP(hAPP(c_member(_1062989), _1062981), hAPP(c_Set_Ovimage(_1062989, _1062985, _1062979), _1062987))))], (1854 ^ _780478) ^ [_806517, _806519] : [-(class_Power_Opower(_806517)), _806519 = _806517, class_Power_Opower(_806519)], (8682 ^ _780478) ^ [_930744, _930746, _930748] : [class_Lattices_Oab__semigroup__idem__mult(_930744), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930744), _930746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930744), _930746), _930748)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930744), _930746), _930748))], (40145 ^ _780478) ^ [_1563817, _1563819, _1563821, _1563823, _1563825, _1563827] : [c_Finite__Set_Ofolding__idem(_1563817, _1563819, _1563821, _1563823), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563817), _1563825)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1563817), _1563827)), -(hAPP(_1563823, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1563817, tc_HOL_Obool)), _1563825), _1563827)) = hAPP(c_Fun_Ocomp(_1563819, _1563819, _1563819, hAPP(_1563823, _1563825)), hAPP(_1563823, _1563827)))], (46543 ^ _780478) ^ [_1716894, _1716896, _1716898, _1716900] : [class_Orderings_Olinorder(_1716894), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1716894), _1716896), _1716898)), c_List_Olinorder__class_Osorted(_1716894, hAPP(hAPP(c_List_Olist_OCons(_1716894), _1716898), _1716900)), -(c_List_Olinorder__class_Osorted(_1716894, hAPP(hAPP(c_List_Olist_OCons(_1716894), _1716896), hAPP(hAPP(c_List_Olist_OCons(_1716894), _1716898), _1716900))))], (39607 ^ _780478) ^ [_1551262, _1551264] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1551262, tc_HOL_Obool), _1551264) = hAPP(c_Set_OCollect(_1551262), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1551262, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1551262), c_HOL_OAll(tc_fun(_1551262, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1551262, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1551262, tc_HOL_Obool), tc_HOL_Obool), _1551262), hAPP(c_COMBS(tc_fun(_1551262, 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(_1551262, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1551262, tc_HOL_Obool), tc_fun(tc_fun(_1551262, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1551262, tc_HOL_Obool))), _1551264)))), c_member(_1551262)))))], (48543 ^ _780478) ^ [_1759987, _1759989, _1759991] : [-(hAPP(c_List_Orev(_1759987), c_List_Oreplicate(_1759987, _1759989, _1759991)) = c_List_Oreplicate(_1759987, _1759989, _1759991))], (24229 ^ _780478) ^ [_1231364, _1231366, _1231368, _1231370] : [class_Divides_Osemiring__div(_1231364), 24232 ^ _780478 : [(24239 ^ _780478) ^ [] : [-(_1231366 = c_Groups_Ozero__class_Ozero(_1231364)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231364), _1231366), _1231368)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231364), _1231366), _1231370)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231364), _1231368), _1231370))], (24233 ^ _780478) ^ [] : [_1231366 = c_Groups_Ozero__class_Ozero(_1231364), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231364), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231364), _1231366), _1231368)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231364), _1231366), _1231370)) = c_Groups_Ozero__class_Ozero(_1231364))]]], (2172 ^ _780478) ^ [_812185, _812187, _812189, _812191] : [-(c_SMT_Oz3div(_812191, _812187) = c_SMT_Oz3div(_812189, _812185)), _812191 = _812189, _812187 = _812185], (14903 ^ _780478) ^ [_1048185, _1048187, _1048189, _1048191] : [hBOOL(hAPP(hAPP(c_member(_1048185), _1048187), c_SetInterval_Oord_OatLeast(_1048185, _1048189, _1048191))), -(hBOOL(hAPP(hAPP(_1048189, _1048191), _1048187)))], (46417 ^ _780478) ^ [_1714965, _1714967, _1714969, _1714971, _1714973] : [class_Orderings_Olinorder(_1714965), hBOOL(hAPP(hAPP(c_member(_1714967), _1714969), hAPP(c_List_Oset(_1714967), _1714971))), c_List_Olinorder__class_Osorted(_1714965, hAPP(hAPP(c_List_Omap(_1714967, _1714965), _1714973), _1714971)), hAPP(c_List_Ohd(_1714967), hAPP(c_List_Ofilter(_1714967, hAPP(hAPP(c_COMBB(_1714965, tc_HOL_Obool, _1714967), hAPP(c_fequal, hAPP(_1714973, _1714969))), _1714973)), _1714971)) = _1714969, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1714967, _1714965, _1714973), _1714969), c_List_Oremove1(_1714967, _1714969, _1714971)) = _1714971)], (35363 ^ _780478) ^ [] : [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)], (31195 ^ _780478) ^ [_1361021, _1361023] : [-(hBOOL(hAPP(_1361023, 31196 ^ [_1361021, _1361023]))), -(hAPP(c_Set_OCollect(_1361021), _1361023) = c_Orderings_Obot__class_Obot(tc_fun(_1361021, tc_HOL_Obool)))], (4124 ^ _780478) ^ [_842839, _842841, _842843, _842845, _842847, _842849, _842851, _842853] : [-(c_New__Random__Sequence_Opos__map(_842853, _842849, _842845, _842841) = c_New__Random__Sequence_Opos__map(_842851, _842847, _842843, _842839)), _842853 = _842851, _842849 = _842847, _842845 = _842843, _842841 = _842839], (17243 ^ _780478) ^ [_1098018, _1098020, _1098022, _1098024, _1098026, _1098028] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098018, tc_fun(_1098020, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098022, tc_fun(_1098018, tc_HOL_Obool)), _1098024), _1098026)), _1098028) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098022, tc_fun(_1098020, tc_HOL_Obool)), _1098024), hAPP(hAPP(c_COMBC(_1098022, tc_fun(_1098018, tc_fun(_1098020, tc_HOL_Obool)), tc_fun(_1098020, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1098018, tc_HOL_Obool), tc_fun(tc_fun(_1098018, tc_fun(_1098020, tc_HOL_Obool)), tc_fun(_1098020, tc_HOL_Obool)), _1098022), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098018, tc_fun(_1098020, tc_HOL_Obool))), _1098026)), _1098028)))], (33580 ^ _780478) ^ [_1413823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1413823)), -(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), _1413823))))], (3768 ^ _780478) ^ [_836925, _836927, _836929, _836931, _836933, _836935, _836937, _836939] : [-(c_List_Ofoldl(_836939, _836935, _836931, _836927) = c_List_Ofoldl(_836937, _836933, _836929, _836925)), _836939 = _836937, _836935 = _836933, _836931 = _836929, _836927 = _836925], (23339 ^ _780478) ^ [_1214701, _1214703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1214701), _1214703)), 23342 ^ _780478 : [(23345 ^ _780478) ^ [] : [_1214701 = _1214703], (23343 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1214701), _1214703)))]]], (47746 ^ _780478) ^ [_1742002, _1742004, _1742006, _1742008, _1742010] : [47747 ^ _780478 : [(47750 ^ _780478) ^ [] : [hBOOL(hAPP(_1742010, hAPP(hAPP(c_List_Ozip(_1742002, _1742006), hAPP(hAPP(c_List_Otake(_1742002), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742002)), _1742004)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742006)), _1742008))), _1742004)), hAPP(hAPP(c_List_Otake(_1742006), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742002)), _1742004)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742006)), _1742008))), _1742008))))], (47748 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742002)), hAPP(hAPP(c_List_Otake(_1742002), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742002)), _1742004)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742006)), _1742008))), _1742004)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742006)), hAPP(hAPP(c_List_Otake(_1742006), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742002)), _1742004)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742006)), _1742008))), _1742008)))]], -(hBOOL(hAPP(_1742010, hAPP(hAPP(c_List_Ozip(_1742002, _1742006), _1742004), _1742008))))], (32026 ^ _780478) ^ [_1385460, _1385462] : [class_Int_Onumber__ring(_1385460), 32029 ^ _780478 : [(32036 ^ _780478) ^ [] : [-(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), _1385462)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1385460), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1385462)) = c_Groups_Ozero__class_Ozero(_1385460))], (32030 ^ _780478) ^ [] : [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), _1385462))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1385460), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1385462)) = hAPP(c_Int_Onumber__class_Onumber__of(_1385460), _1385462))]]], (9492 ^ _780478) ^ [_943249, _943251, _943253] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_943249, tc_HOL_Obool)), _943251), _943253))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943249, tc_HOL_Obool)), _943251), _943253)), -(_943251 = _943253)], (10581 ^ _780478) ^ [_965024, _965026, _965028] : [class_Groups_Oordered__ab__group__add(_965024), 10584 ^ _780478 : [(10591 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965024), _965028), hAPP(c_Groups_Ouminus__class_Ouminus(_965024), _965026))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965024), _965026), hAPP(c_Groups_Ouminus__class_Ouminus(_965024), _965028))))], (10585 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965024), _965026), hAPP(c_Groups_Ouminus__class_Ouminus(_965024), _965028))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965024), _965028), hAPP(c_Groups_Ouminus__class_Ouminus(_965024), _965026))))]]], (49932 ^ _780478) ^ [_1789555, _1789557] : [-(c_Equiv__Relations_Opart__equivp(_1789555, _1789557)), 49935 ^ _780478 : [(49936 ^ _780478) ^ [_1789675] : [hBOOL(hAPP(hAPP(_1789557, _1789675), _1789675))]], 49953 ^ _780478 : [(49956 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1789557, 49938 ^ [_1789555, _1789557]), 49938 ^ [_1789555, _1789557])))], (49958 ^ _780478) ^ [] : [-(hAPP(_1789557, 49937 ^ [_1789555, _1789557]) = hAPP(_1789557, 49938 ^ [_1789555, _1789557]))], (49960 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1789557, 49937 ^ [_1789555, _1789557]), 49938 ^ [_1789555, _1789557]))], (49954 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1789557, 49937 ^ [_1789555, _1789557]), 49937 ^ [_1789555, _1789557])))]], 49941 ^ _780478 : [(49944 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1789557, 49937 ^ [_1789555, _1789557]), 49937 ^ [_1789555, _1789557])), hBOOL(hAPP(hAPP(_1789557, 49938 ^ [_1789555, _1789557]), 49938 ^ [_1789555, _1789557])), hAPP(_1789557, 49937 ^ [_1789555, _1789557]) = hAPP(_1789557, 49938 ^ [_1789555, _1789557])], (49942 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1789557, 49937 ^ [_1789555, _1789557]), 49938 ^ [_1789555, _1789557])))]]], (38742 ^ _780478) ^ [_1527482, _1527484, _1527486, _1527488] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1527482, _1527484), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1527482, tc_HOL_Obool), _1527486)), _1527488) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1527482, tc_HOL_Obool), tc_fun(tc_prod(_1527482, _1527484), tc_HOL_Obool)), _1527486), hAPP(hAPP(c_COMBC(tc_fun(_1527482, tc_HOL_Obool), tc_fun(_1527482, tc_fun(_1527484, tc_HOL_Obool)), tc_fun(tc_prod(_1527482, _1527484), tc_HOL_Obool)), c_Product__Type_OSigma(_1527482, _1527484)), _1527488)))], (3130 ^ _780478) ^ [_826992, _826994, _826996, _826998] : [-(c_Nat_Ocompow(_826998, _826994) = c_Nat_Ocompow(_826996, _826992)), _826998 = _826996, _826994 = _826992], (22875 ^ _780478) ^ [_1206227, _1206229, _1206231] : [class_Rings_Osemiring__1(_1206227), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206227), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206229), _1206231)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206227), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206227), _1206229)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1206227), _1206231)))], (31204 ^ _780478) ^ [_1361108] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1361108, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1361108), hAPP(c_COMBK(tc_HOL_Obool, _1361108), c_fTrue)))], (50847 ^ _780478) ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1810191, _1810193), tc_prod(_1810191, _1810193))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1810191, _1810193), tc_prod(_1810191, _1810193)), hAPP(hAPP(c_Product__Type_OPair(_1810191, _1810193), _1810195), _1810197)), hAPP(hAPP(c_Product__Type_OPair(_1810191, _1810193), _1810199), _1810201))), c_Transitive__Closure_Ortrancl(tc_prod(_1810191, _1810193), _1810203))), hBOOL(hAPP(hAPP(_1810205, _1810199), _1810201)), 50860 ^ _780478 : [(50863 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1810191, _1810193), tc_prod(_1810191, _1810193))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1810191, _1810193), tc_prod(_1810191, _1810193)), hAPP(hAPP(c_Product__Type_OPair(_1810191, _1810193), 50858 ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205]), 50859 ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205])), hAPP(hAPP(c_Product__Type_OPair(_1810191, _1810193), _1810199), _1810201))), c_Transitive__Closure_Ortrancl(tc_prod(_1810191, _1810193), _1810203))))], (50865 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1810205, 50858 ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205]), 50859 ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205])))], (50867 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1810205, 50856 ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205]), 50857 ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205]))], (50861 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1810191, _1810193), tc_prod(_1810191, _1810193))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1810191, _1810193), tc_prod(_1810191, _1810193)), hAPP(hAPP(c_Product__Type_OPair(_1810191, _1810193), 50856 ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205]), 50857 ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205])), hAPP(hAPP(c_Product__Type_OPair(_1810191, _1810193), 50858 ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205]), 50859 ^ [_1810191, _1810193, _1810195, _1810197, _1810199, _1810201, _1810203, _1810205]))), _1810203)))]], -(hBOOL(hAPP(hAPP(_1810205, _1810195), _1810197)))], (40183 ^ _780478) ^ [_1564576, _1564578, _1564580, _1564582, _1564584, _1564586, _1564588] : [c_Finite__Set_Ofolding__idem(_1564576, _1564578, _1564580, _1564582), -(hAPP(c_Fun_Ocomp(_1564578, _1564578, _1564584, hAPP(_1564580, _1564586)), hAPP(c_Fun_Ocomp(_1564578, _1564578, _1564584, hAPP(_1564580, _1564586)), _1564588)) = hAPP(c_Fun_Ocomp(_1564578, _1564578, _1564584, hAPP(_1564580, _1564586)), _1564588))], (6656 ^ _780478) ^ [_890021, _890023, _890025] : [-(hBOOL(hAPP(hAPP(c_member(_890021), _890023), _890025))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890021, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_890021), _890023), _890025)), hAPP(hAPP(c_Set_Oinsert(_890021), _890023), c_Orderings_Obot__class_Obot(tc_fun(_890021, tc_HOL_Obool)))) = _890025)], (19562 ^ _780478) ^ [_1146015, _1146017] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1146015), _1146017) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1146017), _1146015) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1146015 = _1146017)], (44845 ^ _780478) ^ [_1679091, _1679093, _1679095, _1679097, _1679099] : [c_Fun_Oinj__on(_1679091, _1679093, _1679095, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1679091, tc_HOL_Obool)), hAPP(c_List_Oset(_1679091), _1679097)), hAPP(c_List_Oset(_1679091), _1679099))), 44848 ^ _780478 : [(44855 ^ _780478) ^ [] : [_1679097 = _1679099, -(hAPP(hAPP(c_List_Omap(_1679091, _1679093), _1679095), _1679097) = hAPP(hAPP(c_List_Omap(_1679091, _1679093), _1679095), _1679099))], (44849 ^ _780478) ^ [] : [hAPP(hAPP(c_List_Omap(_1679091, _1679093), _1679095), _1679097) = hAPP(hAPP(c_List_Omap(_1679091, _1679093), _1679095), _1679099), -(_1679097 = _1679099)]]], (37724 ^ _780478) ^ [_1500462, _1500464] : [-(hAPP(c_Relation_OField(_1500462), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1500462, _1500462), tc_HOL_Obool), _1500464)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1500462, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1500462, _1500462), tc_HOL_Obool), tc_fun(_1500462, tc_HOL_Obool), c_Relation_OField(_1500462)), _1500464)))], (27275 ^ _780478) ^ [_1285306, _1285308, _1285310] : [class_Groups_Ocomm__monoid__add(_1285306), class_Groups_Ocomm__monoid__mult(_1285306), c_Nat__Transfer_Onat__set(_1285308), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1285306), _1285310), _1285308) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1285306), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1285306, tc_Nat_Onat), _1285310), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1285308)))], (43173 ^ _780478) ^ [_1641313, _1641315, _1641317] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641313), tc_List_Olist(_1641313))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641313), tc_List_Olist(_1641313)), _1641315), c_List_Olist_ONil(_1641313))), c_List_Olexord(_1641313, _1641317)))], (51927 ^ _780478) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (29676 ^ _780478) ^ [_1331443, _1331445, _1331447, _1331449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331443)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331445), _1331447)), -(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), _1331447), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1331449, _1331443))), _1331445)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1331447), _1331443))))], (28174 ^ _780478) ^ [_1301956, _1301958, _1301960] : [class_Orderings_Olinorder(_1301956), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301956), _1301958), _1301960)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301956, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1301956), _1301958), c_Orderings_Obot__class_Obot(tc_fun(_1301956, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1301956, _1301958, _1301960)) = c_SetInterval_Oord__class_OatLeastAtMost(_1301956, _1301958, _1301960))], (14677 ^ _780478) ^ [_1042987, _1042989, _1042991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042987), _1042989)), _1042991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042987), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042991), _1042989))))], (5438 ^ _780478) ^ [_863654, _863656] : [_863656 = _863654, -(c_Groups_Ominus__class_Ominus(_863656) = c_Groups_Ominus__class_Ominus(_863654))], (32116 ^ _780478) ^ [_1386909, _1386911, _1386913, _1386915, _1386917] : [c_Com_Ocom_OLocal(_1386909, _1386911, _1386913) = c_Com_Ocom_OWhile(_1386915, _1386917)], (39285 ^ _780478) ^ [_1543170, _1543172, _1543174, _1543176, _1543178] : [c_Relation_Orefl__on(_1543170, _1543172, _1543174), c_Relation_Orefl__on(_1543170, _1543176, _1543178), -(c_Relation_Orefl__on(_1543170, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1543170, tc_HOL_Obool)), _1543172), _1543176), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1543170, _1543170), tc_HOL_Obool)), _1543174), _1543178)))], (36882 ^ _780478) ^ [_1482058, _1482060, _1482062, _1482064, _1482066] : [-(hAPP(c_Product__Type_Osnd(_1482058, _1482060), hAPP(c_Product__Type_Oapsnd(_1482062, _1482060, _1482058, _1482064), _1482066)) = hAPP(_1482064, hAPP(c_Product__Type_Osnd(_1482058, _1482062), _1482066)))], (49706 ^ _780478) ^ [_1785986, _1785988] : [c_Relation_Osym(_1785986, _1785988), -(c_Relation_Osym(_1785986, c_Transitive__Closure_Ortrancl(_1785986, _1785988)))], (26932 ^ _780478) ^ [_1279488, _1279490, _1279492, _1279494] : [class_Fields_Ofield(_1279488), -(_1279490 = c_Groups_Ozero__class_Ozero(_1279488)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279488), _1279492), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279488), _1279494), _1279490)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279488), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1279488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279488), _1279490), _1279492)), _1279494)), _1279490))], (40097 ^ _780478) ^ [_1562517, _1562519, _1562521, _1562523, _1562525] : [c_Hoare__Mirabelle_Ohoare__derivs(_1562517, _1562519, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1562517)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1562517), c_Hoare__Mirabelle_Opeek__and(_1562517, _1562521, _1562523)), _1562525), _1562521)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1562517), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1562517, _1562519, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1562517)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1562517), _1562521), c_Com_Ocom_OWhile(_1562523, _1562525)), c_Hoare__Mirabelle_Opeek__and(_1562517, _1562521, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1562523)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1562517), tc_HOL_Obool)))))], (41582 ^ _780478) ^ [_1599629, _1599631, _1599633, _1599635, _1599637, _1599639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599629, _1599631)), _1599633), hAPP(hAPP(c_Relation_Orel__comp(_1599629, _1599635, _1599631), _1599637), _1599639))), 41588 ^ _780478 : [(41593 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599635, _1599631)), hAPP(hAPP(c_Product__Type_OPair(_1599635, _1599631), 41586 ^ [_1599629, _1599631, _1599633, _1599635, _1599637, _1599639]), 41587 ^ [_1599629, _1599631, _1599633, _1599635, _1599637, _1599639])), _1599639)))], (41591 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599629, _1599635)), hAPP(hAPP(c_Product__Type_OPair(_1599629, _1599635), 41585 ^ [_1599629, _1599631, _1599633, _1599635, _1599637, _1599639]), 41586 ^ [_1599629, _1599631, _1599633, _1599635, _1599637, _1599639])), _1599637)))], (41589 ^ _780478) ^ [] : [-(_1599633 = hAPP(hAPP(c_Product__Type_OPair(_1599629, _1599631), 41585 ^ [_1599629, _1599631, _1599633, _1599635, _1599637, _1599639]), 41587 ^ [_1599629, _1599631, _1599633, _1599635, _1599637, _1599639]))]]], (2014 ^ _780478) ^ [_809650, _809652, _809654, _809656, _809658, _809660, _809662, _809664, _809666, _809668] : [-(c_Finite__Set_Ofold__graph(_809668, _809664, _809660, _809656, _809652) = c_Finite__Set_Ofold__graph(_809666, _809662, _809658, _809654, _809650)), _809668 = _809666, _809664 = _809662, _809660 = _809658, _809656 = _809654, _809652 = _809650], (10205 ^ _780478) ^ [_957982, _957984, _957986, _957988] : [class_Orderings_Olinorder(_957982), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_957982), hAPP(hAPP(c_Orderings_Oord__class_Omin(_957982), _957984), _957986)), _957988) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_957982), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957982), _957984), _957988)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_957982), _957986), _957988)))], (19520 ^ _780478) ^ [_1145417, _1145419] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1145417), _1145419) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 19523 ^ _780478 : [(19526 ^ _780478) ^ [] : [-(_1145419 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19524 ^ _780478) ^ [] : [-(_1145417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (36373 ^ _780478) ^ [_1472685, _1472687] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1472685, _1472687) = 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), _1472685), _1472687)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1472685, _1472687)))], (17963 ^ _780478) ^ [_1114966, _1114968] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114966)), _1114968) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114966), _1114968)))], (10847 ^ _780478) ^ [_969661, _969663, _969665, _969667] : [class_Orderings_Olinorder(_969661), 10850 ^ _780478 : [(10851 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969661), _969663), hAPP(hAPP(c_Orderings_Oord__class_Omax(_969661), _969665), _969667))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969661), _969663), _969665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969661), _969663), _969667)))], (10861 ^ _780478) ^ [] : [10862 ^ _780478 : [(10865 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969661), _969663), _969667))], (10863 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969661), _969663), _969665))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_969661), _969663), hAPP(hAPP(c_Orderings_Oord__class_Omax(_969661), _969665), _969667))))]]], (36820 ^ _780478) ^ [_1480922, _1480924] : [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), _1480922), _1480924))), 36823 ^ _780478 : [(36832 ^ _780478) ^ [] : [-(c_Divides_OnegDivAlg(_1480922, _1480924) = hAPP(c_Divides_Oadjust(_1480924), c_Divides_OnegDivAlg(_1480922, 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)))), _1480924)))), -(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), _1480922), _1480924)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480924), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36824 ^ _780478) ^ [] : [36825 ^ _780478 : [(36828 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480924), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36826 ^ _780478) ^ [] : [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), _1480922), _1480924)))]], -(c_Divides_OnegDivAlg(_1480922, _1480924) = 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), _1480922), _1480924)))]]], (16170 ^ _780478) ^ [_1073305, _1073307, _1073309, _1073311, _1073313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073305, tc_HOL_Obool)), _1073307), _1073309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073311, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1073311, _1073305, _1073313), _1073307)), hAPP(c_Set_Ovimage(_1073311, _1073305, _1073313), _1073309))))], (16320 ^ _780478) ^ [_1077278, _1077280, _1077282, _1077284] : [-(hBOOL(hAPP(hAPP(c_member(_1077278), _1077280), _1077282))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077278, tc_HOL_Obool)), _1077282), hAPP(hAPP(c_Set_Oinsert(_1077278), _1077280), _1077284)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077278, tc_HOL_Obool)), _1077282), _1077284))], (36784 ^ _780478) ^ [_1480160, _1480162, _1480164] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1480160, _1480162), _1480164)), -(c_Divides_Odivmod__nat(_1480160, _1480162) = _1480164)], (50279 ^ _780478) ^ [_1797617, _1797619, _1797621, _1797623, _1797625] : [hBOOL(hAPP(_1797617, hAPP(hAPP(c_Product__Type_OPair(_1797619, _1797621), _1797623), _1797625))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1797619, _1797621, tc_HOL_Obool, _1797617), _1797623), _1797625)))], (39815 ^ _780478) ^ [_1556005, _1556007, _1556009, _1556011, _1556013, _1556015, _1556017, _1556019] : [class_Groups_Ocomm__monoid__mult(_1556005), c_Fun_Oinj__on(_1556007, _1556009, _1556011, _1556013), _1556015 = hAPP(c_Set_Oimage(_1556007, _1556009, _1556011), _1556013), _1556017 = hAPP(c_Fun_Ocomp(_1556009, _1556005, _1556007, _1556019), _1556011), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1556009, _1556005), _1556019), _1556015) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1556007, _1556005), _1556017), _1556013))], (12536 ^ _780478) ^ [_1001760, _1001762] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1001760, _1001762)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1001760, _1001762), tc_HOL_Obool)))), 12539 ^ _780478 : [(12542 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1001762), c_Orderings_Otop__class_Otop(tc_fun(_1001762, tc_HOL_Obool)))))], (12540 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1001760), c_Orderings_Otop__class_Otop(tc_fun(_1001760, tc_HOL_Obool)))))]]], (574 ^ _780478) ^ [_789151, _789153] : [-(c_List_Onat__list(_789151)), _789153 = _789151, c_List_Onat__list(_789153)], (1724 ^ _780478) ^ [_804892, _804894] : [-(class_Nat_Osemiring__char__0(_804892)), _804894 = _804892, class_Nat_Osemiring__char__0(_804894)], (45323 ^ _780478) ^ [_1689028, _1689030, _1689032, _1689034] : [-(hBOOL(hAPP(c_List_Olistsp(_1689028, _1689030), hAPP(hAPP(c_List_Olist_OCons(_1689028), _1689032), _1689034)))), hBOOL(hAPP(_1689030, _1689032)), hBOOL(hAPP(c_List_Olistsp(_1689028, _1689030), _1689034))], (5474 ^ _780478) ^ [_864210, _864212, _864214, _864216, _864218, _864220, _864222, _864224, _864226, _864228] : [-(c_SetInterval_Oord_OatLeastLessThan(_864228, _864224, _864220, _864216, _864212) = c_SetInterval_Oord_OatLeastLessThan(_864226, _864222, _864218, _864214, _864210)), _864228 = _864226, _864224 = _864222, _864220 = _864218, _864216 = _864214, _864212 = _864210], (34043 ^ _780478) ^ [_1423248, _1423250] : [class_Int_Onumber__ring(_1423248), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423248), _1423250), hAPP(c_Int_Onumber__class_Onumber__of(_1423248), c_Int_OBit1(c_Int_OPls))) = _1423250)], (33304 ^ _780478) ^ [_1409572, _1409574] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1409572)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409574)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1409574))), 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), _1409572)), c_Int_Onat)))))], (18245 ^ _780478) ^ [_1121704] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1121704))], (18179 ^ _780478) ^ [_1120125, _1120127, _1120129, _1120131, _1120133] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120125, tc_fun(_1120127, tc_HOL_Obool)), _1120129), hAPP(hAPP(c_COMBB(tc_fun(_1120127, tc_HOL_Obool), tc_fun(_1120127, tc_HOL_Obool), _1120125), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1120127, tc_HOL_Obool)), _1120131)), _1120133)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1120127, tc_HOL_Obool)), _1120131), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1120125, tc_fun(_1120127, tc_HOL_Obool)), _1120129), _1120133)))], (4466 ^ _780478) ^ [_848250, _848252] : [_848252 = _848250, -(c_Lazy__Sequence_Oyieldn(_848252) = c_Lazy__Sequence_Oyieldn(_848250))], (52107 ^ _780478) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (24869 ^ _780478) ^ [_1242352, _1242354, _1242356, _1242358] : [class_Orderings_Oorder(_1242352), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1242352, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1242352, _1242354, _1242356)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1242352, _1242356, _1242358)) = c_Orderings_Obot__class_Obot(tc_fun(_1242352, tc_HOL_Obool)))], (49305 ^ _780478) ^ [_1776658, _1776660] : [-(hBOOL(hAPP(_1776660, 49312 ^ [_1776658, _1776660]))), 49306 ^ _780478 : [(49307 ^ _780478) ^ [_1776719] : [hBOOL(hAPP(hAPP(c_member(_1776658), _1776719), c_Orderings_Otop__class_Otop(tc_fun(_1776658, tc_HOL_Obool)))), hBOOL(hAPP(_1776660, _1776719))]]], (45933 ^ _780478) ^ [_1702664, _1702666, _1702668, _1702670] : [-(hAPP(hAPP(c_List_Omap(_1702664, _1702666), _1702668), c_List_Oconcat(_1702664, _1702670)) = c_List_Oconcat(_1702666, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1702664), tc_List_Olist(_1702666)), hAPP(c_List_Omap(_1702664, _1702666), _1702668)), _1702670)))], (29474 ^ _780478) ^ [_1327738, _1327740] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1327738), _1327740) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327738, _1327740) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (24553 ^ _780478) ^ [_1236620, _1236622, _1236624] : [class_Divides_Osemiring__div(_1236620), -(_1236622 = c_Groups_Ozero__class_Ozero(_1236620)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236620), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236620), _1236622), _1236624)), _1236622) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1236620), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1236620), _1236624), _1236622)), c_Groups_Oone__class_Oone(_1236620)))], (49333 ^ _780478) ^ [_1777164, _1777166, _1777168, _1777170] : [c_Relation_Otrans(_1777164, _1777166), -(c_Relation_Otrans(_1777168, hAPP(hAPP(c_Relation_Oinv__image(_1777164, _1777168), _1777166), _1777170)))], (3370 ^ _780478) ^ [_830710, _830712, _830714, _830716] : [-(c_HOL_OLet(_830716, _830712) = c_HOL_OLet(_830714, _830710)), _830716 = _830714, _830712 = _830710], (39973 ^ _780478) ^ [_1559704, _1559706, _1559708, _1559710, _1559712, _1559714, _1559716] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1559704, _1559706, _1559708), hAPP(c_Fun_Ocomp(_1559710, tc_fun(_1559706, _1559708), _1559704, _1559712), _1559714)), _1559716) = hAPP(hAPP(_1559712, hAPP(_1559714, hAPP(c_Product__Type_Ofst(_1559704, _1559706), _1559716))), hAPP(c_Product__Type_Osnd(_1559704, _1559706), _1559716)))], (26556 ^ _780478) ^ [_1272420, _1272422, _1272424, _1272426, _1272428] : [class_Fields_Olinordered__field(_1272420), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272420), c_Groups_Ozero__class_Ozero(_1272420)), _1272422)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272420), _1272422), _1272424)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272420), c_Groups_Ozero__class_Ozero(_1272420)), _1272426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272420), _1272426), _1272428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272420), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272420), _1272422), _1272428)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272420), _1272424), _1272426))))], (14789 ^ _780478) ^ [_1045421, _1045423, _1045425, _1045427, _1045429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1045421), _1045423)), 14792 ^ _780478 : [(14799 ^ _780478) ^ [] : [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), _1045423), _1045421)), _1045425)), _1045427)), _1045429)), -(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), _1045423), _1045425)), _1045427)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045421), _1045425)), _1045429))))], (14793 ^ _780478) ^ [] : [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), _1045423), _1045425)), _1045427)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1045421), _1045425)), _1045429))), -(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), _1045423), _1045421)), _1045425)), _1045427)), _1045429)))]]], (33388 ^ _780478) ^ [_1410777, _1410779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1410777), _1410779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1410777)), _1410779)))], (35235 ^ _780478) ^ [_1445012, _1445014] : [class_Int_Onumber__ring(_1445012), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1445012), hAPP(c_Int_Onumber__class_Onumber__of(_1445012), 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)))), _1445014))) = hAPP(c_Int_Onumber__class_Onumber__of(_1445012), c_Int_OMin))], (1834 ^ _780478) ^ [_806267, _806269] : [-(class_Orderings_Oord(_806267)), _806269 = _806267, class_Orderings_Oord(_806269)], (40532 ^ _780478) ^ [_1573220, _1573222] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1573220, _1573220, _1573220), _1573222), c_Transitive__Closure_Ortrancl(_1573220, _1573222)) = hAPP(hAPP(c_Relation_Orel__comp(_1573220, _1573220, _1573220), c_Transitive__Closure_Ortrancl(_1573220, _1573222)), _1573222))], (13082 ^ _780478) ^ [_1012289, _1012291, _1012293] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012289, tc_HOL_Obool)), _1012291), _1012293) = c_Orderings_Obot__class_Obot(tc_fun(_1012289, tc_HOL_Obool))), _1012291 = c_Orderings_Obot__class_Obot(tc_fun(_1012289, tc_HOL_Obool)), _1012293 = c_Orderings_Obot__class_Obot(tc_fun(_1012289, tc_HOL_Obool))], (47383 ^ _780478) ^ [_1733936, _1733938] : [-(c_List_OdropWhile(_1733936, _1733938, c_List_Olist_ONil(_1733936)) = c_List_Olist_ONil(_1733936))], (50461 ^ _780478) ^ [_1801495, _1801497, _1801499, _1801501, _1801503] : [-(c_Fun_Obij__betw(_1801495, _1801497, _1801499, _1801501, _1801503)), c_Fun_Oinj__on(_1801495, _1801497, _1801499, _1801501), hAPP(c_Set_Oimage(_1801495, _1801497, _1801499), _1801501) = _1801503], (32048 ^ _780478) ^ [_1385795, _1385797] : [class_Int_Onumber__ring(_1385795), -(hAPP(c_Int_Oring__1__class_Oof__int(_1385795), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1385797)) = hAPP(c_Int_Onumber__class_Onumber__of(_1385795), _1385797))], (40496 ^ _780478) ^ [_1572177, _1572179, _1572181, _1572183] : [-(c_Transitive__Closure_Otrancl(_1572177, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1572177, _1572177)), hAPP(hAPP(c_Product__Type_OPair(_1572177, _1572177), _1572179), _1572181)), _1572183)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572177, _1572177), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1572177, _1572183)), hAPP(c_Set_OCollect(tc_prod(_1572177, _1572177)), hAPP(c_Product__Type_Oprod_Oprod__case(_1572177, _1572177, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1572177, tc_fun(_1572177, tc_HOL_Obool), tc_fun(_1572177, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1572177, tc_HOL_Obool), tc_fun(_1572177, tc_HOL_Obool)), _1572177), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1572177)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572177), c_fconj), hAPP(hAPP(c_COMBC(_1572177, tc_fun(tc_prod(_1572177, _1572177), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1572177, _1572177), tc_fun(tc_fun(tc_prod(_1572177, _1572177), tc_HOL_Obool), tc_HOL_Obool), _1572177), c_member(tc_prod(_1572177, _1572177))), hAPP(hAPP(c_COMBC(_1572177, _1572177, tc_prod(_1572177, _1572177)), c_Product__Type_OPair(_1572177, _1572177)), _1572179))), c_Transitive__Closure_Ortrancl(_1572177, _1572183))))), hAPP(hAPP(c_COMBC(_1572177, tc_fun(tc_prod(_1572177, _1572177), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1572177, _1572177), tc_fun(tc_fun(tc_prod(_1572177, _1572177), tc_HOL_Obool), tc_HOL_Obool), _1572177), c_member(tc_prod(_1572177, _1572177))), hAPP(c_Product__Type_OPair(_1572177, _1572177), _1572181))), c_Transitive__Closure_Ortrancl(_1572177, _1572183)))))))], (24143 ^ _780478) ^ [_1230028, _1230030] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1230028, _1230030))))], (24207 ^ _780478) ^ [_1231069, _1231071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231069)), 24210 ^ _780478 : [(24217 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231071), 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), _1231071), _1231069)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24211 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1231071), _1231069)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231071), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (17187 ^ _780478) ^ [_1096805, _1096807, _1096809, _1096811] : [-(hAPP(c_Set_Oimage(_1096805, _1096807, _1096809), _1096811) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1096805, tc_fun(_1096807, tc_HOL_Obool)), _1096811), hAPP(hAPP(c_COMBC(_1096805, tc_fun(_1096807, tc_HOL_Obool), tc_fun(_1096807, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1096807, tc_fun(tc_fun(_1096807, tc_HOL_Obool), tc_fun(_1096807, tc_HOL_Obool)), _1096805), c_Set_Oinsert(_1096807)), _1096809)), c_Orderings_Obot__class_Obot(tc_fun(_1096807, tc_HOL_Obool)))))], (36242 ^ _780478) ^ [_1469626, _1469628, _1469630, _1469632, _1469634, _1469636, _1469638] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1469626, _1469628, tc_fun(_1469630, tc_HOL_Obool)), _1469632), hAPP(hAPP(c_Product__Type_OPair(_1469626, _1469628), _1469634), _1469636)), _1469638)), -(hBOOL(hAPP(hAPP(hAPP(_1469632, _1469634), _1469636), _1469638)))], (27697 ^ _780478) ^ [_1292366, _1292368] : [class_Rings_Olinordered__idom(_1292366), 27700 ^ _780478 : [(27707 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1292368), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292366), hAPP(c_Int_Oring__1__class_Oof__int(_1292366), _1292368)), c_Groups_Ozero__class_Ozero(_1292366))))], (27701 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1292366), hAPP(c_Int_Oring__1__class_Oof__int(_1292366), _1292368)), c_Groups_Ozero__class_Ozero(_1292366))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1292368), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29792 ^ _780478) ^ [_1333716, _1333718] : [-(_1333716 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29795 ^ _780478 : [(29802 ^ _780478) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333718, _1333716) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333718), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1333716)) = 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), _1333718), _1333716))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (29796 ^ _780478) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1333718, _1333716) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333718), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1333716)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1333718), _1333716)))]]], (39597 ^ _780478) ^ [_1550993, _1550995, _1550997, _1550999, _1551001, _1551003] : [hBOOL(hAPP(hAPP(c_member(_1550993), _1550995), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1550997, _1550999, tc_fun(_1550993, tc_HOL_Obool)), _1551001), _1551003))), 39602 ^ _780478 : [(39605 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1550993), _1550995), hAPP(hAPP(_1551001, 39600 ^ [_1550993, _1550995, _1550997, _1550999, _1551001, _1551003]), 39601 ^ [_1550993, _1550995, _1550997, _1550999, _1551001, _1551003]))))], (39603 ^ _780478) ^ [] : [-(_1551003 = hAPP(hAPP(c_Product__Type_OPair(_1550997, _1550999), 39600 ^ [_1550993, _1550995, _1550997, _1550999, _1551001, _1551003]), 39601 ^ [_1550993, _1550995, _1550997, _1550999, _1551001, _1551003]))]]], (48796 ^ _780478) ^ [_1764671, _1764673, _1764675] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1764671)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1764671, _1764673, _1764675)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1764671)), _1764675)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7409 ^ _780478) ^ [_904596, _904598, _904600, _904602, _904604, _904606] : [c_Fun_Oinj__on(_904596, _904598, _904600, _904602), hBOOL(hAPP(hAPP(c_member(_904598), _904604), hAPP(c_Set_Oimage(_904596, _904598, _904600), _904602))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904596, tc_HOL_Obool)), _904602), _904606)), -(hBOOL(hAPP(hAPP(c_member(_904596), hAPP(c_Fun_Othe__inv__into(_904596, _904598, _904602, _904600), _904604)), _904606)))], (2934 ^ _780478) ^ [_823926, _823928] : [_823928 = _823926, -(c_Nitpick_Ofrac(_823928) = c_Nitpick_Ofrac(_823926))], (24775 ^ _780478) ^ [_1240809, _1240811] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1240809, _1240811))))], (31835 ^ _780478) ^ [_1381668, _1381670, _1381672] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_1381668, _1381670, _1381672)) = 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(_1381670)), c_Com_Ocom_Ocom__size(_1381672))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29912 ^ _780478) ^ [_1335706, _1335708] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335706, _1335708)), _1335706)))], (38869 ^ _780478) ^ [_1531471, _1531473, _1531475, _1531477, _1531479, _1531481] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531471, _1531473)), hAPP(hAPP(c_Product__Type_OPair(_1531471, _1531473), _1531475), _1531477)), hAPP(hAPP(c_Product__Type_OSigma(_1531471, _1531473), _1531479), _1531481))), -(hBOOL(hAPP(hAPP(c_member(_1531473), _1531477), hAPP(_1531481, _1531475))))], (30238 ^ _780478) ^ [_1341414, _1341416, _1341418, _1341420] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1341414, tc_HOL_Obool)), _1341416), _1341418)), hBOOL(hAPP(hAPP(c_member(_1341414), _1341420), _1341416)), -(hBOOL(hAPP(hAPP(c_member(_1341414), _1341420), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1341414, tc_HOL_Obool), _1341418))))], (34295 ^ _780478) ^ [_1427324, _1427326] : [class_Int_Onumber__ring(_1427324), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1427324), c_Groups_Oone__class_Oone(_1427324)), hAPP(c_Int_Onumber__class_Onumber__of(_1427324), _1427326)) = hAPP(c_Int_Onumber__class_Onumber__of(_1427324), 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), _1427326))))], (1960 ^ _780478) ^ [_808739, _808741, _808743, _808745, _808747, _808749, _808751, _808753] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_808753, _808749, _808745, _808741) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_808751, _808747, _808743, _808739)), _808753 = _808751, _808749 = _808747, _808745 = _808743, _808741 = _808739], (14957 ^ _780478) ^ [_1049283, _1049285, _1049287, _1049289, _1049291] : [hBOOL(hAPP(hAPP(c_member(_1049283), _1049285), c_SetInterval_Oord_OgreaterThanLessThan(_1049283, _1049287, _1049289, _1049291))), 14960 ^ _780478 : [(14963 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1049287, _1049285), _1049291)))], (14961 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1049287, _1049289), _1049285)))]]], (52269 ^ _780478) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (48780 ^ _780478) ^ [_1764415, _1764417] : [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), _1764415), _1764417))), 48783 ^ _780478 : [(48790 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1764415), _1764417))), -(c_Lazy__Sequence_Osmall__lazy_H(_1764415, _1764417) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1764417), c_Lazy__Sequence_Osmall__lazy_H(_1764415, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1764417), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48784 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1764415), _1764417)), -(c_Lazy__Sequence_Osmall__lazy_H(_1764415, _1764417) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (21265 ^ _780478) ^ [_1175532, _1175534] : [_1175532 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1175532), _1175534), -(_1175534 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1175532 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43041 ^ _780478) ^ [_1638894, _1638896] : [-(hAPP(hAPP(c_List_Otake(_1638894), _1638896), c_List_Olist_ONil(_1638894)) = c_List_Olist_ONil(_1638894))], (8258 ^ _780478) ^ [_921853, _921855, _921857, _921859] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_921853), 8261 ^ _780478 : [(8268 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921853), _921857), _921859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921853), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921853), _921855), _921857)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921853), _921855), _921859))))], (8262 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921853), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921853), _921855), _921857)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921853), _921855), _921859))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_921853), _921857), _921859)))]]], (4594 ^ _780478) ^ [_850364, _850366, _850368, _850370] : [-(c_HOL_OThe(_850370, _850366) = c_HOL_OThe(_850368, _850364)), _850370 = _850368, _850366 = _850364], (19276 ^ _780478) ^ [_1141908, _1141910, _1141912] : [class_Rings_Ono__zero__divisors(_1141908), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141908), _1141910), _1141912) = c_Groups_Ozero__class_Ozero(_1141908), -(_1141910 = c_Groups_Ozero__class_Ozero(_1141908)), -(_1141912 = c_Groups_Ozero__class_Ozero(_1141908))], (19754 ^ _780478) ^ [_1149166, _1149168, _1149170] : [class_Rings_Olinordered__ring__strict(_1149166), 19757 ^ _780478 : [(19758 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149166), c_Groups_Ozero__class_Ozero(_1149166)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149166), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149166), _1149168), _1149168)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149166), _1149170), _1149170)))), _1149168 = c_Groups_Ozero__class_Ozero(_1149166), _1149170 = c_Groups_Ozero__class_Ozero(_1149166)], (19768 ^ _780478) ^ [] : [19769 ^ _780478 : [(19772 ^ _780478) ^ [] : [-(_1149170 = c_Groups_Ozero__class_Ozero(_1149166))], (19770 ^ _780478) ^ [] : [-(_1149168 = c_Groups_Ozero__class_Ozero(_1149166))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149166), c_Groups_Ozero__class_Ozero(_1149166)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149166), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149166), _1149168), _1149168)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1149166), _1149170), _1149170)))))]]], (37844 ^ _780478) ^ [_1503743, _1503745, _1503747, _1503749] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1503743), _1503749) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1503747), _1503745), -(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), _1503743), _1503745)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1503747), _1503749))), c_Int_Ointrel)))], (37173 ^ _780478) ^ [_1487673, _1487675, _1487677] : [-(hAPP(c_Product__Type_Ofst(_1487673, _1487675), _1487677) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1487673, _1487675, _1487673), c_COMBK(_1487673, _1487675)), _1487677))], (21994 ^ _780478) ^ [_1188926, _1188928, _1188930, _1188932, _1188934] : [class_Groups_Ocomm__monoid__add(_1188926), hBOOL(hAPP(c_Finite__Set_Ofinite(_1188928), _1188930)), 22001 ^ _780478 : [(22008 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1188928), _1188932), _1188930))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1188928, _1188926), hAPP(hAPP(c_COMBC(_1188928, _1188926, _1188926), hAPP(hAPP(c_COMBS(_1188928, _1188926, tc_fun(_1188926, _1188926)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1188926, tc_fun(_1188926, _1188926)), _1188928), c_If(_1188926)), hAPP(hAPP(c_COMBC(_1188928, _1188928, tc_HOL_Obool), c_fequal), _1188932))), _1188934)), c_Groups_Ozero__class_Ozero(_1188926))), _1188930) = c_Groups_Ozero__class_Ozero(_1188926))], (22002 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1188928), _1188932), _1188930)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1188928, _1188926), hAPP(hAPP(c_COMBC(_1188928, _1188926, _1188926), hAPP(hAPP(c_COMBS(_1188928, _1188926, tc_fun(_1188926, _1188926)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1188926, tc_fun(_1188926, _1188926)), _1188928), c_If(_1188926)), hAPP(hAPP(c_COMBC(_1188928, _1188928, tc_HOL_Obool), c_fequal), _1188932))), _1188934)), c_Groups_Ozero__class_Ozero(_1188926))), _1188930) = hAPP(_1188934, _1188932))]]], (48362 ^ _780478) ^ [_1755242, _1755244, _1755246] : [-(c_List_Olist__ex1(_1755242, _1755244, _1755246)), 48363 ^ _780478 : [(48364 ^ _780478) ^ [_1755336] : [hBOOL(hAPP(hAPP(c_member(_1755242), _1755336), hAPP(c_List_Oset(_1755242), _1755246))), hBOOL(hAPP(_1755244, _1755336)), 48372 ^ _780478 : [(48377 ^ _780478) ^ [] : [48371 ^ [_1755242, _1755244, _1755246, _1755336] = _1755336], (48375 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1755244, 48371 ^ [_1755242, _1755244, _1755246, _1755336])))], (48373 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1755242), 48371 ^ [_1755242, _1755244, _1755246, _1755336]), hAPP(c_List_Oset(_1755242), _1755246))))]]]]], (29906 ^ _780478) ^ [_1335557, _1335559] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1335557), _1335559) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335557, _1335559)), _1335559))], (41679 ^ _780478) ^ [_1601940, _1601942, _1601944, _1601946, _1601948, _1601950] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1601940, _1601942, _1601944), _1601946), hAPP(hAPP(c_Product__Type_OPair(_1601940, _1601942), _1601948), _1601950)) = hAPP(hAPP(_1601946, _1601948), _1601950))], (25005 ^ _780478) ^ [_1244924, _1244926, _1244928, _1244930] : [class_Orderings_Oorder(_1244924), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1244924, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1244924, _1244926, _1244928)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1244924, _1244928, _1244930)) = c_Orderings_Obot__class_Obot(tc_fun(_1244924, tc_HOL_Obool)))], (46111 ^ _780478) ^ [_1707259, _1707261, _1707263] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1707259), tc_List_Olist(_1707259)), c_List_Opartition(_1707259, _1707261, _1707263)) = hAPP(c_List_Ofilter(_1707259, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1707259, c_fNot), _1707261)), _1707263))], (13070 ^ _780478) ^ [_1012036, _1012038] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012036, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1012036, tc_HOL_Obool))), _1012038) = _1012038)], (8204 ^ _780478) ^ [_920802, _920804, _920806, _920808] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_920802), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920802), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920802), _920804), _920806)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_920802), _920804), _920808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920802), _920806), _920808)))], (13252 ^ _780478) ^ [_1015988, _1015990, _1015992] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1015988), _1015990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1015988), _1015990)), hAPP(c_Finite__Set_Ocard(_1015988), hAPP(hAPP(c_Set_Oinsert(_1015988), _1015992), _1015990)))))], (10629 ^ _780478) ^ [_965873, _965875, _965877] : [class_Groups_Oordered__ab__group__add(_965873), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965873), _965875), _965877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_965873), hAPP(c_Groups_Ouminus__class_Ouminus(_965873), _965877)), hAPP(c_Groups_Ouminus__class_Ouminus(_965873), _965875))))], (48859 ^ _780478) ^ [_1766302, _1766304, _1766306] : [hBOOL(hAPP(hAPP(c_member(_1766302), _1766304), hAPP(c_List_Oset(_1766302), _1766306))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1766302), _1766306), _1766304)))], (10115 ^ _780478) ^ [_956298, _956300] : [class_Groups_Oordered__ab__group__add(_956298), -(c_Fun_Oinj__on(_956298, _956298, c_Groups_Ouminus__class_Ouminus(_956298), _956300))], (14689 ^ _780478) ^ [_1043231, _1043233, _1043235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1043231), _1043233)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043235), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1043233), _1043231)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1043235), _1043231)), _1043233))], (29455 ^ _780478) ^ [_1327402, _1327404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327402), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1327402), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327404, _1327402))))], (52381 ^ _780478) ^ [_1834212, _1834214] : [hBOOL(hAPP(hAPP(c_fconj, _1834212), _1834214)), -(hBOOL(_1834214))], (20436 ^ _780478) ^ [_1161552, _1161554, _1161556, _1161558] : [class_Rings_Olinordered__ring__strict(_1161552), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161552), _1161554), c_Groups_Ozero__class_Ozero(_1161552))), 20443 ^ _780478 : [(20450 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161552), _1161558), _1161556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161552), _1161554), _1161556)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161552), _1161554), _1161558))))], (20444 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161552), _1161554), _1161556)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161552), _1161554), _1161558))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161552), _1161558), _1161556)))]]], (10473 ^ _780478) ^ [_963184, _963186, _963188, _963190] : [class_Orderings_Olinorder(_963184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963184), _963186), _963188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963184), _963186), hAPP(hAPP(c_Orderings_Oord__class_Omax(_963184), _963188), _963190))))], (14375 ^ _780478) ^ [_1037195, _1037197, _1037199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037195), _1037197)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037195), _1037199))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037197), _1037199)))], (48663 ^ _780478) ^ [_1762118, _1762120, _1762122] : [c_List_Olist_ONil(_1762118) = c_List_Oreplicate(_1762118, _1762120, _1762122), -(_1762120 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48808 ^ _780478) ^ [_1764912, _1764914, _1764916, _1764918, _1764920] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1764912, _1764914, _1764916) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1764912, _1764918, _1764920)), _1764914 = _1764918, _1764916 = _1764920], (14387 ^ _780478) ^ [_1037451, _1037453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037451), _1037453)), _1037453))], (18642 ^ _780478) ^ [_1130398, _1130400, _1130402, _1130404, _1130406] : [_1130398 = c_Orderings_Obot__class_Obot(tc_fun(_1130400, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130400, tc_fun(_1130402, tc_HOL_Obool)), _1130398), hAPP(hAPP(c_COMBC(_1130400, tc_fun(_1130402, tc_HOL_Obool), tc_fun(_1130402, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1130402, tc_HOL_Obool), tc_fun(tc_fun(_1130402, tc_HOL_Obool), tc_fun(_1130402, tc_HOL_Obool)), _1130400), c_Groups_Ominus__class_Ominus(tc_fun(_1130402, tc_HOL_Obool))), _1130404)), _1130406)) = c_Orderings_Otop__class_Otop(tc_fun(_1130402, tc_HOL_Obool)))], (18702 ^ _780478) ^ [_1131709, _1131711, _1131713] : [class_Lattices_Olattice(_1131709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131709), _1131711)), hBOOL(hAPP(hAPP(c_member(_1131709), _1131713), _1131711)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1131709), _1131713), c_Big__Operators_Olattice__class_OInf__fin(_1131709, _1131711)) = c_Big__Operators_Olattice__class_OInf__fin(_1131709, _1131711))], (19334 ^ _780478) ^ [_1142752] : [class_Rings_Ozero__neq__one(_1142752), c_Groups_Ozero__class_Ozero(_1142752) = c_Groups_Oone__class_Oone(_1142752)], (37826 ^ _780478) ^ [_1503307, _1503309] : [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)), _1503307), 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)), _1503309), 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)), _1503307), _1503309)), c_Int_Ointrel)))], (24265 ^ _780478) ^ [_1231926, _1231928, _1231930, _1231932] : [class_Divides_Osemiring__div(_1231926), -(_1231928 = c_Groups_Ozero__class_Ozero(_1231926)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231926), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231926), _1231930), _1231928)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231926), _1231932), _1231928)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1231926), _1231930), _1231932))], (9306 ^ _780478) ^ [_939798, _939800, _939802] : [class_Orderings_Olinorder(_939798), 9309 ^ _780478 : [(9316 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939798), _939802), _939800)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939798), _939800), _939802))], (9310 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_939798), _939800), _939802))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_939798), _939802), _939800)))]]], (12516 ^ _780478) ^ [_1001312, _1001314, _1001316, _1001318] : [12517 ^ _780478 : [(12520 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1001312), _1001314), _1001318))], (12518 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1001312), _1001314), _1001316))]], -(hBOOL(hAPP(hAPP(c_member(_1001312), _1001314), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1001312, tc_HOL_Obool)), _1001318), _1001316))))], (35253 ^ _780478) ^ [] : [c_Int_OMin = c_Int_OPls], (12814 ^ _780478) ^ [_1007569, _1007571] : [class_Lattices_Oboolean__algebra(_1007569), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007569), hAPP(c_Groups_Ouminus__class_Ouminus(_1007569), _1007571)), _1007571) = c_Orderings_Otop__class_Otop(_1007569))], (31676 ^ _780478) ^ [_1378030, _1378032] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1378030), c_Orderings_Obot__class_Obot(tc_fun(_1378030, tc_HOL_Obool))), _1378032) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1378030, tc_HOL_Obool), tc_HOL_Obool)))], (45637 ^ _780478) ^ [_1696614] : [-(c_Enum_Osublists(_1696614, c_List_Olist_ONil(_1696614)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1696614)), c_List_Olist_ONil(_1696614)), c_List_Olist_ONil(tc_List_Olist(_1696614))))], (30532 ^ _780478) ^ [_1347223, _1347225, _1347227] : [class_Groups_Oordered__ab__group__add__abs(_1347223), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347223), hAPP(c_Groups_Oabs__class_Oabs(_1347223), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1347223), hAPP(c_Groups_Oabs__class_Oabs(_1347223), _1347225)), hAPP(c_Groups_Oabs__class_Oabs(_1347223), _1347227)))), hAPP(c_Groups_Oabs__class_Oabs(_1347223), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1347223), _1347225), _1347227)))))], (17845 ^ _780478) ^ [_1113156, _1113158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1113156)), hAPP(c_Nat_OSuc, _1113158))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113156), _1113158)))], (30284 ^ _780478) ^ [_1342346] : [class_Rings_Olinordered__idom(_1342346), -(hAPP(c_Groups_Oabs__class_Oabs(_1342346), c_Groups_Oone__class_Oone(_1342346)) = c_Groups_Oone__class_Oone(_1342346))], (46320 ^ _780478) ^ [_1712799, _1712801] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1712799, _1712801)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1712801), _1712799))], (29383 ^ _780478) ^ [_1326180, _1326182] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1326180), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1326182)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1326180, _1326182)))], (6296 ^ _780478) ^ [_881916, _881918, _881920, _881922] : [c_Finite__Set_Ofolding__one__idem(_881916, _881918, _881920), -(hAPP(hAPP(_881918, _881922), _881922) = _881922)], (35870 ^ _780478) ^ [_1461383] : [class_Rings_Osemiring__1(_1461383), -(hBOOL(hAPP(hAPP(c_member(_1461383), c_Groups_Oone__class_Oone(_1461383)), c_Nat_Osemiring__1__class_ONats(_1461383))))], (35543 ^ _780478) ^ [_1449619, _1449621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449619), _1449621)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1449619), _1449621) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (39961 ^ _780478) ^ [_1559372, _1559374, _1559376, _1559378, _1559380, _1559382] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1559372, _1559374), _1559374, tc_prod(_1559376, _1559378), c_Product__Type_Osnd(_1559372, _1559374)), c_Product__Type_Omap__pair(_1559376, _1559372, _1559378, _1559374, _1559380, _1559382)) = hAPP(c_Fun_Ocomp(_1559378, _1559374, tc_prod(_1559376, _1559378), _1559382), c_Product__Type_Osnd(_1559376, _1559378)))], (47729 ^ _780478) ^ [_1741759, _1741761] : [class_Enum_Oenum(_1741759), 47732 ^ _780478 : [(47739 ^ _780478) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1741759), _1741761)), -(hBOOL(hAPP(_1741761, 47742 ^ [_1741759, _1741761])))], (47733 ^ _780478) ^ [] : [47734 ^ _780478 : [(47735 ^ _780478) ^ [_1741861] : [hBOOL(hAPP(_1741761, _1741861))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1741759), _1741761)))]]], (22739 ^ _780478) ^ [_1203777, _1203779, _1203781] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203777)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1203779)), _1203781)) = 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), _1203777), _1203779))), _1203781))], (41055 ^ _780478) ^ [_1585922, _1585924] : [-(c_Relation_Osingle__valued(_1585922, _1585922, c_Relation_OId__on(_1585922, _1585924)))], (25039 ^ _780478) ^ [_1245571, _1245573, _1245575, _1245577] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1245571, _1245573)), c_Sum__Type_OPlus(_1245571, _1245573, _1245575, _1245577))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1245571), _1245575)))], (37756 ^ _780478) ^ [_1501176, _1501178] : [-(c_Relation_OId__on(_1501176, _1501178) = hAPP(c_Product__Type_Oprod_Oprod__case(_1501176, _1501176, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1501176, tc_HOL_Obool, tc_fun(_1501176, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501176, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1501176, tc_HOL_Obool)), _1501176), c_COMBC(_1501176, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501176, tc_HOL_Obool), tc_fun(_1501176, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1501176), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1501176), c_fconj)), c_fequal))), _1501178)))], (44043 ^ _780478) ^ [_1662012, _1662014, _1662016, _1662018, _1662020] : [-(hAPP(hAPP(c_List_Ozip(_1662012, _1662014), _1662016), hAPP(hAPP(c_List_Oappend(_1662014), _1662018), _1662020)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1662012, _1662014)), hAPP(hAPP(c_List_Ozip(_1662012, _1662014), hAPP(hAPP(c_List_Otake(_1662012), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662014)), _1662018)), _1662016)), _1662018)), hAPP(hAPP(c_List_Ozip(_1662012, _1662014), hAPP(hAPP(c_List_Odrop(_1662012), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662014)), _1662018)), _1662016)), _1662020)))], (50936 ^ _780478) ^ [_1812835, _1812837, _1812839] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1812835), _1812837, _1812839)), -(c_List_Olist__ex(tc_Nat_Onat, _1812835, c_List_Oupt(_1812837, _1812839)))], (8647 ^ _780478) ^ [_930157, _930159, _930161] : [class_Orderings_Olinorder(_930157), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_930157, tc_HOL_Obool)), _930159), _930161)), -(_930159 = c_Orderings_Obot__class_Obot(tc_fun(_930157, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_930157), _930161)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930157), c_Big__Operators_Olinorder__class_OMin(_930157, _930161)), c_Big__Operators_Olinorder__class_OMin(_930157, _930159))))], (46641 ^ _780478) ^ [_1718526, _1718528, _1718530, _1718532, _1718534] : [class_Orderings_Olinorder(_1718526), 46644 ^ _780478 : [(46651 ^ _780478) ^ [] : [c_List_Olinorder__class_Osorted(_1718526, hAPP(hAPP(c_List_Omap(_1718528, _1718526), _1718530), _1718534)), -(c_List_Olinorder__class_Osorted(_1718526, hAPP(hAPP(c_List_Omap(_1718528, _1718526), _1718530), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1718528, _1718526, _1718530), _1718532), _1718534))))], (46645 ^ _780478) ^ [] : [c_List_Olinorder__class_Osorted(_1718526, hAPP(hAPP(c_List_Omap(_1718528, _1718526), _1718530), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1718528, _1718526, _1718530), _1718532), _1718534))), -(c_List_Olinorder__class_Osorted(_1718526, hAPP(hAPP(c_List_Omap(_1718528, _1718526), _1718530), _1718534)))]]], (5320 ^ _780478) ^ [_861799, _861801, _861803, _861805, _861807, _861809] : [-(c_Lazy__Sequence_Obind(_861809, _861805, _861801) = c_Lazy__Sequence_Obind(_861807, _861803, _861799)), _861809 = _861807, _861805 = _861803, _861801 = _861799], (27513 ^ _780478) ^ [_1289160, _1289162, _1289164] : [class_Rings_Olinordered__idom(_1289160), 27516 ^ _780478 : [(27523 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1289162), _1289164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289160), hAPP(c_Int_Oring__1__class_Oof__int(_1289160), _1289162)), hAPP(c_Int_Oring__1__class_Oof__int(_1289160), _1289164))))], (27517 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289160), hAPP(c_Int_Oring__1__class_Oof__int(_1289160), _1289162)), hAPP(c_Int_Oring__1__class_Oof__int(_1289160), _1289164))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1289162), _1289164)))]]], (22662 ^ _780478) ^ [_1202474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1202474)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1202474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23053 ^ _780478) ^ [_1209482, _1209484] : [class_Int_Oring__char__0(_1209482), hBOOL(hAPP(hAPP(c_member(_1209482), _1209484), c_Int_Oring__1__class_OInts(_1209482))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209482), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209482), c_Groups_Oone__class_Oone(_1209482)), _1209484)), _1209484) = c_Groups_Ozero__class_Ozero(_1209482)], (1214 ^ _780478) ^ [_798517, _798519] : [-(class_Rings_Oordered__ring(_798517)), _798519 = _798517, class_Rings_Oordered__ring(_798519)], (5967 ^ _780478) ^ [_875357, _875359] : [class_Finite__Set_Ofinite(_875357), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_875357), _875359)))], (37373 ^ _780478) ^ [_1491599, _1491601, _1491603, _1491605] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1491599, _1491601), _1491603), _1491605) = hAPP(c_Set_OCollect(tc_prod(_1491601, _1491601)), hAPP(c_Product__Type_Oprod_Oprod__case(_1491601, _1491601, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1491601, tc_fun(tc_prod(_1491599, _1491599), tc_HOL_Obool), tc_fun(_1491601, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491601, tc_fun(tc_fun(tc_prod(_1491599, _1491599), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1491599, _1491599), tc_HOL_Obool), tc_fun(_1491601, tc_HOL_Obool)), _1491601), c_COMBC(_1491601, tc_fun(tc_prod(_1491599, _1491599), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491601, tc_prod(_1491599, _1491599)), tc_fun(_1491601, tc_fun(tc_fun(tc_prod(_1491599, _1491599), tc_HOL_Obool), tc_HOL_Obool)), _1491601), hAPP(c_COMBB(tc_prod(_1491599, _1491599), tc_fun(tc_fun(tc_prod(_1491599, _1491599), tc_HOL_Obool), tc_HOL_Obool), _1491601), c_member(tc_prod(_1491599, _1491599)))), hAPP(hAPP(c_COMBC(_1491601, tc_fun(_1491601, _1491599), tc_fun(_1491601, tc_prod(_1491599, _1491599))), hAPP(hAPP(c_COMBB(tc_fun(_1491599, tc_prod(_1491599, _1491599)), tc_fun(tc_fun(_1491601, _1491599), tc_fun(_1491601, tc_prod(_1491599, _1491599))), _1491601), c_COMBB(_1491599, tc_prod(_1491599, _1491599), _1491601)), hAPP(hAPP(c_COMBB(_1491599, tc_fun(_1491599, tc_prod(_1491599, _1491599)), _1491601), c_Product__Type_OPair(_1491599, _1491599)), _1491605))), _1491605)))), _1491603))))], (3700 ^ _780478) ^ [_835871, _835873] : [_835873 = _835871, -(c_List_Omonoid__add__class_Olistsum(_835873) = c_List_Omonoid__add__class_Olistsum(_835871))], (39566 ^ _780478) ^ [_1550001, _1550003] : [class_Complete__Lattice_Ocomplete__lattice(_1550001), -(c_Complete__Lattice_OInf__class_OInf(_1550001, _1550003) = c_Complete__Lattice_OSup__class_OSup(_1550001, hAPP(c_Set_OCollect(_1550001), hAPP(hAPP(c_COMBB(tc_fun(_1550001, tc_HOL_Obool), tc_HOL_Obool, _1550001), c_HOL_OAll(_1550001)), hAPP(hAPP(c_COMBB(tc_fun(_1550001, tc_HOL_Obool), tc_fun(_1550001, tc_HOL_Obool), _1550001), hAPP(c_COMBS(_1550001, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550001), c_fimplies), hAPP(hAPP(c_COMBC(_1550001, tc_fun(_1550001, tc_HOL_Obool), tc_HOL_Obool), c_member(_1550001)), _1550003)))), c_Orderings_Oord__class_Oless__eq(_1550001))))))], (18146 ^ _780478) ^ [_1118911, _1118913, _1118915, _1118917] : [c_Orderings_Otop__class_Otop(tc_fun(_1118911, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1118913, tc_fun(_1118911, tc_HOL_Obool)), _1118915), _1118917), 18149 ^ _780478 : [(18150 ^ _780478) ^ [_1119027] : [hBOOL(hAPP(hAPP(c_member(_1118913), _1119027), _1118915)), -(hAPP(_1118917, _1119027) = c_Orderings_Otop__class_Otop(tc_fun(_1118911, tc_HOL_Obool)))]]], (47350 ^ _780478) ^ [_1733286, _1733288, _1733290] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733286)), c_List_OdropWhile(_1733286, _1733288, _1733290))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733286)), _1733290))))], (14495 ^ _780478) ^ [_1039292, _1039294, _1039296, _1039298, _1039300] : [class_Groups_Ocomm__monoid__mult(_1039292), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039294), _1039296)), 14502 ^ _780478 : [(14509 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1039294), _1039298), _1039296))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1039294, _1039292), hAPP(hAPP(c_COMBC(_1039294, _1039292, _1039292), hAPP(hAPP(c_COMBS(_1039294, _1039292, tc_fun(_1039292, _1039292)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1039292, tc_fun(_1039292, _1039292)), _1039294), c_If(_1039292)), hAPP(c_fequal, _1039298))), _1039300)), c_Groups_Oone__class_Oone(_1039292))), _1039296) = c_Groups_Oone__class_Oone(_1039292))], (14503 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1039294), _1039298), _1039296)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1039294, _1039292), hAPP(hAPP(c_COMBC(_1039294, _1039292, _1039292), hAPP(hAPP(c_COMBS(_1039294, _1039292, tc_fun(_1039292, _1039292)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1039292, tc_fun(_1039292, _1039292)), _1039294), c_If(_1039292)), hAPP(c_fequal, _1039298))), _1039300)), c_Groups_Oone__class_Oone(_1039292))), _1039296) = hAPP(_1039300, _1039298))]]], (35017 ^ _780478) ^ [_1440243, _1440245, _1440247] : [class_Rings_Olinordered__idom(_1440243), 35020 ^ _780478 : [(35029 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1440243), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440243), hAPP(hAPP(c_Power_Opower__class_Opower(_1440243), _1440245), 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(_1440243), _1440247), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1440243)))), _1440245 = c_Groups_Ozero__class_Ozero(_1440243), _1440247 = c_Groups_Ozero__class_Ozero(_1440243)], (35021 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1440243), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1440243), hAPP(hAPP(c_Power_Opower__class_Opower(_1440243), _1440245), 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(_1440243), _1440247), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1440243))), 35024 ^ _780478 : [(35027 ^ _780478) ^ [] : [-(_1440247 = c_Groups_Ozero__class_Ozero(_1440243))], (35025 ^ _780478) ^ [] : [-(_1440245 = c_Groups_Ozero__class_Ozero(_1440243))]]]]], (37111 ^ _780478) ^ [_1486436, _1486438] : [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), _1486436), _1486438))), 37114 ^ _780478 : [(37121 ^ _780478) ^ [] : [-(_1486438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1486436, _1486438) = c_Nitpick_Onat__gcd(_1486438, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1486436, _1486438)))], (37115 ^ _780478) ^ [] : [_1486438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1486436, _1486438) = _1486436)]]], (22917 ^ _780478) ^ [_1207034, _1207036, _1207038] : [class_Rings_Oring__1(_1207034), hBOOL(hAPP(hAPP(c_member(_1207034), _1207036), c_Int_Oring__1__class_OInts(_1207034))), hBOOL(hAPP(hAPP(c_member(_1207034), _1207038), c_Int_Oring__1__class_OInts(_1207034))), -(hBOOL(hAPP(hAPP(c_member(_1207034), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207034), _1207036), _1207038)), c_Int_Oring__1__class_OInts(_1207034))))], (48405 ^ _780478) ^ [_1756061, _1756063, _1756065, _1756067, _1756069, _1756071, _1756073] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1756061, _1756063, _1756065, _1756067, _1756069, _1756071, _1756073) = c_New__DSequence_Oneg__decr__bind(_1756061, _1756063, hAPP(hAPP(hAPP(_1756065, _1756069), _1756071), _1756073), hAPP(hAPP(c_COMBC(_1756061, 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(_1756063)))), hAPP(hAPP(c_COMBC(_1756061, 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(_1756063))))), hAPP(hAPP(c_COMBC(_1756061, 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(_1756063)))))), _1756067), _1756069)), _1756071)), _1756073)))], (12692 ^ _780478) ^ [_1005038, _1005040] : [class_Lattices_Osemilattice__sup(_1005038), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005038), _1005040), _1005040) = _1005040)], (52251 ^ _780478) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (14933 ^ _780478) ^ [_1048784, _1048786, _1048788, _1048790] : [hBOOL(hAPP(hAPP(_1048788, _1048790), _1048786)), -(hBOOL(hAPP(hAPP(c_member(_1048784), _1048786), c_SetInterval_Oord_OgreaterThan(_1048784, _1048788, _1048790))))], (18339 ^ _780478) ^ [_1123548, _1123550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123548), _1123550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123548)), _1123550)))], (29987 ^ _780478) ^ [_1336896, _1336898] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1336896), _1336898))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336896, _1336898) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1336896), _1336898), _1336898))], (44137 ^ _780478) ^ [_1663805, _1663807, _1663809] : [-(c_List_Orotate(_1663805, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1663807), _1663809)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1663805), tc_List_Olist(_1663805), tc_List_Olist(_1663805), c_List_Orotate(_1663805, _1663807)), c_List_Orotate(_1663805, _1663809)))], (17961 ^ _780478) ^ [_1114923, _1114925] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114923), hAPP(c_Nat_OSuc, _1114925)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114923), _1114925)))], (6844 ^ _780478) ^ [_893670, _893672, _893674, _893676] : [-(c_Com_Ocom_OSemi(_893670, _893672) = c_Com_Ocom_OSemi(_893674, _893676)), _893670 = _893674, _893672 = _893676], (41573 ^ _780478) ^ [_1599437, _1599439, _1599441] : [hBOOL(hAPP(hAPP(c_member(_1599437), _1599439), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1599437, tc_HOL_Obool), _1599441))), 41577 ^ _780478 : [(41580 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1599437, tc_HOL_Obool)), 41576 ^ [_1599437, _1599439, _1599441]), _1599441)))], (41578 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1599437), _1599439), 41576 ^ [_1599437, _1599439, _1599441])))]]], (38216 ^ _780478) ^ [_1514624, _1514626] : [c_Wellfounded_Owf(_1514624, hAPP(hAPP(c_Relation_Orel__comp(_1514624, _1514624, _1514624), _1514626), _1514626)), -(c_Wellfounded_Owf(_1514624, _1514626))], (45219 ^ _780478) ^ [_1686745, _1686747] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1686745, _1686747) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1686745), hAPP(c_Code__Numeral_Onat__of, _1686747))))], (8766 ^ _780478) ^ [_932031, _932033, _932035, _932037] : [class_Orderings_Oord(_932031), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932031), _932033), _932035)), _932035 = _932037, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932031), _932033), _932037)))], (41685 ^ _780478) ^ [_1602034, _1602036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41686 ^ [_1602034, _1602036]), hAPP(_1602034, 41686 ^ [_1602034, _1602036]))), -(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)), _1602034)), _1602036)))))], (48505 ^ _780478) ^ [_1758533] : [-(c_Predicate_Oconversep(_1758533, _1758533, c_fequal) = c_fequal)], (27118 ^ _780478) ^ [] : [-(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))))], (4498 ^ _780478) ^ [_848726, _848728] : [_848728 = _848726, -(c_List_Olist_ONil(_848728) = c_List_Olist_ONil(_848726))], (49656 ^ _780478) ^ [_1784882, _1784884] : [c_Relation_Osym(_1784882, _1784884), c_Relation_Otrans(_1784882, _1784884), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1784882, _1784882), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1784882, _1784882, _1784882), hAPP(c_Relation_Oconverse(_1784882, _1784882), _1784884)), _1784884)), _1784884)))], (29600 ^ _780478) ^ [_1330057, _1330059, _1330061] : [-(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), _1330057), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1330059), _1330057))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330059, _1330057))), _1330061) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1330059), _1330061))], (28274 ^ _780478) ^ [_1303835, _1303837, _1303839] : [class_Orderings_Olinorder(_1303835), 28277 ^ _780478 : [(28284 ^ _780478) ^ [] : [_1303837 = _1303839, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1303835), _1303837) = hAPP(c_SetInterval_Oord__class_OatLeast(_1303835), _1303839))], (28278 ^ _780478) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1303835), _1303837) = hAPP(c_SetInterval_Oord__class_OatLeast(_1303835), _1303839), -(_1303837 = _1303839)]]], (33983 ^ _780478) ^ [_1422214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422214), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1422214)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28502 ^ _780478) ^ [_1308011, _1308013, _1308015, _1308017] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1308011, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1308013)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1308011, tc_HOL_Obool), tc_Nat_Onat), _1308015), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1308017))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1308011, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1308017, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1308013), _1308017))), _1308015))], (28404 ^ _780478) ^ [_1306094, _1306096] : [class_Orderings_Olinorder(_1306094), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1306094, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1306094), _1306096)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1306094), _1306096))], (29215 ^ _780478) ^ [_1322736, _1322738, _1322740, _1322742] : [class_Divides_Oring__div(_1322736), -(c_Divides_Odiv__class_Omod(_1322736, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322736), _1322738), _1322740), _1322742) = c_Divides_Odiv__class_Omod(_1322736, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1322736), c_Divides_Odiv__class_Omod(_1322736, _1322738, _1322742)), _1322740), _1322742))], (38770 ^ _780478) ^ [_1528264, _1528266, _1528268] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1528264, _1528266), _1528268), hAPP(c_COMBK(tc_fun(_1528266, tc_HOL_Obool), _1528264), c_Orderings_Obot__class_Obot(tc_fun(_1528266, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1528264, _1528266), tc_HOL_Obool)))], (42732 ^ _780478) ^ [_1632260, _1632262, _1632264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632260), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632262)), _1632264))), -(hAPP(hAPP(c_List_Otake(_1632262), _1632260), c_List_Obutlast(_1632262, _1632264)) = hAPP(hAPP(c_List_Otake(_1632262), _1632260), _1632264))], (35339 ^ _780478) ^ [_1446563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446563)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446563), c_Int_OMin)))], (5114 ^ _780478) ^ [_858616, _858618] : [_858618 = _858616, -(c_Fun_Oid(_858618) = c_Fun_Oid(_858616))], (3706 ^ _780478) ^ [_835956, _835958, _835960, _835962] : [-(c_List_Oremdups(_835962, _835958) = c_List_Oremdups(_835960, _835956)), _835962 = _835960, _835958 = _835956], (18542 ^ _780478) ^ [_1128225, _1128227, _1128229, _1128231] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1128225, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1128227, tc_fun(_1128225, tc_HOL_Obool)), _1128229), _1128231)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1128227, tc_fun(_1128225, tc_HOL_Obool)), _1128229), hAPP(hAPP(c_COMBB(tc_fun(_1128225, tc_HOL_Obool), tc_fun(_1128225, tc_HOL_Obool), _1128227), c_Groups_Ouminus__class_Ouminus(tc_fun(_1128225, tc_HOL_Obool))), _1128231)))], (5292 ^ _780478) ^ [_861349, _861351, _861353, _861355] : [-(c_List_Oupt(_861355, _861351) = c_List_Oupt(_861353, _861349)), _861355 = _861353, _861351 = _861349], (33362 ^ _780478) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (17769 ^ _780478) ^ [_1111432, _1111434, _1111436, _1111438, _1111440, _1111442, _1111444, _1111446] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1111432, tc_fun(_1111434, tc_fun(_1111436, tc_HOL_Obool))), _1111438), _1111440), _1111442), _1111444)), hBOOL(hAPP(hAPP(c_member(_1111432), _1111446), _1111438)), -(hBOOL(hAPP(hAPP(hAPP(_1111440, _1111446), _1111442), _1111444)))], (51639 ^ _780478) ^ [_1825566, _1825568, _1825570, _1825572] : [class_Divides_Osemiring__div(_1825566), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825566), _1825568), c_Divides_Odiv__class_Omod(_1825566, _1825570, _1825572))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825566), _1825568), _1825572)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825566), _1825568), _1825570)))], (13030 ^ _780478) ^ [_1011306, _1011308, _1011310, _1011312] : [hBOOL(hAPP(hAPP(c_member(_1011306), _1011308), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1011306, tc_HOL_Obool)), _1011310), _1011312))), -(hBOOL(hAPP(hAPP(c_member(_1011306), _1011308), _1011310))), -(hBOOL(hAPP(hAPP(c_member(_1011306), _1011308), _1011312)))], (2986 ^ _780478) ^ [_824700, _824702] : [_824702 = _824700, -(c_Nitpick_ORep__Frac(_824702) = c_Nitpick_ORep__Frac(_824700))], (28969 ^ _780478) ^ [_1317200, _1317202] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1317200), _1317202)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1317200, tc_HOL_Obool)), hAPP(c_Set_OPow(_1317200), _1317202)) = 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(_1317200), _1317202)))], (49060 ^ _780478) ^ [_1770881, _1770883, _1770885] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770881) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1770881, _1770883, _1770885)], (37235 ^ _780478) ^ [_1488963, _1488965, _1488967, _1488969, _1488971] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1488963, _1488965, _1488967), _1488969), _1488971) = hAPP(hAPP(_1488969, hAPP(c_Product__Type_Ofst(_1488963, _1488965), _1488971)), hAPP(c_Product__Type_Osnd(_1488963, _1488965), _1488971)))], (264 ^ _780478) ^ [_784568, _784570, _784572, _784574] : [-(c_Nitpick_Orefl_H(_784572, _784568)), c_Nitpick_Orefl_H(_784574, _784570), _784574 = _784572, _784570 = _784568], (10981 ^ _780478) ^ [_971946, _971948, _971950, _971952] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_971946), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971946), hAPP(hAPP(c_Orderings_Oord__class_Omax(_971946), _971948), _971950)), _971952) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_971946), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971946), _971948), _971952)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971946), _971950), _971952)))], (47621 ^ _780478) ^ [_1739197, _1739199] : [-(c_Wellfounded_Owf(_1739197, c_List_Omeasures(_1739197, _1739199)))], (18976 ^ _780478) ^ [_1136677, _1136679] : [class_Lattices_Olattice(_1136677), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136677), _1136679)), -(_1136679 = c_Orderings_Obot__class_Obot(tc_fun(_1136677, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1136677), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1136677), 18989 ^ [_1136677, _1136679]), 18990 ^ [_1136677, _1136679])), hAPP(hAPP(c_Set_Oinsert(_1136677), 18989 ^ [_1136677, _1136679]), hAPP(hAPP(c_Set_Oinsert(_1136677), 18990 ^ [_1136677, _1136679]), c_Orderings_Obot__class_Obot(tc_fun(_1136677, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1136677), c_Big__Operators_Olattice__class_OInf__fin(_1136677, _1136679)), _1136679)))], (5827 ^ _780478) ^ [_872772, _872774, _872776, _872778, _872780, _872782] : [_872772 = hAPP(_872774, _872776), hBOOL(hAPP(hAPP(c_member(_872778), _872776), _872780)), -(hBOOL(hAPP(hAPP(c_member(_872782), _872772), hAPP(c_Set_Oimage(_872778, _872782, _872774), _872780))))], (34991 ^ _780478) ^ [_1439706, _1439708, _1439710] : [class_Rings_Oring__1(_1439706), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1439706), hAPP(c_Groups_Ouminus__class_Ouminus(_1439706), _1439708)), 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)))), _1439710)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1439706), _1439708), 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)))), _1439710)))], (35814 ^ _780478) ^ [_1460478, _1460480, _1460482, _1460484] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1460478, _1460480), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1460482), _1460484))), -(_1460480 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1460478, _1460480) = _1460484)], (24181 ^ _780478) ^ [_1230648, _1230650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1230648), 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)), _1230650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1230648), _1230650)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (43063 ^ _780478) ^ [_1639296, _1639298] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639296)), _1639298) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1639298 = c_List_Olist_ONil(_1639296))], (37911 ^ _780478) ^ [_1505587] : [-(_1505587 = 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), 37908 ^ [_1505587]), 37909 ^ [_1505587])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (9146 ^ _780478) ^ [_937505, _937507, _937509] : [class_Orderings_Oorder(_937505), -(_937507 = _937509), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937505), _937509), _937507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_937505), _937509), _937507)))], (50056 ^ _780478) ^ [_1792278, _1792280, _1792282, _1792284, _1792286, _1792288] : [hAPP(c_Hilbert__Choice_Oinv__into(_1792278, _1792280, _1792282, _1792284), _1792286) = hAPP(c_Hilbert__Choice_Oinv__into(_1792278, _1792280, _1792282, _1792284), _1792288), hBOOL(hAPP(hAPP(c_member(_1792280), _1792286), hAPP(c_Set_Oimage(_1792278, _1792280, _1792284), _1792282))), hBOOL(hAPP(hAPP(c_member(_1792280), _1792288), hAPP(c_Set_Oimage(_1792278, _1792280, _1792284), _1792282))), -(_1792286 = _1792288)], (44139 ^ _780478) ^ [_1663861] : [-(c_List_Orotate(_1663861, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1663861)))], (25196 ^ _780478) ^ [_1248649, _1248651, _1248653, _1248655, _1248657] : [class_Groups_Oordered__ab__group__add(_1248649), hBOOL(hAPP(c_Finite__Set_Ofinite(_1248651), _1248653)), 25206 ^ _780478 : [(25209 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248649), c_Groups_Ozero__class_Ozero(_1248649)), hAPP(_1248655, 25205 ^ [_1248649, _1248651, _1248653, _1248655, _1248657])))], (25207 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1248651), 25205 ^ [_1248649, _1248651, _1248653, _1248655, _1248657]), _1248653)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1248651, _1248649), _1248655), _1248653) = c_Groups_Ozero__class_Ozero(_1248649), hBOOL(hAPP(hAPP(c_member(_1248651), _1248657), _1248653)), -(hAPP(_1248655, _1248657) = c_Groups_Ozero__class_Ozero(_1248649))], (39624 ^ _780478) ^ [_1551819, _1551821, _1551823] : [-(hAPP(c_Fun_Ocomp(_1551819, _1551821, _1551819, _1551823), c_Fun_Oid(_1551819)) = _1551823)], (48643 ^ _780478) ^ [_1761737, _1761739, _1761741, _1761743] : [-(hAPP(hAPP(c_List_Oappend(_1761737), c_List_Oreplicate(_1761737, _1761739, _1761741)), c_List_Oreplicate(_1761737, _1761743, _1761741)) = hAPP(hAPP(c_List_Oappend(_1761737), c_List_Oreplicate(_1761737, _1761743, _1761741)), c_List_Oreplicate(_1761737, _1761739, _1761741)))], (33694 ^ _780478) ^ [_1416105, _1416107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416105)), hAPP(c_Nat_OSuc, _1416107))), -(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(_1416105))), 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)), _1416107)))))], (49764 ^ _780478) ^ [_1786880, _1786882, _1786884, _1786886] : [c_Relation_Osym(_1786880, _1786882), -(c_Relation_Osym(_1786884, hAPP(hAPP(c_Relation_Oinv__image(_1786880, _1786884), _1786882), _1786886)))], (13472 ^ _780478) ^ [_1020660, _1020662, _1020664, _1020666] : [class_Lattices_Osemilattice__sup(_1020660), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020660), _1020662)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1020660, _1020660, c_Lattices_Osemilattice__sup__class_Osup(_1020660)), _1020664), hAPP(hAPP(c_Set_Oinsert(_1020660), _1020666), _1020662)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1020660), _1020666), hAPP(hAPP(c_Finite__Set_Ofold(_1020660, _1020660, c_Lattices_Osemilattice__sup__class_Osup(_1020660)), _1020664), _1020662)))], (38708 ^ _780478) ^ [_1526740, _1526742, _1526744, _1526746, _1526748] : [hBOOL(hAPP(hAPP(_1526740, _1526742), _1526744)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1526746, _1526748, _1526740), _1526742)))], (40851 ^ _780478) ^ [_1580373, _1580375, _1580377, _1580379, _1580381] : [-(hAPP(c_Relation_Oconverse(_1580373, _1580375), hAPP(hAPP(c_Relation_Orel__comp(_1580373, _1580377, _1580375), _1580379), _1580381)) = hAPP(hAPP(c_Relation_Orel__comp(_1580375, _1580377, _1580373), hAPP(c_Relation_Oconverse(_1580377, _1580375), _1580381)), hAPP(c_Relation_Oconverse(_1580373, _1580377), _1580379)))], (35553 ^ _780478) ^ [_1449786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1449786)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1449786) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1449786), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (43475 ^ _780478) ^ [_1648260, _1648262, _1648264, _1648266, _1648268] : [hAPP(hAPP(c_List_Oappend(_1648260), _1648262), _1648264) = hAPP(hAPP(c_List_Oappend(_1648260), _1648266), _1648268), 43481 ^ _780478 : [(43484 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1648260), 43478 ^ [_1648260, _1648262, _1648264, _1648266, _1648268]), _1648264) = _1648268)], (43482 ^ _780478) ^ [] : [-(_1648262 = hAPP(hAPP(c_List_Oappend(_1648260), _1648266), 43478 ^ [_1648260, _1648262, _1648264, _1648266, _1648268]))]], 43485 ^ _780478 : [(43488 ^ _780478) ^ [] : [-(_1648264 = hAPP(hAPP(c_List_Oappend(_1648260), 43478 ^ [_1648260, _1648262, _1648264, _1648266, _1648268]), _1648268))], (43486 ^ _780478) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1648260), _1648262), 43478 ^ [_1648260, _1648262, _1648264, _1648266, _1648268]) = _1648266)]]], (41712 ^ _780478) ^ [_1603218, _1603220, _1603222] : [-(hAPP(c_List_Olexn(_1603218, _1603220), hAPP(c_Nat_OSuc, _1603222)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1603218), tc_List_Olist(_1603218)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1603218, tc_List_Olist(_1603218)), tc_prod(_1603218, tc_List_Olist(_1603218))), tc_prod(tc_List_Olist(_1603218), tc_List_Olist(_1603218)), c_Product__Type_Omap__pair(tc_prod(_1603218, tc_List_Olist(_1603218)), tc_List_Olist(_1603218), tc_prod(_1603218, tc_List_Olist(_1603218)), tc_List_Olist(_1603218), hAPP(c_Product__Type_Oprod_Oprod__case(_1603218, tc_List_Olist(_1603218), tc_List_Olist(_1603218)), c_List_Olist_OCons(_1603218)), hAPP(c_Product__Type_Oprod_Oprod__case(_1603218, tc_List_Olist(_1603218), tc_List_Olist(_1603218)), c_List_Olist_OCons(_1603218)))), c_Wellfounded_Olex__prod(_1603218, tc_List_Olist(_1603218), _1603220, hAPP(c_List_Olexn(_1603218, _1603220), _1603222)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1603218), tc_List_Olist(_1603218))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1603218), tc_List_Olist(_1603218), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1603218), tc_fun(tc_List_Olist(_1603218), tc_HOL_Obool), tc_fun(tc_List_Olist(_1603218), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1603218), tc_HOL_Obool), tc_fun(tc_List_Olist(_1603218), tc_HOL_Obool)), tc_List_Olist(_1603218)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1603218))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1603218)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1603218), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1603218)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1603218)))), hAPP(c_Nat_OSuc, _1603222))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1603218), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1603218)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1603218)))), hAPP(c_Nat_OSuc, _1603222)))))))], (41225 ^ _780478) ^ [_1590055, _1590057, _1590059] : [41226 ^ _780478 : [(41227 ^ _780478) ^ [_1590131] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590055, _1590055)), _1590057), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590055, _1590055), tc_HOL_Obool), _1590131), _1590059)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590055, _1590055)), _1590057), c_Transitive__Closure_Ortrancl(_1590055, _1590059))))], (7882 ^ _780478) ^ [_914186, _914188, _914190, _914192] : [-(c_Fun_Ooverride__on(_914186, _914188, _914190, _914192, c_Orderings_Obot__class_Obot(tc_fun(_914186, tc_HOL_Obool))) = _914190)], (30378 ^ _780478) ^ [_1344266, _1344268, _1344270] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1344266, tc_HOL_Obool)), _1344268), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1344266, tc_HOL_Obool), _1344270)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1344266, tc_HOL_Obool), tc_fun(_1344266, tc_HOL_Obool)), _1344270), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1344266, tc_HOL_Obool)), _1344268)))], (6854 ^ _780478) ^ [_893821, _893823] : [-(c_HOL_OThe(_893821, hAPP(hAPP(c_COMBC(_893821, _893821, tc_HOL_Obool), c_fequal), _893823)) = _893823)], (44017 ^ _780478) ^ [_1661399, _1661401, _1661403, _1661405] : [-(hAPP(c_List_Orotate1(_1661401), hAPP(hAPP(c_List_Olist_OCons(_1661401), _1661403), _1661405)) = hAPP(hAPP(c_List_Oappend(_1661401), _1661405), hAPP(hAPP(c_List_Olist_OCons(_1661401), _1661403), c_List_Olist_ONil(_1661401))))], (34029 ^ _780478) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (31562 ^ _780478) ^ [_1374106, _1374108, _1374110] : [class_Lattices_Odistrib__lattice(_1374106), hBOOL(hAPP(c_Finite__Set_Ofinite(_1374106), _1374108)), -(_1374108 = c_Orderings_Obot__class_Obot(tc_fun(_1374106, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1374106), _1374110), c_Big__Operators_Olattice__class_OSup__fin(_1374106, _1374108)) = c_Big__Operators_Olattice__class_OSup__fin(_1374106, hAPP(c_Set_OCollect(_1374106), hAPP(hAPP(c_COMBB(tc_fun(_1374106, tc_HOL_Obool), tc_HOL_Obool, _1374106), c_HOL_OEx(_1374106)), hAPP(hAPP(c_COMBC(_1374106, tc_fun(_1374106, tc_HOL_Obool), tc_fun(_1374106, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374106, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1374106, tc_HOL_Obool), tc_fun(_1374106, tc_HOL_Obool)), _1374106), c_COMBS(_1374106, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374106, tc_HOL_Obool), tc_fun(_1374106, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1374106), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1374106), c_fconj)), hAPP(hAPP(c_COMBC(_1374106, tc_fun(_1374106, _1374106), tc_fun(_1374106, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374106, tc_HOL_Obool), tc_fun(tc_fun(_1374106, _1374106), tc_fun(_1374106, tc_HOL_Obool)), _1374106), c_COMBB(_1374106, tc_HOL_Obool, _1374106)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1374106), _1374110))))), hAPP(hAPP(c_COMBC(_1374106, tc_fun(_1374106, tc_HOL_Obool), tc_HOL_Obool), c_member(_1374106)), _1374108))))))], (40568 ^ _780478) ^ [_1574087, _1574089] : [-(c_Transitive__Closure_Ortrancl(_1574087, c_Transitive__Closure_Ortrancl(_1574087, _1574089)) = c_Transitive__Closure_Ortrancl(_1574087, _1574089))], (43782 ^ _780478) ^ [_1655491, _1655493, _1655495, _1655497, _1655499, _1655501] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655491), tc_List_Olist(_1655491))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655491), tc_List_Olist(_1655491)), hAPP(hAPP(c_List_Oappend(_1655491), _1655493), hAPP(hAPP(c_List_Olist_OCons(_1655491), _1655495), c_List_Olist_ONil(_1655491)))), hAPP(hAPP(c_List_Oappend(_1655491), _1655497), hAPP(hAPP(c_List_Olist_OCons(_1655491), _1655499), c_List_Olist_ONil(_1655491))))), c_List_Olistrel1(_1655491, _1655501)))), 43783 ^ _780478 : [(43790 ^ _780478) ^ [] : [_1655493 = _1655497, hBOOL(hAPP(hAPP(c_member(tc_prod(_1655491, _1655491)), hAPP(hAPP(c_Product__Type_OPair(_1655491, _1655491), _1655495), _1655499)), _1655501))], (43784 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1655491), tc_List_Olist(_1655491))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1655491), tc_List_Olist(_1655491)), _1655493), _1655497)), c_List_Olistrel1(_1655491, _1655501))), _1655495 = _1655499]]], (52063 ^ _780478) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (44145 ^ _780478) ^ [_1663991, _1663993, _1663995] : [-(hAPP(c_List_Oset(_1663991), hAPP(c_List_Orotate(_1663991, _1663993), _1663995)) = hAPP(c_List_Oset(_1663991), _1663995))], (3380 ^ _780478) ^ [_830859, _830861, _830863, _830865] : [-(c_Enum_Osublists(_830865, _830861) = c_Enum_Osublists(_830863, _830859)), _830865 = _830863, _830861 = _830859], (22723 ^ _780478) ^ [_1203466] : [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, _1203466)))))], (28800 ^ _780478) ^ [_1313857, _1313859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1313857)), 28809 ^ _780478 : [(28812 ^ _780478) ^ [] : [hBOOL(hAPP(_1313859, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28805 ^ [_1313857, _1313859]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 28806 ^ [_1313857, _1313859]), _1313857))))], (28810 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1313859, 28805 ^ [_1313857, _1313859])))]], 28813 ^ _780478 : [(28816 ^ _780478) ^ [] : [hBOOL(hAPP(_1313859, 28805 ^ [_1313857, _1313859]))], (28814 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1313859, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28805 ^ [_1313857, _1313859]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 28806 ^ [_1313857, _1313859]), _1313857)))))]], 28817 ^ _780478 : [(28827 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1313859, 28834 ^ [_1313857, _1313859]))), 28828 ^ _780478 : [(28829 ^ _780478) ^ [_1314404] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1314404), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1313857))), hBOOL(hAPP(_1313859, _1314404))]]], (28818 ^ _780478) ^ [] : [28819 ^ _780478 : [(28820 ^ _780478) ^ [_1314289] : [hBOOL(hAPP(_1313859, _1314289))]], 28822 ^ _780478 : [(28825 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1313859, 28821 ^ [_1313857, _1313859])))], (28823 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28821 ^ [_1313857, _1313859]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1313857))))]]]]], (45945 ^ _780478) ^ [_1702973, _1702975, _1702977] : [-(c_List_Oconcat(_1702973, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1702973)), _1702975), _1702977)) = hAPP(hAPP(c_List_Oappend(_1702973), c_List_Oconcat(_1702973, _1702975)), c_List_Oconcat(_1702973, _1702977)))], (33278 ^ _780478) ^ [_1409145, _1409147] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1409145))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409145)), _1409147)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1409147))], (30500 ^ _780478) ^ [_1346453, _1346455, _1346457] : [class_Groups_Oordered__ab__group__add__abs(_1346453), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346453), hAPP(c_Groups_Oabs__class_Oabs(_1346453), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346453), _1346455), _1346457))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1346453), hAPP(c_Groups_Oabs__class_Oabs(_1346453), _1346455)), hAPP(c_Groups_Oabs__class_Oabs(_1346453), _1346457)))))], (34757 ^ _780478) ^ [] : [-(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))))], (33614 ^ _780478) ^ [_1414427, _1414429] : [class_Int_Onumber__ring(_1414427), -(hAPP(c_Int_Onumber__class_Onumber__of(_1414427), c_Int_Opred(_1414429)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414427), hAPP(c_Groups_Ouminus__class_Ouminus(_1414427), c_Groups_Oone__class_Oone(_1414427))), hAPP(c_Int_Onumber__class_Onumber__of(_1414427), _1414429)))], (49994 ^ _780478) ^ [_1791026, _1791028, _1791030] : [c_Fun_Oinj__on(_1791026, _1791028, _1791030, c_Orderings_Otop__class_Otop(tc_fun(_1791026, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1791028, _1791026, _1791026, c_Hilbert__Choice_Oinv__into(_1791026, _1791028, c_Orderings_Otop__class_Otop(tc_fun(_1791026, tc_HOL_Obool)), _1791030)), _1791030) = c_Fun_Oid(_1791026))], (42840 ^ _780478) ^ [_1634783, _1634785] : [hBOOL(hAPP(c_List_Odistinct(_1634783), _1634785)), 42843 ^ _780478 : [(42844 ^ _780478) ^ [_1634915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1634915), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634783)), _1634785))), 42847 ^ _780478 : [(42848 ^ _780478) ^ [_1635042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1635042), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1634783)), _1634785))), -(_1634915 = _1635042), hAPP(hAPP(c_List_Onth(_1634783), _1634785), _1634915) = hAPP(hAPP(c_List_Onth(_1634783), _1634785), _1635042)]]]]], (40518 ^ _780478) ^ [_1572876, _1572878] : [-(c_Transitive__Closure_Otrancl(_1572876, _1572878) = hAPP(hAPP(c_Relation_Orel__comp(_1572876, _1572876, _1572876), _1572878), c_Transitive__Closure_Ortrancl(_1572876, _1572878)))], (23369 ^ _780478) ^ [_1215102, _1215104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215104)), -(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), _1215102), _1215104))))], (18051 ^ _780478) ^ [_1116483, _1116485] : [class_Complete__Lattice_Ocomplete__lattice(_1116483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1116483), _1116485)), -(_1116485 = c_Orderings_Obot__class_Obot(tc_fun(_1116483, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1116483, _1116485) = c_Complete__Lattice_OInf__class_OInf(_1116483, _1116485))], (34571 ^ _780478) ^ [_1432314, _1432316] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1432314)), c_Int_OBit0(_1432316)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1432314), _1432316)))], (47576 ^ _780478) ^ [_1737974, _1737976] : [-(c_List_Oinsert(_1737974, _1737976, c_List_Olist_ONil(_1737974)) = hAPP(hAPP(c_List_Olist_OCons(_1737974), _1737976), c_List_Olist_ONil(_1737974)))], (43207 ^ _780478) ^ [_1642041, _1642043, _1642045, _1642047] : [_1642041 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1642043), _1642041), hAPP(hAPP(c_List_Olist_OCons(_1642043), _1642045), _1642047)) = c_List_Olist_ONil(_1642043))], (16086 ^ _780478) ^ [_1071632, _1071634, _1071636, _1071638, _1071640] : [hBOOL(hAPP(hAPP(c_member(_1071632), _1071634), hAPP(c_Set_Ovimage(_1071632, _1071636, _1071638), _1071640))), -(hBOOL(hAPP(hAPP(c_member(_1071636), hAPP(_1071638, _1071634)), _1071640)))], (20380 ^ _780478) ^ [_1160532, _1160534, _1160536] : [class_Rings_Olinordered__semiring__strict(_1160532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160532), c_Groups_Ozero__class_Ozero(_1160532)), _1160534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160532), _1160536), c_Groups_Ozero__class_Ozero(_1160532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1160532), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160532), _1160534), _1160536)), c_Groups_Ozero__class_Ozero(_1160532))))], (3730 ^ _780478) ^ [_836326, _836328, _836330, _836332, _836334, _836336, _836338, _836340] : [-(c_List_Omaps(_836340, _836336, _836332, _836328) = c_List_Omaps(_836338, _836334, _836330, _836326)), _836340 = _836338, _836336 = _836334, _836332 = _836330, _836328 = _836326], (45835 ^ _780478) ^ [_1700632, _1700634] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700632)), c_List_Oremdups(_1700632, _1700634)) = hAPP(c_Finite__Set_Ocard(_1700632), hAPP(c_List_Oset(_1700632), _1700634)))], (50679 ^ _780478) ^ [_1805676, _1805678] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805676), _1805678)), -(c_Fun_Obij__betw(_1805676, tc_Nat_Onat, 50682 ^ [_1805676, _1805678], _1805678, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1805676), _1805678))))], (51481 ^ _780478) ^ [_1822996, _1822998] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822996, _1822998), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822996), _1822998))], (4204 ^ _780478) ^ [_844117, _844119] : [_844119 = _844117, -(c_List_Otl(_844119) = c_List_Otl(_844117))], (41466 ^ _780478) ^ [_1596805, _1596807] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1596805, _1596805)), _1596807), c_Relation_OId(_1596805))), -(_1596807 = hAPP(hAPP(c_Product__Type_OPair(_1596805, _1596805), 41469 ^ [_1596805, _1596807]), 41469 ^ [_1596805, _1596807]))], (46851 ^ _780478) ^ [_1722672, _1722674, _1722676, _1722678] : [class_Orderings_Olinorder(_1722672), c_List_Olinorder__class_Osorted(_1722672, _1722674), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1722676), _1722678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722678), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722672)), _1722674))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1722672), hAPP(hAPP(c_List_Onth(_1722672), _1722674), _1722676)), hAPP(hAPP(c_List_Onth(_1722672), _1722674), _1722678))))], (38281 ^ _780478) ^ [_1515776, _1515778] : [c_Wellfounded_Owf(_1515776, _1515778), -(c_Wellfounded_Owf(tc_fun(_1515776, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1515776, _1515778)))], (47847 ^ _780478) ^ [_1744687, _1744689, _1744691, _1744693, _1744695] : [-(hAPP(hAPP(c_List_Olist_OCons(_1744687), _1744689), _1744691) = hAPP(c_List_Ofilter(_1744687, _1744693), _1744695)), 47848 ^ _780478 : [(47849 ^ _780478) ^ [_1744815, _1744817] : [_1744695 = hAPP(hAPP(c_List_Oappend(_1744687), _1744817), hAPP(hAPP(c_List_Olist_OCons(_1744687), _1744689), _1744815)), 47855 ^ _780478 : [(47858 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1744693, 47854 ^ [_1744687, _1744689, _1744691, _1744693, _1744695, _1744815, _1744817])))], (47856 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744687), 47854 ^ [_1744687, _1744689, _1744691, _1744693, _1744695, _1744815, _1744817]), hAPP(c_List_Oset(_1744687), _1744817))))]], hBOOL(hAPP(_1744693, _1744689)), _1744691 = hAPP(c_List_Ofilter(_1744687, _1744693), _1744815)]]], (36262 ^ _780478) ^ [_1470101, _1470103, _1470105, _1470107, _1470109, _1470111] : [hBOOL(hAPP(hAPP(_1470101, _1470103), _1470105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470107, tc_fun(_1470109, tc_HOL_Obool))), _1470101), _1470111)), -(hBOOL(hAPP(hAPP(_1470111, _1470103), _1470105)))], (42113 ^ _780478) ^ [_1615662, _1615664, _1615666] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615662)), _1615664), c_List_Olists(_1615662, c_Wellfounded_Oacc(_1615662, _1615666)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615662)), _1615664), c_Wellfounded_Oacc(tc_List_Olist(_1615662), c_List_Olistrel1(_1615662, _1615666)))))], (35097 ^ _780478) ^ [_1441936, _1441938] : [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), _1441936))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1441938))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1441936))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441938)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1441936)))], (22713 ^ _780478) ^ [_1203259, _1203261] : [22714 ^ _780478 : [(22715 ^ _780478) ^ [_1203315] : [_1203261 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1203259), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1203315)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1203259), _1203261)))], (21151 ^ _780478) ^ [_1173582, _1173584, _1173586] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173582), _1173584)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1173582), _1173586)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173582)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173584), _1173586))], (52157 ^ _780478) ^ [_1831610] : [-(class_Nat_Osize(tc_List_Olist(_1831610)))], (21011 ^ _780478) ^ [_1171438, _1171440] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1171438), _1171440) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21016 ^ _780478 : [(21019 ^ _780478) ^ [] : [-(_1171440 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21017 ^ _780478) ^ [] : [-(_1171438 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 21020 ^ _780478 : [(21023 ^ _780478) ^ [] : [-(_1171440 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21021 ^ _780478) ^ [] : [-(_1171438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23781 ^ _780478) ^ [_1222731, _1222733, _1222735] : [class_Orderings_Olinorder(_1222731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222731), _1222733), _1222735)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222731, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1222731), _1222733)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222731, _1222733), _1222735)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1222731), _1222735))], (33062 ^ _780478) ^ [_1405331, _1405333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405331)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1405333))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405331), _1405333)))], (34007 ^ _780478) ^ [_1422606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422606), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1422606)), c_Int_OPls)))], (4412 ^ _780478) ^ [_847393, _847395] : [_847395 = _847393, -(c_Lazy__Sequence_Oempty(_847395) = c_Lazy__Sequence_Oempty(_847393))], (3688 ^ _780478) ^ [_835701, _835703] : [_835703 = _835701, -(c_List_Oreturn__list(_835703) = c_List_Oreturn__list(_835701))], (44925 ^ _780478) ^ [_1680841, _1680843, _1680845] : [c_Fun_Oinj__on(tc_List_Olist(_1680841), tc_List_Olist(_1680843), hAPP(c_List_Omap(_1680841, _1680843), _1680845), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1680841), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1680841, _1680843, _1680845, c_Orderings_Otop__class_Otop(tc_fun(_1680841, tc_HOL_Obool))))], (25904 ^ _780478) ^ [_1260673, _1260675] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1260673), _1260675)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1260675), _1260673)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1260675)), hAPP(c_Int_Onat, _1260673)))], (42646 ^ _780478) ^ [_1630351, _1630353, _1630355, _1630357] : [_1630351 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630353)), _1630355)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1630353, hAPP(hAPP(c_List_Olist__update(_1630353, _1630355), _1630351), _1630357)) = c_List_Obutlast(_1630353, _1630355))], (29461 ^ _780478) ^ [_1327522, _1327524] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327522, _1327524) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1327522 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1327524), 29464 ^ [_1327522, _1327524]))], (35251 ^ _780478) ^ [] : [c_Int_OPls = c_Int_OMin], (32730 ^ _780478) ^ [_1398710, _1398712] : [class_Int_Onumber__ring(_1398710), class_Rings_Olinordered__idom(_1398710), 32737 ^ _780478 : [(32744 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398710), hAPP(c_Int_Onumber__class_Onumber__of(_1398710), _1398712)), c_Groups_Ozero__class_Ozero(_1398710)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1398710), hAPP(c_Int_Onumber__class_Onumber__of(_1398710), _1398712)) = hAPP(c_Int_Onumber__class_Onumber__of(_1398710), _1398712))], (32738 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1398710), hAPP(c_Int_Onumber__class_Onumber__of(_1398710), _1398712)), c_Groups_Ozero__class_Ozero(_1398710))), -(hAPP(c_Groups_Oabs__class_Oabs(_1398710), hAPP(c_Int_Onumber__class_Onumber__of(_1398710), _1398712)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1398710), hAPP(c_Int_Onumber__class_Onumber__of(_1398710), _1398712)))]]], (34659 ^ _780478) ^ [_1433894, _1433896] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433894), _1433896)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1433894)), c_Int_OBit1(_1433896))))], (4210 ^ _780478) ^ [_844202, _844204] : [_844204 = _844202, -(c_List_Orev(_844204) = c_List_Orev(_844202))], (41973 ^ _780478) ^ [_1611522, _1611524, _1611526, _1611528] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611522), tc_List_Olist(_1611522))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611522), tc_List_Olist(_1611522)), _1611524), _1611526)), c_List_Olistrel1(_1611522, _1611528))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611522), tc_List_Olist(_1611522))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611522), tc_List_Olist(_1611522)), _1611524), _1611526)), c_List_Olistrel(_1611522, c_Transitive__Closure_Ortrancl(_1611522, _1611528)))))], (34229 ^ _780478) ^ [_1426071, _1426073] : [class_Int_Onumber__ring(_1426071), class_Rings_Olinordered__idom(_1426071), 34236 ^ _780478 : [(34243 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1426073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1426071), c_Groups_Oone__class_Oone(_1426071)), hAPP(c_Int_Onumber__class_Onumber__of(_1426071), _1426073))))], (34237 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1426071), c_Groups_Oone__class_Oone(_1426071)), hAPP(c_Int_Onumber__class_Onumber__of(_1426071), _1426073))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1426073)))]]], (42264 ^ _780478) ^ [_1619818, _1619820, _1619822] : [-(hAPP(c_List_Oset(_1619818), c_List_Osublist(_1619818, _1619820, _1619822)) = hAPP(c_Set_OCollect(_1619818), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1619818), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1619818, 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)), _1619818), 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)), _1619818), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1619818, tc_fun(tc_Nat_Onat, _1619818), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1619818, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1619818), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1619818), c_COMBB(_1619818, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1619818), _1619820))))), 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(_1619818)), _1619820)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1619822))))))], (15783 ^ _780478) ^ [_1065973, _1065975, _1065977, _1065979, _1065981] : [class_Lattices_Olattice(_1065973), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1065975, _1065973)), _1065977), _1065979), _1065981) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065973), hAPP(_1065977, _1065981)), hAPP(_1065979, _1065981)))], (13859 ^ _780478) ^ [_1028282, _1028284] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1028282), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1028284), _1028282))))], (2848 ^ _780478) ^ [_822633, _822635, _822637, _822639] : [-(c_Relation_ODomain(_822639, _822635) = c_Relation_ODomain(_822637, _822633)), _822639 = _822637, _822635 = _822633], (28472 ^ _780478) ^ [_1307369, _1307371, _1307373, _1307375] : [class_Orderings_Olinorder(_1307369), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307369, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1307369, _1307371, _1307373)), hAPP(c_SetInterval_Oord__class_OatMost(_1307369), _1307375)) = c_SetInterval_Oord__class_OatLeastAtMost(_1307369, _1307371, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1307369), _1307373), _1307375)))], (12009 ^ _780478) ^ [_991478, _991480, _991482] : [class_Orderings_Olinorder(_991478), hBOOL(hAPP(c_Finite__Set_Ofinite(_991478), _991480)), hBOOL(hAPP(hAPP(c_member(_991478), _991482), _991480)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_991478), _991482), c_Big__Operators_Olattice_OSup__fin(_991478, c_Orderings_Oord__class_Omax(_991478), _991480)) = _991482)], (48202 ^ _780478) ^ [_1752125, _1752127] : [-(c_FunDef_Ois__measure(_1752125, _1752127))], (49666 ^ _780478) ^ [_1785069, _1785071, _1785073, _1785075] : [c_Relation_Osym(_1785069, _1785071), hBOOL(hAPP(hAPP(c_member(tc_prod(_1785069, _1785069)), hAPP(hAPP(c_Product__Type_OPair(_1785069, _1785069), _1785073), _1785075)), _1785071)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785069, _1785069)), hAPP(hAPP(c_Product__Type_OPair(_1785069, _1785069), _1785075), _1785073)), _1785071)))], (26460 ^ _780478) ^ [_1270922, _1270924, _1270926, _1270928] : [class_Fields_Ofield__inverse__zero(_1270922), 26463 ^ _780478 : [(26464 ^ _780478) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270922), _1270924), _1270926) = _1270928, 26467 ^ _780478 : [(26474 ^ _780478) ^ [] : [_1270926 = c_Groups_Ozero__class_Ozero(_1270922), -(_1270928 = c_Groups_Ozero__class_Ozero(_1270922))], (26468 ^ _780478) ^ [] : [-(_1270926 = c_Groups_Ozero__class_Ozero(_1270922)), -(_1270924 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270922), _1270928), _1270926))]]], (26480 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270922), _1270924), _1270926) = _1270928), 26483 ^ _780478 : [(26486 ^ _780478) ^ [] : [_1270924 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270922), _1270928), _1270926)], (26484 ^ _780478) ^ [] : [_1270926 = c_Groups_Ozero__class_Ozero(_1270922)]], 26487 ^ _780478 : [(26490 ^ _780478) ^ [] : [_1270928 = c_Groups_Ozero__class_Ozero(_1270922)], (26488 ^ _780478) ^ [] : [-(_1270926 = c_Groups_Ozero__class_Ozero(_1270922))]]]]], (36714 ^ _780478) ^ [_1478424, _1478426, _1478428, _1478430, _1478432, _1478434, _1478436] : [c_Equiv__Relations_Oequiv(_1478424, _1478426, _1478428), c_Equiv__Relations_Ocongruent(_1478424, tc_fun(_1478430, tc_HOL_Obool), _1478428, _1478432), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478424, tc_fun(_1478430, tc_HOL_Obool)), _1478434), _1478432) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1478424, tc_fun(_1478430, tc_HOL_Obool)), _1478436), _1478432), hBOOL(hAPP(hAPP(c_member(tc_fun(_1478424, tc_HOL_Obool)), _1478434), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1478424), _1478426), _1478428))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1478424, tc_HOL_Obool)), _1478436), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1478424), _1478426), _1478428))), 36736 ^ _780478 : [(36740 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1478424), 36738 ^ [_1478424, _1478426, _1478428, _1478430, _1478432, _1478434, _1478436]), _1478426)))], (36742 ^ _780478) ^ [] : [-(hAPP(_1478432, 36735 ^ [_1478424, _1478426, _1478428, _1478430, _1478432, _1478434, _1478436]) = hAPP(_1478432, 36738 ^ [_1478424, _1478426, _1478428, _1478430, _1478432, _1478434, _1478436]))], (36744 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1478424, _1478424)), hAPP(hAPP(c_Product__Type_OPair(_1478424, _1478424), 36735 ^ [_1478424, _1478426, _1478428, _1478430, _1478432, _1478434, _1478436]), 36738 ^ [_1478424, _1478426, _1478428, _1478430, _1478432, _1478434, _1478436])), _1478428))], (36737 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1478424), 36735 ^ [_1478424, _1478426, _1478428, _1478430, _1478432, _1478434, _1478436]), _1478426)))]], -(_1478434 = _1478436)], (47580 ^ _780478) ^ [_1738063, _1738065, _1738067, _1738069] : [-(c_List_Oconcat(_1738063, hAPP(hAPP(c_List_Omap(_1738065, tc_List_Olist(_1738063)), _1738067), _1738069)) = c_List_Omaps(_1738065, _1738063, _1738067, _1738069))], (38681 ^ _780478) ^ [_1525465, _1525467] : [-(hAPP(c_Relation_OField(_1525465), _1525467) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525465, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1525465, _1525465), _1525467)), hAPP(c_Relation_ORange(_1525465, _1525465), _1525467)))], (52101 ^ _780478) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (14259 ^ _780478) ^ [_1035282, _1035284, _1035286, _1035288] : [class_Groups_Ocomm__monoid__mult(_1035282), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1035284), _1035286))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1035284, _1035282), _1035288), _1035286) = c_Groups_Oone__class_Oone(_1035282))], (49393 ^ _780478) ^ [_1779253, _1779255, _1779257, _1779259] : [class_Complete__Lattice_Ocomplete__lattice(_1779253), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1779255, _1779253), _1779257), _1779259) = c_Complete__Lattice_OInf__class_OInf(_1779253, hAPP(c_Set_OCollect(_1779253), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779255, _1779253), tc_HOL_Obool), tc_HOL_Obool, _1779253), c_HOL_OEx(tc_fun(_1779255, _1779253))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1779255, _1779253), tc_HOL_Obool), tc_fun(tc_fun(_1779255, _1779253), tc_HOL_Obool), _1779253), hAPP(c_COMBS(tc_fun(_1779255, _1779253), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1779255, _1779253)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1779255, _1779253), tc_fun(tc_fun(_1779255, _1779253), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1779255, _1779253))), _1779257)))), hAPP(hAPP(c_COMBC(_1779253, tc_fun(tc_fun(_1779255, _1779253), _1779253), tc_fun(tc_fun(_1779255, _1779253), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1779253, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1779255, _1779253), _1779253), tc_fun(tc_fun(_1779255, _1779253), tc_HOL_Obool)), _1779253), c_COMBB(_1779253, tc_HOL_Obool, tc_fun(_1779255, _1779253))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1779255, _1779253), _1779255, _1779253), c_COMBI(tc_fun(_1779255, _1779253))), _1779259)))))))], (47627 ^ _780478) ^ [_1739415, _1739417, _1739419, _1739421, _1739423] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1739415, _1739415)), hAPP(hAPP(c_Product__Type_OPair(_1739415, _1739415), _1739417), _1739419)), c_List_Omeasures(_1739415, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1739415, tc_Nat_Onat)), _1739421), _1739423)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1739421, _1739417)), hAPP(_1739421, _1739419)))), 47634 ^ _780478 : [(47637 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1739415, _1739415)), hAPP(hAPP(c_Product__Type_OPair(_1739415, _1739415), _1739417), _1739419)), c_List_Omeasures(_1739415, _1739423))))], (47635 ^ _780478) ^ [] : [-(hAPP(_1739421, _1739417) = hAPP(_1739421, _1739419))]]], (14515 ^ _780478) ^ [_1039802, _1039804] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1039802), _1039804)), _1039804) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1039802), _1039804))], (36896 ^ _780478) ^ [_1482358, _1482360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1482358), 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)), _1482360)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1482358, _1482360) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1482358, _1482360)))], (25513 ^ _780478) ^ [_1254099, _1254101] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1254099), _1254101) = 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)), _1254099)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1254101))))], (48439 ^ _780478) ^ [_1757170, _1757172, _1757174] : [-(c_List_Osplice(_1757170, hAPP(hAPP(c_List_Olist_OCons(_1757170), _1757172), _1757174), c_List_Olist_ONil(_1757170)) = hAPP(hAPP(c_List_Olist_OCons(_1757170), _1757172), _1757174))], (47322 ^ _780478) ^ [_1732702, _1732704, _1732706] : [hBOOL(hAPP(c_List_Odistinct(_1732702), _1732704)), hBOOL(hAPP(hAPP(c_member(_1732702), _1732706), hAPP(c_List_Oset(_1732702), _1732704))), -(c_List_OdropWhile(_1732702, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732702), c_fNot), hAPP(hAPP(c_COMBC(_1732702, _1732702, tc_HOL_Obool), c_fequal), _1732706)), hAPP(c_List_Orev(_1732702), _1732704)) = hAPP(hAPP(c_List_Olist_OCons(_1732702), _1732706), hAPP(c_List_Orev(_1732702), c_List_OtakeWhile(_1732702, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732702), c_fNot), hAPP(hAPP(c_COMBC(_1732702, _1732702, tc_HOL_Obool), c_fequal), _1732706)), _1732704))))], (28492 ^ _780478) ^ [_1307816, _1307818, _1307820] : [class_Orderings_Olinorder(_1307816), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307816), _1307818), _1307820)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307816, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1307816), _1307818)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1307816, _1307818, _1307820)) = hAPP(c_SetInterval_Oord__class_OatMost(_1307816), _1307820))], (32008 ^ _780478) ^ [_1385179, _1385181, _1385183] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_1385179, _1385181, _1385183)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1385183)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2494 ^ _780478) ^ [_817086, _817088, _817090, _817092, _817094, _817096, _817098, _817100, _817102, _817104] : [-(c_Product__Type_Oprod_Oprod__rec(_817104, _817100, _817096, _817092, _817088) = c_Product__Type_Oprod_Oprod__rec(_817102, _817098, _817094, _817090, _817086)), _817104 = _817102, _817100 = _817098, _817096 = _817094, _817092 = _817090, _817088 = _817086], (21344 ^ _780478) ^ [_1176812, _1176814, _1176816, _1176818] : [class_Groups_Oordered__comm__monoid__add(_1176812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176812), c_Groups_Ozero__class_Ozero(_1176812)), _1176814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176812), _1176816), _1176818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176812), _1176816), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176812), _1176814), _1176818))))], (42953 ^ _780478) ^ [_1637385, _1637387] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637385)), c_List_Olist_ONil(_1637385)), c_List_Olists(_1637385, _1637387))))], (4388 ^ _780478) ^ [_847023, _847025, _847027, _847029, _847031, _847033] : [-(c_New__DSequence_Opos__union(_847033, _847029, _847025) = c_New__DSequence_Opos__union(_847031, _847027, _847023)), _847033 = _847031, _847029 = _847027, _847025 = _847023], (44300 ^ _780478) ^ [_1667190, _1667192, _1667194] : [class_Lattices_Olattice(_1667190), -(c_Big__Operators_Olattice__class_OInf__fin(_1667190, hAPP(c_List_Oset(_1667190), hAPP(hAPP(c_List_Olist_OCons(_1667190), _1667192), _1667194))) = hAPP(c_List_Ofoldl(_1667190, _1667190, c_Lattices_Osemilattice__inf__class_Oinf(_1667190), _1667192), _1667194))], (27449 ^ _780478) ^ [_1288215, _1288217] : [c_Nat__Transfer_Ois__nat(_1288215), c_Nat__Transfer_Ois__nat(_1288217), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1288215, _1288217)))], (8665 ^ _780478) ^ [_930463, _930465, _930467] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_930463), _930465)), -(_930465 = c_Orderings_Obot__class_Obot(tc_fun(_930463, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_930463, _930467, _930465), 8672 ^ [_930463, _930465, _930467])))], (4142 ^ _780478) ^ [_843140, _843142, _843144, _843146, _843148, _843150, _843152, _843154] : [-(c_New__Random__Sequence_Opos__bind(_843154, _843150, _843146, _843142) = c_New__Random__Sequence_Opos__bind(_843152, _843148, _843144, _843140)), _843154 = _843152, _843150 = _843148, _843146 = _843144, _843142 = _843140], (38875 ^ _780478) ^ [_1531632, _1531634, _1531636, _1531638, _1531640, _1531642] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531632, _1531634)), hAPP(hAPP(c_Product__Type_OPair(_1531632, _1531634), _1531636), _1531638)), hAPP(hAPP(c_Product__Type_OSigma(_1531632, _1531634), _1531640), _1531642))), 38878 ^ _780478 : [(38881 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531634), _1531638), hAPP(_1531642, _1531636))))], (38879 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1531632), _1531636), _1531640)))]]], (44700 ^ _780478) ^ [_1675469, _1675471, _1675473, _1675475] : [hAPP(hAPP(c_List_Omap(_1675469, _1675471), _1675473), _1675475) = c_List_Olist_ONil(_1675471), -(_1675475 = c_List_Olist_ONil(_1675469))], (16915 ^ _780478) ^ [_1091280, _1091282, _1091284, _1091286, _1091288] : [class_Groups_Ocomm__monoid__mult(_1091280), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091282), _1091284)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091282), _1091286)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091280), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1091280, _1091282, c_Groups_Otimes__class_Otimes(_1091280)), _1091288), c_Groups_Oone__class_Oone(_1091280)), _1091284)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1091280, _1091282, c_Groups_Otimes__class_Otimes(_1091280)), _1091288), c_Groups_Oone__class_Oone(_1091280)), _1091286)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091280), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1091280, _1091282, c_Groups_Otimes__class_Otimes(_1091280)), _1091288), c_Groups_Oone__class_Oone(_1091280)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1091282, tc_HOL_Obool)), _1091284), _1091286))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1091280, _1091282, c_Groups_Otimes__class_Otimes(_1091280)), _1091288), c_Groups_Oone__class_Oone(_1091280)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1091282, tc_HOL_Obool)), _1091284), _1091286))))], (29954 ^ _780478) ^ [_1336381, _1336383] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336381, _1336383)) = _1336383), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1336381), _1336383) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1336381, _1336383)))], (21680 ^ _780478) ^ [_1183080, _1183082, _1183084, _1183086] : [class_Rings_Olinordered__semidom(_1183080), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183080), hAPP(hAPP(c_Power_Opower__class_Opower(_1183080), _1183082), hAPP(c_Nat_OSuc, _1183084))), hAPP(hAPP(c_Power_Opower__class_Opower(_1183080), _1183086), hAPP(c_Nat_OSuc, _1183084)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183080), c_Groups_Ozero__class_Ozero(_1183080)), _1183086)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183080), _1183082), _1183086)))], (13970 ^ _780478) ^ [_1030244] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1030244)), 13974 ^ _780478 : [(13975 ^ _780478) ^ [_1030324] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1030324), _1030244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1030324), 13973 ^ [_1030244])))]]], (25511 ^ _780478) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (32330 ^ _780478) ^ [_1391370, _1391372, _1391374] : [c_Equiv__Relations_Oequiv(_1391370, _1391372, _1391374), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1391370, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1391370), _1391372), _1391374)) = _1391372)], (18732 ^ _780478) ^ [_1132288, _1132290, _1132292, _1132294, _1132296] : [-(_1132288 = c_Orderings_Obot__class_Obot(tc_fun(_1132290, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1132290, tc_fun(_1132292, tc_HOL_Obool)), _1132288), hAPP(hAPP(c_COMBB(tc_fun(_1132292, tc_HOL_Obool), tc_fun(_1132292, tc_HOL_Obool), _1132290), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1132292, tc_HOL_Obool)), _1132294)), _1132296)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1132292, tc_HOL_Obool)), _1132294), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1132290, tc_fun(_1132292, tc_HOL_Obool)), _1132288), _1132296)))], (30943 ^ _780478) ^ [_1355414, _1355416, _1355418] : [30945 ^ _780478 : [(30948 ^ _780478) ^ [] : [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(_1355416, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 30944 ^ [_1355414, _1355416, _1355418]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1355416, 30944 ^ [_1355414, _1355416, _1355418])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30946 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30944 ^ [_1355414, _1355416, _1355418]), _1355414)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1355416, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1355418)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1355418), hAPP(_1355416, _1355414))), 30958 ^ _780478 : [(30961 ^ _780478) ^ [] : [-(hAPP(_1355416, 30957 ^ [_1355414, _1355416, _1355418]) = _1355418)], (30959 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 30957 ^ [_1355414, _1355416, _1355418]), _1355414)))]]], (52097 ^ _780478) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (46993 ^ _780478) ^ [_1725743, _1725745, _1725747] : [-(hAPP(c_List_Orev(_1725743), hAPP(c_List_Ofilter(_1725743, _1725745), _1725747)) = hAPP(c_List_Ofilter(_1725743, _1725745), hAPP(c_List_Orev(_1725743), _1725747)))], (50961 ^ _780478) ^ [_1813334, _1813336, _1813338, _1813340, _1813342] : [-(c_Lazy__Sequence_Omap(_1813334, _1813336, _1813338, c_Lazy__Sequence_Olazy__sequence_OInsert(_1813334, _1813340, _1813342)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1813336, hAPP(_1813338, _1813340), c_Lazy__Sequence_Omap(_1813334, _1813336, _1813338, _1813342)))], (25663 ^ _780478) ^ [_1256617, _1256619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256619)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1256617)), hAPP(c_Int_Onat, _1256619)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1256617), _1256619)))], (24999 ^ _780478) ^ [_1244789, _1244791, _1244793] : [class_Groups_Oordered__ab__group__add(_1244789), -(hAPP(c_Set_Oimage(_1244789, _1244789, c_Groups_Ouminus__class_Ouminus(_1244789)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1244789, _1244791, _1244793)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244789, hAPP(c_Groups_Ouminus__class_Ouminus(_1244789), _1244793)), hAPP(c_Groups_Ouminus__class_Ouminus(_1244789), _1244791)))], (41097 ^ _780478) ^ [_1586790, _1586792, _1586794] : [c_Relation_Osingle__valued(_1586790, _1586792, _1586794), 41100 ^ _780478 : [(41101 ^ _780478) ^ [_1586911, _1586913] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586790, _1586792)), hAPP(hAPP(c_Product__Type_OPair(_1586790, _1586792), _1586913), _1586911)), _1586794)), 41104 ^ _780478 : [(41105 ^ _780478) ^ [_1587037] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586790, _1586792)), hAPP(hAPP(c_Product__Type_OPair(_1586790, _1586792), _1586913), _1587037)), _1586794)), -(_1586911 = _1587037)]]]]], (19038 ^ _780478) ^ [_1137969, _1137971, _1137973, _1137975, _1137977, _1137979, _1137981] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1137969, tc_fun(_1137971, tc_fun(_1137973, tc_HOL_Obool))), _1137975), _1137977), _1137979), _1137981)), 19041 ^ _780478 : [(19042 ^ _780478) ^ [_1138097] : [hBOOL(hAPP(hAPP(c_member(_1137969), _1138097), _1137975)), -(hBOOL(hAPP(hAPP(hAPP(_1137977, _1138097), _1137979), _1137981)))]]], (9684 ^ _780478) ^ [_947171, _947173, _947175, _947177, _947179, _947181] : [class_Rings_Oordered__ring(_947171), 9687 ^ _780478 : [(9694 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947171), _947177), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947171), _947179), _947173)), _947175)), _947181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947171), _947173), _947175)), _947177)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947171), _947179), _947175)), _947181))))], (9688 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947171), _947173), _947175)), _947177)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947171), _947179), _947175)), _947181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_947171), _947177), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_947171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_947171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_947171), _947179), _947173)), _947175)), _947181))))]]], (36876 ^ _780478) ^ [_1481903, _1481905, _1481907, _1481909, _1481911, _1481913] : [hAPP(_1481909, hAPP(c_Product__Type_Osnd(_1481907, _1481903), _1481911)) = hAPP(_1481913, hAPP(c_Product__Type_Osnd(_1481907, _1481903), _1481911)), -(hAPP(c_Product__Type_Oapsnd(_1481903, _1481905, _1481907, _1481909), _1481911) = hAPP(c_Product__Type_Oapsnd(_1481903, _1481905, _1481907, _1481913), _1481911))], (25866 ^ _780478) ^ [_1259967, _1259969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259969)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1259967), _1259969)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1259967)), hAPP(c_Int_Onat, _1259969)))], (8986 ^ _780478) ^ [_935086, _935088, _935090, _935092] : [class_Orderings_Oord(_935086), 8989 ^ _780478 : [(8998 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_935088, _935086)), _935090), _935092))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935088, _935086)), _935090), _935092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935088, _935086)), _935092), _935090)))], (8990 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_935088, _935086)), _935090), _935092)), 8993 ^ _780478 : [(8996 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935088, _935086)), _935092), _935090))], (8994 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935088, _935086)), _935090), _935092)))]]]]], (17919 ^ _780478) ^ [_1114277, _1114279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114277)), hAPP(c_Nat_OSuc, _1114279))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114277), _1114279)))], (46258 ^ _780478) ^ [_1711808, _1711810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1711808), _1711810)), -(c_List_Oupt(_1711808, _1711810) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1711808), c_List_Oupt(hAPP(c_Nat_OSuc, _1711808), _1711810)))], (6692 ^ _780478) ^ [_890809, _890811] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_890809, _890811)], (12686 ^ _780478) ^ [_1004939, _1004941] : [class_Lattices_Obounded__lattice__top(_1004939), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1004939), _1004941), c_Orderings_Otop__class_Otop(_1004939)) = c_Orderings_Otop__class_Otop(_1004939))], (39029 ^ _780478) ^ [_1537000, _1537002] : [-(c_Product__Type_Oapfst(_1537000, _1537000, _1537002, c_Fun_Oid(_1537000)) = c_Fun_Oid(tc_prod(_1537000, _1537002)))], (2446 ^ _780478) ^ [_816314, _816316, _816318, _816320, _816322, _816324, _816326, _816328, _816330, _816332] : [-(c_Product__Type_Oprod_Oprod__size(_816332, _816328, _816324, _816320, _816316) = c_Product__Type_Oprod_Oprod__size(_816330, _816326, _816322, _816318, _816314)), _816332 = _816330, _816328 = _816326, _816324 = _816322, _816320 = _816318, _816316 = _816314], (19670 ^ _780478) ^ [_1147659] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1147659) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35527 ^ _780478) ^ [_1449369, _1449371] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1449369), hAPP(hAPP(c_Power_Opower__class_Opower(_1449369), hAPP(c_Int_Onumber__class_Onumber__of(_1449369), c_Int_OMin)), _1449371)) = c_Groups_Oone__class_Oone(_1449369)), class_Int_Onumber__ring(_1449369), class_Rings_Olinordered__idom(_1449369)], (45173 ^ _780478) ^ [_1685932, _1685934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1685932)), hAPP(c_Code__Numeral_Onat__of, _1685934))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1685932), _1685934)))], (40524 ^ _780478) ^ [_1572995, _1572997, _1572999, _1573001] : [40525 ^ _780478 : [(40528 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572995, _1572995)), _1572997), c_Transitive__Closure_Ortrancl(_1572995, _1573001)))], (40526 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572995, _1572995)), _1572997), c_Transitive__Closure_Ortrancl(_1572995, _1572999)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572995, _1572995)), _1572997), c_Transitive__Closure_Ortrancl(_1572995, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1572995, _1572995), tc_HOL_Obool)), _1572999), _1573001)))))], (49068 ^ _780478) ^ [_1771030, _1771032] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1771030, _1771032), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1771030)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19594 ^ _780478) ^ [_1146511, _1146513] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1146511), _1146513) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1146511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1146513 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17231 ^ _780478) ^ [_1097741, _1097743, _1097745, _1097747, _1097749] : [_1097741 = c_Orderings_Obot__class_Obot(tc_fun(_1097743, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097743, tc_fun(_1097745, tc_HOL_Obool)), _1097741), hAPP(hAPP(c_COMBB(tc_fun(_1097745, tc_HOL_Obool), tc_fun(_1097745, tc_HOL_Obool), _1097743), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1097745, tc_HOL_Obool)), _1097747)), _1097749)) = c_Orderings_Obot__class_Obot(tc_fun(_1097745, tc_HOL_Obool)))], (5795 ^ _780478) ^ [_872154, _872156, _872158, _872160] : [c_Hoare__Mirabelle_Ohoare__derivs(_872154, _872156, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872154)), _872158), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_872154), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_872154, _872156, _872160), -(c_Hoare__Mirabelle_Ohoare__derivs(_872154, _872156, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_872154)), _872158), _872160)))], (17301 ^ _780478) ^ [_1099746, _1099748, _1099750, _1099752, _1099754, _1099756, _1099758] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1099746, tc_fun(_1099748, tc_fun(_1099750, tc_HOL_Obool))), _1099752), _1099754), _1099756), _1099758)), 17305 ^ _780478 : [(17308 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1099754, 17304 ^ [_1099746, _1099748, _1099750, _1099752, _1099754, _1099756, _1099758]), _1099756), _1099758)))], (17306 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099746), 17304 ^ [_1099746, _1099748, _1099750, _1099752, _1099754, _1099756, _1099758]), _1099752)))]]], (7730 ^ _780478) ^ [_911057, _911059, _911061, _911063, _911065] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911057, _911059, _911061, _911063, c_Orderings_Obot__class_Obot(tc_fun(_911057, tc_HOL_Obool))), _911065)), -(_911065 = _911063)], (17799 ^ _780478) ^ [_1112110, _1112112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112110), _1112112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1112110)), hAPP(c_Nat_OSuc, _1112112))))], (29602 ^ _780478) ^ [_1330118, _1330120, _1330122] : [-(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), _1330118), _1330120)), _1330120)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1330118, _1330120))), _1330122) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1330118), _1330122))], (35693 ^ _780478) ^ [_1456737, _1456739, _1456741, _1456743, _1456745, _1456747, _1456749, _1456751, _1456753, _1456755] : [c_Equiv__Relations_Ocongruent2(_1456737, _1456739, _1456741, _1456743, _1456745, _1456747), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456737, _1456737)), hAPP(hAPP(c_Product__Type_OPair(_1456737, _1456737), _1456749), _1456751)), _1456743)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456739, _1456739)), hAPP(hAPP(c_Product__Type_OPair(_1456739, _1456739), _1456753), _1456755)), _1456745)), -(hAPP(hAPP(_1456747, _1456749), _1456753) = hAPP(hAPP(_1456747, _1456751), _1456755))], (14369 ^ _780478) ^ [_1037066, _1037068, _1037070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037066), _1037068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037066), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037068), _1037070))))], (36256 ^ _780478) ^ [_1469968, _1469970, _1469972, _1469974, _1469976, _1469978] : [hBOOL(hAPP(hAPP(_1469968, _1469970), _1469972)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1469974, tc_fun(_1469976, tc_HOL_Obool))), _1469968), _1469978), _1469970), _1469972)))], (40252 ^ _780478) ^ [_1566244, _1566246, _1566248] : [40254 ^ _780478 : [(40257 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1566244), 40253 ^ [_1566244, _1566246, _1566248]), c_Wellfounded_Oacc(_1566244, _1566248)))], (40255 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566244, _1566244)), hAPP(hAPP(c_Product__Type_OPair(_1566244, _1566244), 40253 ^ [_1566244, _1566246, _1566248]), _1566246)), _1566248)))]], -(hBOOL(hAPP(hAPP(c_member(_1566244), _1566246), c_Wellfounded_Oacc(_1566244, _1566248))))], (29830 ^ _780478) ^ [_1334381, _1334383] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1334381), _1334383)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1334381)), _1334383)))], (25291 ^ _780478) ^ [_1250631, _1250633, _1250635, _1250637] : [class_Rings_Odivision__ring(_1250631), -(_1250633 = c_Groups_Ozero__class_Ozero(_1250631)), _1250635 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250631), _1250637), _1250633), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250631), _1250635), _1250633) = _1250637)], (11789 ^ _780478) ^ [_987349, _987351] : [class_Groups_Oab__semigroup__mult(_987349), hBOOL(hAPP(c_Finite__Set_Ofinite(_987349), _987351)), -(_987351 = c_Orderings_Obot__class_Obot(tc_fun(_987349, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_987349), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987349), 11802 ^ [_987349, _987351]), 11803 ^ [_987349, _987351])), hAPP(hAPP(c_Set_Oinsert(_987349), 11802 ^ [_987349, _987351]), hAPP(hAPP(c_Set_Oinsert(_987349), 11803 ^ [_987349, _987351]), c_Orderings_Obot__class_Obot(tc_fun(_987349, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_987349), hAPP(c_Finite__Set_Ofold1(_987349, c_Groups_Otimes__class_Otimes(_987349)), _987351)), _987351)))], (3830 ^ _780478) ^ [_837918, _837920] : [_837920 = _837918, -(c_List_Odistinct(_837920) = c_List_Odistinct(_837918))], (16799 ^ _780478) ^ [_1088574, _1088576, _1088578, _1088580, _1088582] : [class_Groups_Ocomm__monoid__add(_1088574), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088576), _1088578)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088576), _1088580)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1088576, tc_HOL_Obool)), _1088578), _1088580) = c_Orderings_Obot__class_Obot(tc_fun(_1088576, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088576, _1088574), _1088582), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1088576, tc_HOL_Obool)), _1088578), _1088580)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088574), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088576, _1088574), _1088582), _1088578)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088576, _1088574), _1088582), _1088580)))], (42276 ^ _780478) ^ [_1620170, _1620172, _1620174] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1620170, tc_HOL_Obool)), hAPP(c_List_Oset(_1620170), hAPP(hAPP(c_List_Otake(_1620170), _1620172), _1620174))), hAPP(c_List_Oset(_1620170), _1620174))))], (16332 ^ _780478) ^ [_1077537, _1077539, _1077541, _1077543] : [-(hBOOL(hAPP(hAPP(c_member(_1077537), _1077539), _1077541))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077537, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1077537), _1077539), _1077543)), _1077541) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1077537, tc_HOL_Obool)), _1077543), _1077541))], (4418 ^ _780478) ^ [_847478, _847480] : [_847480 = _847478, -(c_Lazy__Sequence_Osingle(_847480) = c_Lazy__Sequence_Osingle(_847478))], (4266 ^ _780478) ^ [_845010, _845012, _845014, _845016] : [-(c_List_Ofilter(_845016, _845012) = c_List_Ofilter(_845014, _845010)), _845016 = _845014, _845012 = _845010], (34783 ^ _780478) ^ [_1436199, _1436201] : [class_Rings_Oring__1(_1436199), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1436199), hAPP(c_Groups_Ouminus__class_Ouminus(_1436199), _1436201)), 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(_1436199), _1436201), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (34951 ^ _780478) ^ [_1439136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1439136), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1439136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1439136 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (24341 ^ _780478) ^ [_1233068, _1233070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233068)), 24344 ^ _780478 : [(24351 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233070)), -(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), _1233070), _1233068))))], (24345 ^ _780478) ^ [] : [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), _1233070), _1233068))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233070)))]]], (29193 ^ _780478) ^ [_1322259, _1322261, _1322263] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1322259), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1322261, _1322263)), _1322263) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1322259), _1322261), _1322263))], (25271 ^ _780478) ^ [_1250218, _1250220, _1250222, _1250224, _1250226] : [class_Fields_Ofield(_1250218), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250218), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1250220, _1250218), _1250222), _1250224)), _1250226) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1250220, _1250218), hAPP(hAPP(c_COMBC(_1250220, _1250218, _1250218), hAPP(hAPP(c_COMBB(_1250218, tc_fun(_1250218, _1250218), _1250220), c_Rings_Oinverse__class_Odivide(_1250218)), _1250222)), _1250226)), _1250224))], (22147 ^ _780478) ^ [_1192161, _1192163, _1192165] : [class_Rings_Olinordered__semidom(_1192161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192161), c_Groups_Oone__class_Oone(_1192161)), _1192163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1192165)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1192161), c_Groups_Oone__class_Oone(_1192161)), hAPP(hAPP(c_Power_Opower__class_Opower(_1192161), _1192163), _1192165))))], (25577 ^ _780478) ^ [_1255291, _1255293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255291)), 25580 ^ _780478 : [(25587 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255293), _1255291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1255293)), hAPP(c_Int_Onat, _1255291))))], (25581 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1255293)), hAPP(c_Int_Onat, _1255291))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255293), _1255291)))]]], (49714 ^ _780478) ^ [_1786094, _1786096, _1786098] : [c_Relation_Osym(_1786094, _1786096), c_Relation_Osym(_1786094, _1786098), -(c_Relation_Osym(_1786094, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1786094, _1786094), tc_HOL_Obool)), _1786096), _1786098)))], (38971 ^ _780478) ^ [_1534047, _1534049, _1534051, _1534053, _1534055, _1534057, _1534059, _1534061] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1534047, _1534049), tc_fun(tc_prod(_1534051, _1534053), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1534047, _1534049), _1534055), hAPP(c_COMBK(tc_fun(_1534049, tc_HOL_Obool), _1534047), _1534057))), hAPP(c_Product__Type_Oprod_Oprod__case(_1534047, _1534049, tc_fun(tc_prod(_1534051, _1534053), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1534047, tc_fun(_1534049, tc_fun(_1534051, tc_fun(_1534053, tc_HOL_Obool))), tc_fun(_1534049, tc_fun(tc_prod(_1534051, _1534053), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1534051, tc_fun(_1534053, tc_HOL_Obool)), tc_fun(tc_prod(_1534051, _1534053), tc_HOL_Obool)), tc_fun(tc_fun(_1534049, tc_fun(_1534051, tc_fun(_1534053, tc_HOL_Obool))), tc_fun(_1534049, tc_fun(tc_prod(_1534051, _1534053), tc_HOL_Obool))), _1534047), c_COMBB(tc_fun(_1534051, tc_fun(_1534053, tc_HOL_Obool)), tc_fun(tc_prod(_1534051, _1534053), tc_HOL_Obool), _1534049)), hAPP(hAPP(c_COMBB(tc_fun(_1534051, tc_HOL_Obool), tc_fun(tc_fun(_1534051, tc_fun(_1534053, tc_HOL_Obool)), tc_fun(tc_prod(_1534051, _1534053), tc_HOL_Obool)), _1534047), c_Product__Type_OSigma(_1534051, _1534053)), _1534059))), hAPP(hAPP(c_COMBB(tc_fun(_1534053, tc_HOL_Obool), tc_fun(_1534051, tc_fun(_1534053, tc_HOL_Obool)), _1534049), c_COMBK(tc_fun(_1534053, tc_HOL_Obool), _1534051)), _1534061)))) = hAPP(hAPP(c_Product__Type_OSigma(_1534051, _1534053), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534047, tc_fun(_1534051, tc_HOL_Obool)), _1534055), _1534059)), hAPP(c_COMBK(tc_fun(_1534053, tc_HOL_Obool), _1534051), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1534049, tc_fun(_1534053, tc_HOL_Obool)), _1534057), _1534061))))], (42473 ^ _780478) ^ [_1626277, _1626279, _1626281, _1626283] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1626277, _1626279))), hAPP(hAPP(c_List_Ozip(_1626277, _1626279), _1626281), _1626283)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626277)), _1626281)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626279)), _1626283)))], (35091 ^ _780478) ^ [_1441812, _1441814] : [class_Rings_Oring__1(_1441812), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1441812), hAPP(c_Groups_Ouminus__class_Ouminus(_1441812), c_Groups_Oone__class_Oone(_1441812))), 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)))), _1441814)) = c_Groups_Oone__class_Oone(_1441812))], (36884 ^ _780478) ^ [_1482112, _1482114, _1482116] : [-(hAPP(c_Product__Type_Osnd(_1482112, _1482114), _1482116) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1482112, _1482114, _1482114), hAPP(c_COMBK(tc_fun(_1482114, _1482114), _1482112), c_COMBI(_1482114))), _1482116))], (1324 ^ _780478) ^ [_799892, _799894] : [-(class_Rings_Oidom(_799892)), _799894 = _799892, class_Rings_Oidom(_799894)], (33102 ^ _780478) ^ [_1406046, _1406048] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1406046) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406048), 33105 ^ _780478 : [(33108 ^ _780478) ^ [] : [-(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), _1406048))))], (33106 ^ _780478) ^ [] : [-(_1406046 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1406048)))]]], (4190 ^ _780478) ^ [_843896, _843898, _843900, _843902, _843904, _843906] : [-(c_Predicate_Oconversep(_843906, _843902, _843898) = c_Predicate_Oconversep(_843904, _843900, _843896)), _843906 = _843904, _843902 = _843900, _843898 = _843896], (47886 ^ _780478) ^ [_1745755, _1745757, _1745759, _1745761, _1745763] : [-(hAPP(c_List_Ofilter(_1745755, _1745757), _1745759) = hAPP(hAPP(c_List_Olist_OCons(_1745755), _1745761), _1745763)), 47887 ^ _780478 : [(47888 ^ _780478) ^ [_1745883, _1745885] : [_1745759 = hAPP(hAPP(c_List_Oappend(_1745755), _1745885), hAPP(hAPP(c_List_Olist_OCons(_1745755), _1745761), _1745883)), 47894 ^ _780478 : [(47897 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1745757, 47893 ^ [_1745755, _1745757, _1745759, _1745761, _1745763, _1745883, _1745885])))], (47895 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745755), 47893 ^ [_1745755, _1745757, _1745759, _1745761, _1745763, _1745883, _1745885]), hAPP(c_List_Oset(_1745755), _1745885))))]], hBOOL(hAPP(_1745757, _1745761)), _1745763 = hAPP(c_List_Ofilter(_1745755, _1745757), _1745883)]]], (43833 ^ _780478) ^ [_1657021, _1657023, _1657025] : [-(hAPP(hAPP(c_List_Odrop(_1657021), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1657021), _1657023), _1657025)) = _1657025)], (36359 ^ _780478) ^ [_1472324] : [-(c_Divides_Oadjust(_1472324) = 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)), _1472324))))), 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)), _1472324))))), 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))))))))], (44985 ^ _780478) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9856 ^ _780478) ^ [_951262, _951264, _951266, _951268] : [class_Rings_Ocomm__semiring__1(_951262), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951262), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951262), _951264), _951266)), _951268) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951262), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951262), _951264), _951268)), _951266))], (8688 ^ _780478) ^ [_930869, _930871] : [class_Lattices_Oab__semigroup__idem__mult(_930869), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930869), _930871), _930871) = _930871)], (3196 ^ _780478) ^ [_827971, _827973, _827975, _827977, _827979, _827981] : [-(c_Big__Operators_Olattice_OInf__fin(_827981, _827977, _827973) = c_Big__Operators_Olattice_OInf__fin(_827979, _827975, _827971)), _827981 = _827979, _827977 = _827975, _827973 = _827971], (16737 ^ _780478) ^ [_1087328, _1087330, _1087332, _1087334, _1087336] : [c_Finite__Set_Ofolding__one(_1087328, _1087330, _1087332), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087328), _1087334)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087328), _1087336)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1087328, tc_HOL_Obool)), _1087334), _1087336) = c_Orderings_Obot__class_Obot(tc_fun(_1087328, tc_HOL_Obool))), -(hAPP(hAPP(_1087330, hAPP(_1087332, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1087328, tc_HOL_Obool)), _1087334), _1087336))), hAPP(_1087332, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1087328, tc_HOL_Obool)), _1087334), _1087336))) = hAPP(hAPP(_1087330, hAPP(_1087332, _1087334)), hAPP(_1087332, _1087336)))], (23579 ^ _780478) ^ [_1218712, _1218714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1218712), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1218714), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1218712))))), -(_1218712 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1218714), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1218712))))], (38267 ^ _780478) ^ [_1515564, _1515566, _1515568] : [c_Wellfounded_Owf(_1515564, _1515566), -(c_Wellfounded_Owf(_1515564, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1515564, _1515564), tc_HOL_Obool)), _1515566), _1515568)))], (52011 ^ _780478) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (5568 ^ _780478) ^ [_865765, _865767] : [_865767 = _865765, -(c_Rings_Odvd__class_Odvd(_865767) = c_Rings_Odvd__class_Odvd(_865765))], (1694 ^ _780478) ^ [_804517, _804519] : [-(class_Groups_Osemigroup__add(_804517)), _804519 = _804517, class_Groups_Osemigroup__add(_804519)], (424 ^ _780478) ^ [_786902, _786904] : [-(class_Rings_Oinverse(_786902)), _786904 = _786902, class_Rings_Oinverse(_786904)], (28977 ^ _780478) ^ [_1317372, _1317374] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1317372)), _1317374) = 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), _1317372)), _1317374))], (11206 ^ _780478) ^ [_976427, _976429, _976431] : [class_Orderings_Olinorder(_976427), hBOOL(hAPP(c_Finite__Set_Ofinite(_976427), _976429)), -(_976429 = c_Orderings_Obot__class_Obot(tc_fun(_976427, tc_HOL_Obool))), 11217 ^ _780478 : [(11218 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976427), _976431), hAPP(c_Finite__Set_Ofold1(_976427, c_Orderings_Oord__class_Omin(_976427)), _976429))), 11221 ^ _780478 : [(11222 ^ _780478) ^ [_976720] : [hBOOL(hAPP(hAPP(c_member(_976427), _976720), _976429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976427), _976431), _976720)))]]], (11228 ^ _780478) ^ [] : [11230 ^ _780478 : [(11233 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976427), _976431), 11229 ^ [_976427, _976429, _976431]))], (11231 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_976427), 11229 ^ [_976427, _976429, _976431]), _976429)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976427), _976431), hAPP(c_Finite__Set_Ofold1(_976427, c_Orderings_Oord__class_Omin(_976427)), _976429))))]]], (34521 ^ _780478) ^ [_1431445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1431445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1431445)))], (14215 ^ _780478) ^ [_1034633, _1034635] : [class_Rings_Oring__1__no__zero__divisors(_1034633), 14218 ^ _780478 : [(14219 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034633), _1034635), _1034635) = c_Groups_Oone__class_Oone(_1034633), -(_1034635 = c_Groups_Oone__class_Oone(_1034633)), -(_1034635 = hAPP(c_Groups_Ouminus__class_Ouminus(_1034633), c_Groups_Oone__class_Oone(_1034633)))], (14229 ^ _780478) ^ [] : [14230 ^ _780478 : [(14233 ^ _780478) ^ [] : [_1034635 = hAPP(c_Groups_Ouminus__class_Ouminus(_1034633), c_Groups_Oone__class_Oone(_1034633))], (14231 ^ _780478) ^ [] : [_1034635 = c_Groups_Oone__class_Oone(_1034633)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034633), _1034635), _1034635) = c_Groups_Oone__class_Oone(_1034633))]]], (30885 ^ _780478) ^ [_1354348, _1354350, _1354352] : [class_Complete__Lattice_Ocomplete__lattice(_1354348), -(c_Complete__Lattice_OSup__class_OSup(_1354348, hAPP(hAPP(c_Set_Oinsert(_1354348), _1354350), hAPP(hAPP(c_Set_Oinsert(_1354348), _1354352), c_Orderings_Obot__class_Obot(tc_fun(_1354348, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1354348), _1354350), _1354352))], (15321 ^ _780478) ^ [_1056350, _1056352, _1056354, _1056356] : [class_Rings_Olinordered__semidom(_1056350), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1056352), _1056354)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056350), c_Groups_Oone__class_Oone(_1056350)), _1056356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056350), hAPP(hAPP(c_Power_Opower__class_Opower(_1056350), _1056356), _1056352)), hAPP(hAPP(c_Power_Opower__class_Opower(_1056350), _1056356), _1056354))))], (24579 ^ _780478) ^ [_1237133, _1237135] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1237133), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1237135) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1237133, _1237135))], (35389 ^ _780478) ^ [_1447260, _1447262] : [class_Int_Onumber__ring(_1447260), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1447260), _1447262), hAPP(c_Int_Onumber__class_Onumber__of(_1447260), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1447260), _1447262))], (45914 ^ _780478) ^ [_1702267, _1702269] : [c_List_Olist_ONil(_1702267) = c_List_Oconcat(_1702267, _1702269), 45917 ^ _780478 : [(45918 ^ _780478) ^ [_1702358] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1702267)), _1702358), hAPP(c_List_Oset(tc_List_Olist(_1702267)), _1702269))), -(_1702358 = c_List_Olist_ONil(_1702267))]]], (42201 ^ _780478) ^ [_1618132, _1618134, _1618136, _1618138] : [-(hAPP(hAPP(c_List_Onth(_1618132), hAPP(hAPP(c_List_Olist_OCons(_1618132), _1618134), _1618136)), _1618138) = c_Nat_Onat_Onat__case(_1618132, _1618134, hAPP(c_List_Onth(_1618132), _1618136), _1618138))], (35561 ^ _780478) ^ [_1449903, _1449905] : [class_Int_Onumber__ring(_1449903), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1449903), hAPP(c_Int_Onumber__class_Onumber__of(_1449903), 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)))), _1449905)) = c_Groups_Oone__class_Oone(_1449903))], (31272 ^ _780478) ^ [_1362887, _1362889, _1362891] : [hBOOL(hAPP(_1362887, _1362889)), -(hAPP(c_Set_OCollect(_1362891), hAPP(hAPP(c_COMBS(_1362891, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1362891), c_fconj), hAPP(hAPP(c_COMBC(_1362891, _1362891, tc_HOL_Obool), c_fequal), _1362889))), _1362887)) = hAPP(hAPP(c_Set_Oinsert(_1362891), _1362889), c_Orderings_Obot__class_Obot(tc_fun(_1362891, tc_HOL_Obool))))], (23311 ^ _780478) ^ [_1214107, _1214109] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214107), _1214109) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214109), _1214107))], (38810 ^ _780478) ^ [_1529722, _1529724, _1529726] : [c_Equiv__Relations_Oequiv(_1529722, _1529724, _1529726), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1529722, _1529722), tc_HOL_Obool)), _1529726), hAPP(hAPP(c_Product__Type_OSigma(_1529722, _1529722), _1529724), hAPP(c_COMBK(tc_fun(_1529722, tc_HOL_Obool), _1529722), _1529724)))))], (34269 ^ _780478) ^ [_1426798, _1426800] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426798))), _1426800) = 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)))), _1426798), _1426800))], (51931 ^ _780478) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (52231 ^ _780478) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (38118 ^ _780478) ^ [_1512194, _1512196, _1512198, _1512200, _1512202, _1512204, _1512206] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1512194, _1512198)), hAPP(hAPP(c_Product__Type_OPair(_1512194, _1512198), _1512204), _1512206)), hAPP(hAPP(c_Relation_Orel__comp(_1512194, _1512196, _1512198), _1512200), _1512202))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1512194, _1512196, _1512198, hAPP(hAPP(c_COMBC(_1512194, tc_fun(tc_prod(_1512194, _1512196), tc_HOL_Obool), tc_fun(_1512196, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512196, tc_fun(tc_fun(tc_prod(_1512194, _1512196), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1512194, _1512196), tc_HOL_Obool), tc_fun(_1512196, tc_HOL_Obool)), _1512194), c_COMBC(_1512196, tc_fun(tc_prod(_1512194, _1512196), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512196, tc_prod(_1512194, _1512196)), tc_fun(_1512196, tc_fun(tc_fun(tc_prod(_1512194, _1512196), tc_HOL_Obool), tc_HOL_Obool)), _1512194), hAPP(c_COMBB(tc_prod(_1512194, _1512196), tc_fun(tc_fun(tc_prod(_1512194, _1512196), tc_HOL_Obool), tc_HOL_Obool), _1512196), c_member(tc_prod(_1512194, _1512196)))), c_Product__Type_OPair(_1512194, _1512196)))), _1512200), hAPP(hAPP(c_COMBC(_1512196, tc_fun(tc_prod(_1512196, _1512198), tc_HOL_Obool), tc_fun(_1512198, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512198, tc_fun(tc_fun(tc_prod(_1512196, _1512198), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1512196, _1512198), tc_HOL_Obool), tc_fun(_1512198, tc_HOL_Obool)), _1512196), c_COMBC(_1512198, tc_fun(tc_prod(_1512196, _1512198), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1512198, tc_prod(_1512196, _1512198)), tc_fun(_1512198, tc_fun(tc_fun(tc_prod(_1512196, _1512198), tc_HOL_Obool), tc_HOL_Obool)), _1512196), hAPP(c_COMBB(tc_prod(_1512196, _1512198), tc_fun(tc_fun(tc_prod(_1512196, _1512198), tc_HOL_Obool), tc_HOL_Obool), _1512198), c_member(tc_prod(_1512196, _1512198)))), c_Product__Type_OPair(_1512196, _1512198)))), _1512202)), _1512204), _1512206)))], (44015 ^ _780478) ^ [_1661364, _1661366, _1661368, _1661370] : [-(hAPP(c_List_Orotate1(_1661364), c_List_Olist_ONil(_1661364)) = c_List_Olist_ONil(_1661364))], (48818 ^ _780478) ^ [_1765071, _1765073, _1765075, _1765077] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1765071, _1765073), c_Lazy__Sequence_Olazy__sequence_OInsert(_1765071, _1765075, _1765077)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1765073, _1765075)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1765071, _1765073), _1765077))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10305 ^ _780478) ^ [_960219, _960221, _960223] : [class_Orderings_Olinorder(_960219), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_960219), _960221), hAPP(hAPP(c_Orderings_Oord__class_Omax(_960219), _960221), _960223)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_960219), _960221), _960223))], (33784 ^ _780478) ^ [_1418641, _1418643, _1418645, _1418647, _1418649, _1418651, _1418653] : [c_Equiv__Relations_Oequiv(_1418641, _1418643, _1418645), c_Equiv__Relations_Ocongruent(_1418641, tc_fun(_1418647, tc_HOL_Obool), _1418645, _1418649), hBOOL(hAPP(hAPP(c_member(tc_fun(_1418641, tc_HOL_Obool)), _1418651), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1418641), _1418643), _1418645))), 33798 ^ _780478 : [(33801 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1418647, tc_HOL_Obool)), hAPP(_1418649, 33797 ^ [_1418641, _1418643, _1418645, _1418647, _1418649, _1418651, _1418653])), _1418653))], (33799 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418641), 33797 ^ [_1418641, _1418643, _1418645, _1418647, _1418649, _1418651, _1418653]), _1418643)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1418647, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418641, tc_fun(_1418647, tc_HOL_Obool)), _1418651), _1418649)), _1418653)))], (1564 ^ _780478) ^ [_802892, _802894] : [-(class_Groups_Ocancel__ab__semigroup__add(_802892)), _802894 = _802892, class_Groups_Ocancel__ab__semigroup__add(_802894)], (47807 ^ _780478) ^ [_1743592, _1743594, _1743596, _1743598] : [47809 ^ _780478 : [(47812 ^ _780478) ^ [] : [hBOOL(hAPP(_1743596, 47808 ^ [_1743592, _1743594, _1743596, _1743598]))], (47810 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743592), 47808 ^ [_1743592, _1743594, _1743596, _1743598]), hAPP(c_List_Oset(_1743592), _1743594))))]], -(c_List_OtakeWhile(_1743592, _1743596, hAPP(hAPP(c_List_Oappend(_1743592), _1743594), _1743598)) = hAPP(hAPP(c_List_Oappend(_1743592), _1743594), c_List_OtakeWhile(_1743592, _1743596, _1743598)))], (44282 ^ _780478) ^ [_1666831, _1666833] : [class_Complete__Lattice_Ocomplete__lattice(_1666831), -(c_Complete__Lattice_OSup__class_OSup(_1666831, hAPP(c_List_Oset(_1666831), _1666833)) = hAPP(c_List_Ofoldl(_1666831, _1666831, c_Lattices_Osemilattice__sup__class_Osup(_1666831), c_Orderings_Obot__class_Obot(_1666831)), _1666833))], (43646 ^ _780478) ^ [_1651820, _1651822, _1651824, _1651826, _1651828] : [-(hAPP(hAPP(c_List_Olist__update(_1651820, hAPP(hAPP(c_List_Oappend(_1651820), _1651822), hAPP(hAPP(c_List_Olist_OCons(_1651820), _1651824), _1651826))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651820)), _1651822)), _1651828) = hAPP(hAPP(c_List_Oappend(_1651820), _1651822), hAPP(hAPP(c_List_Olist_OCons(_1651820), _1651828), _1651826)))], (42609 ^ _780478) ^ [_1629490, _1629492, _1629494, _1629496] : [42611 ^ _780478 : [(42614 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1629494, 42610 ^ [_1629490, _1629492, _1629494, _1629496])), hAPP(_1629496, 42610 ^ [_1629490, _1629492, _1629494, _1629496])))], (42612 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1629490), 42610 ^ [_1629490, _1629492, _1629494, _1629496]), hAPP(c_List_Oset(_1629490), _1629492))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1629490, _1629494, _1629492)), c_List_Olist_Olist__size(_1629490, _1629496, _1629492))))], (41081 ^ _780478) ^ [_1586442, _1586444] : [-(c_Transitive__Closure_Ortrancl(_1586442, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1586442, _1586442), tc_HOL_Obool)), _1586444), c_Relation_OId(_1586442))) = c_Transitive__Closure_Ortrancl(_1586442, _1586444))], (26702 ^ _780478) ^ [_1275152, _1275154, _1275156, _1275158] : [class_Fields_Olinordered__field__inverse__zero(_1275152), 26705 ^ _780478 : [(26706 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275152), _1275154), _1275156)), _1275158)), 26709 ^ _780478 : [(26716 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), c_Groups_Ozero__class_Ozero(_1275152)), _1275156))), 26719 ^ _780478 : [(26726 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), _1275156), c_Groups_Ozero__class_Ozero(_1275152)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), c_Groups_Ozero__class_Ozero(_1275152)), _1275158)))], (26720 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), _1275156), c_Groups_Ozero__class_Ozero(_1275152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1275152), _1275158), _1275156)), _1275154)))]]], (26710 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), c_Groups_Ozero__class_Ozero(_1275152)), _1275156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), _1275154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1275152), _1275158), _1275156))))]]], (26732 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275152), _1275154), _1275156)), _1275158))), 26735 ^ _780478 : [(26738 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), _1275154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1275152), _1275158), _1275156)))], (26736 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), c_Groups_Ozero__class_Ozero(_1275152)), _1275156)))]], 26739 ^ _780478 : [(26742 ^ _780478) ^ [] : [26743 ^ _780478 : [(26746 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1275152), _1275158), _1275156)), _1275154))], (26744 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), _1275156), c_Groups_Ozero__class_Ozero(_1275152))))]], 26747 ^ _780478 : [(26750 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), c_Groups_Ozero__class_Ozero(_1275152)), _1275158))], (26748 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), _1275156), c_Groups_Ozero__class_Ozero(_1275152)))]]], (26740 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275152), c_Groups_Ozero__class_Ozero(_1275152)), _1275156))]]]]], (18540 ^ _780478) ^ [_1128143, _1128145, _1128147, _1128149] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1128143, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1128145, tc_fun(_1128143, tc_HOL_Obool)), _1128147), _1128149)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1128145, tc_fun(_1128143, tc_HOL_Obool)), _1128147), hAPP(hAPP(c_COMBB(tc_fun(_1128143, tc_HOL_Obool), tc_fun(_1128143, tc_HOL_Obool), _1128145), c_Groups_Ouminus__class_Ouminus(tc_fun(_1128143, tc_HOL_Obool))), _1128149)))], (40446 ^ _780478) ^ [_1570967, _1570969, _1570971, _1570973, _1570975] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570967, _1570967)), hAPP(hAPP(c_Product__Type_OPair(_1570967, _1570967), _1570969), _1570971)), _1570973)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570967, _1570967)), hAPP(hAPP(c_Product__Type_OPair(_1570967, _1570967), _1570971), _1570975)), c_Transitive__Closure_Otrancl(_1570967, _1570973))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570967, _1570967)), hAPP(hAPP(c_Product__Type_OPair(_1570967, _1570967), _1570969), _1570975)), c_Transitive__Closure_Otrancl(_1570967, _1570973))))], (46184 ^ _780478) ^ [_1709797, _1709799] : [-(c_Random_Oselect__weight(_1709797, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1709797), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1709797, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1709797, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1709797)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1709799)) = c_Random_Oselect__weight(_1709797, _1709799))], (17017 ^ _780478) ^ [_1093385, _1093387, _1093389] : [class_Orderings_Olinorder(_1093385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093385), _1093387)), -(_1093387 = c_Orderings_Obot__class_Obot(tc_fun(_1093385, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093385), _1093389)), -(_1093389 = c_Orderings_Obot__class_Obot(tc_fun(_1093385, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1093385, tc_HOL_Obool)), _1093387), _1093389) = c_Orderings_Obot__class_Obot(tc_fun(_1093385, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1093385, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1093385, tc_HOL_Obool)), _1093387), _1093389)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093385), c_Big__Operators_Olinorder__class_OMin(_1093385, _1093387)), c_Big__Operators_Olinorder__class_OMin(_1093385, _1093389)))], (45863 ^ _780478) ^ [_1701275, _1701277, _1701279, _1701281] : [class_Orderings_Olinorder(_1701275), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701277)), c_List_Olinorder__class_Osort__key(_1701277, _1701275, _1701279, _1701281)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701277)), _1701281))], (34433 ^ _780478) ^ [_1429857, _1429859] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1429857)), _1429859) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1429857), _1429859)))], (16238 ^ _780478) ^ [_1075239, _1075241, _1075243, _1075245] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075239, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075239, tc_HOL_Obool)), _1075241), _1075243)), _1075245) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075239, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075239, tc_HOL_Obool)), _1075241), _1075245)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075239, tc_HOL_Obool)), _1075243), _1075245)))], (10927 ^ _780478) ^ [_971038, _971040, _971042, _971044] : [class_Orderings_Olinorder(_971038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971038), _971040), _971042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971038), hAPP(hAPP(c_Orderings_Oord__class_Omin(_971038), _971040), _971044)), _971042)))], (7309 ^ _780478) ^ [_902587, _902589, _902591] : [_902587 = _902589, 7312 ^ _780478 : [(7315 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902591, tc_HOL_Obool)), _902589), _902587)))], (7313 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902591, tc_HOL_Obool)), _902587), _902589)))]]], (44095 ^ _780478) ^ [_1663142, _1663144] : [-(_1663142 = c_List_Olist_ONil(_1663144)), -(hAPP(c_List_Ohd(_1663144), _1663142) = hAPP(hAPP(c_List_Onth(_1663144), _1663142), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (15487 ^ _780478) ^ [_1059741, _1059743, _1059745] : [class_Lattices_Olattice(_1059741), hAPP(_1059743, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1059741), 15492 ^ [_1059741, _1059743, _1059745]), 15493 ^ [_1059741, _1059743, _1059745])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1059741), hAPP(_1059743, 15492 ^ [_1059741, _1059743, _1059745])), hAPP(_1059743, 15493 ^ [_1059741, _1059743, _1059745])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059741), _1059745)), -(_1059745 = c_Orderings_Obot__class_Obot(tc_fun(_1059741, tc_HOL_Obool))), -(hAPP(_1059743, c_Big__Operators_Olattice__class_OSup__fin(_1059741, _1059745)) = c_Big__Operators_Olattice__class_OSup__fin(_1059741, hAPP(c_Set_Oimage(_1059741, _1059741, _1059743), _1059745)))], (48637 ^ _780478) ^ [_1761622, _1761624, _1761626, _1761628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1761622), _1761624)), -(hAPP(hAPP(c_List_Onth(_1761626), c_List_Oreplicate(_1761626, _1761624, _1761628)), _1761622) = _1761628)], (19900 ^ _780478) ^ [_1151738, _1151740] : [class_Rings_Olinordered__ring(_1151738), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151738), c_Groups_Ozero__class_Ozero(_1151738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151738), _1151740), _1151740))))], (17490 ^ _780478) ^ [_1105339, _1105341, _1105343, _1105345, _1105347] : [-(_1105339 = c_Orderings_Obot__class_Obot(tc_fun(_1105341, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105341, tc_fun(_1105343, tc_HOL_Obool)), _1105339), hAPP(hAPP(c_COMBB(tc_fun(_1105343, tc_HOL_Obool), tc_fun(_1105343, tc_HOL_Obool), _1105341), hAPP(c_Set_Oinsert(_1105343), _1105345)), _1105347)) = hAPP(hAPP(c_Set_Oinsert(_1105343), _1105345), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1105341, tc_fun(_1105343, tc_HOL_Obool)), _1105339), _1105347)))], (28290 ^ _780478) ^ [_1304076, _1304078] : [class_Groups_Oordered__ab__group__add(_1304076), -(hAPP(c_Set_Oimage(_1304076, _1304076, c_Groups_Ouminus__class_Ouminus(_1304076)), hAPP(c_SetInterval_Oord__class_OatMost(_1304076), _1304078)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1304076), hAPP(c_Groups_Ouminus__class_Ouminus(_1304076), _1304078)))], (20408 ^ _780478) ^ [_1161042, _1161044, _1161046] : [class_Rings_Olinordered__semiring__strict(_1161042), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161042), c_Groups_Ozero__class_Ozero(_1161042)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161042), _1161044), _1161046))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161042), c_Groups_Ozero__class_Ozero(_1161042)), _1161044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1161042), c_Groups_Ozero__class_Ozero(_1161042)), _1161046)))], (20800 ^ _780478) ^ [_1167974, _1167976, _1167978, _1167980] : [class_Rings_Olinordered__semidom(_1167974), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167974), _1167976), _1167978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167974), c_Groups_Ozero__class_Ozero(_1167974)), _1167976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167974), hAPP(hAPP(c_Power_Opower__class_Opower(_1167974), _1167976), _1167980)), hAPP(hAPP(c_Power_Opower__class_Opower(_1167974), _1167978), _1167980))))], (7327 ^ _780478) ^ [_902903, _902905] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902903, tc_HOL_Obool)), _902905), _902905)))], (51995 ^ _780478) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (33638 ^ _780478) ^ [_1414865, _1414867, _1414869] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414865), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414865)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414867)), _1414869)) = 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), _1414865), _1414867))), _1414869))], (41079 ^ _780478) ^ [_1586411] : [-(c_Relation_Orefl__on(_1586411, c_Orderings_Otop__class_Otop(tc_fun(_1586411, tc_HOL_Obool)), c_Relation_OId(_1586411)))], (51935 ^ _780478) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (43490 ^ _780478) ^ [_1648591, _1648593, _1648595, _1648597, _1648599] : [-(hAPP(hAPP(c_List_Oappend(_1648591), _1648593), _1648595) = hAPP(hAPP(c_List_Oappend(_1648591), _1648597), _1648599)), 43491 ^ _780478 : [(43498 ^ _780478) ^ [_1648815] : [hAPP(hAPP(c_List_Oappend(_1648591), _1648593), _1648815) = _1648597, _1648595 = hAPP(hAPP(c_List_Oappend(_1648591), _1648815), _1648599)], (43492 ^ _780478) ^ [_1648703] : [_1648593 = hAPP(hAPP(c_List_Oappend(_1648591), _1648597), _1648703), hAPP(hAPP(c_List_Oappend(_1648591), _1648703), _1648595) = _1648599]]], (38488 ^ _780478) ^ [_1520569, _1520571, _1520573] : [c_Wellfounded_Owf(_1520569, _1520571), -(c_Wellfounded_Owf(tc_List_Olist(_1520569), hAPP(c_List_Olexn(_1520569, _1520571), _1520573)))], (23275 ^ _780478) ^ [_1213636, _1213638] : [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)), _1213636)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1213638))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1213636), _1213638)))], (45633 ^ _780478) ^ [_1696508, _1696510] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1696508), tc_fun(_1696508, tc_HOL_Obool), c_List_Oset(_1696508)), hAPP(c_List_Oset(tc_List_Olist(_1696508)), c_Enum_Osublists(_1696508, _1696510))) = hAPP(c_Set_OPow(_1696508), hAPP(c_List_Oset(_1696508), _1696510)))], (47151 ^ _780478) ^ [_1729058, _1729060] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729058), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1729058))), _1729060))), 47154 ^ _780478 : [(47161 ^ _780478) ^ [] : [-(_1729060 = c_List_Olist_ONil(tc_List_Olist(_1729058))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1729058))), c_List_Otranspose(_1729058, _1729060)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729058)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1729058)), _1729060), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (47155 ^ _780478) ^ [] : [_1729060 = c_List_Olist_ONil(tc_List_Olist(_1729058)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1729058))), c_List_Otranspose(_1729058, _1729060)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (14020 ^ _780478) ^ [_1031193, _1031195] : [class_Groups_Oone(_1031193), 14023 ^ _780478 : [(14030 ^ _780478) ^ [] : [_1031195 = c_Groups_Oone__class_Oone(_1031193), -(c_Groups_Oone__class_Oone(_1031193) = _1031195)], (14024 ^ _780478) ^ [] : [c_Groups_Oone__class_Oone(_1031193) = _1031195, -(_1031195 = c_Groups_Oone__class_Oone(_1031193))]]], (1804 ^ _780478) ^ [_805892, _805894] : [-(class_Rings_Omult__zero(_805892)), _805894 = _805892, class_Rings_Omult__zero(_805894)], (19502 ^ _780478) ^ [_1145193, _1145195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1145193), _1145195)), _1145195 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47228 ^ _780478) ^ [_1730794, _1730796, _1730798, _1730800, _1730802] : [-(c_List_OtakeWhile(_1730794, _1730796, hAPP(hAPP(c_List_Omap(_1730798, _1730794), _1730800), _1730802)) = hAPP(hAPP(c_List_Omap(_1730798, _1730794), _1730800), c_List_OtakeWhile(_1730798, hAPP(c_Fun_Ocomp(_1730794, tc_HOL_Obool, _1730798, _1730796), _1730800), _1730802)))], (41326 ^ _780478) ^ [_1592602, _1592604, _1592606] : [41328 ^ _780478 : [(41329 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592602), 41327 ^ [_1592602, _1592604, _1592606]), _1592604)))], (41334 ^ _780478) ^ [] : [41327 ^ [_1592602, _1592604, _1592606] = 41330 ^ [_1592602, _1592604, _1592606]], (41338 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592602, _1592602)), hAPP(hAPP(c_Product__Type_OPair(_1592602, _1592602), 41330 ^ [_1592602, _1592604, _1592606]), 41327 ^ [_1592602, _1592604, _1592606])), _1592606))], (41336 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592602, _1592602)), hAPP(hAPP(c_Product__Type_OPair(_1592602, _1592602), 41327 ^ [_1592602, _1592604, _1592606]), 41330 ^ [_1592602, _1592604, _1592606])), _1592606))], (41332 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1592602), 41330 ^ [_1592602, _1592604, _1592606]), _1592604)))]], -(c_Relation_Ototal__on(_1592602, _1592604, _1592606))], (40756 ^ _780478) ^ [_1578590, _1578592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1578590), _1578592)), -(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), _1578590), _1578592)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (16122 ^ _780478) ^ [_1072416, _1072418, _1072420, _1072422] : [hBOOL(hAPP(hAPP(c_member(_1072416), _1072418), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1072416, tc_HOL_Obool)), _1072420), _1072422))), -(hBOOL(hAPP(hAPP(c_member(_1072416), _1072418), _1072422)))], (44181 ^ _780478) ^ [_1664724, _1664726, _1664728] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1664724, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664726)), _1664728)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1664726, _1664724), _1664728) = _1664728)], (48533 ^ _780478) ^ [_1759723, _1759725, _1759727] : [-(c_List_Oreplicate(_1759723, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759723)), hAPP(c_List_Ofilter(_1759723, hAPP(c_fequal, _1759725)), _1759727)), _1759725) = hAPP(c_List_Ofilter(_1759723, hAPP(c_fequal, _1759725)), _1759727))], (4344 ^ _780478) ^ [_846237, _846239, _846241, _846243, _846245, _846247, _846249, _846251] : [-(c_Lazy__Sequence_Oproduct(_846251, _846247, _846243, _846239) = c_Lazy__Sequence_Oproduct(_846249, _846245, _846241, _846237)), _846251 = _846249, _846247 = _846245, _846243 = _846241, _846239 = _846237], (20824 ^ _780478) ^ [_1168426, _1168428, _1168430] : [class_Rings_Olinordered__semidom(_1168426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168426), c_Groups_Ozero__class_Ozero(_1168426)), _1168428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168426), c_Groups_Ozero__class_Ozero(_1168426)), hAPP(hAPP(c_Power_Opower__class_Opower(_1168426), _1168428), _1168430))))], (34365 ^ _780478) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (52243 ^ _780478) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (44294 ^ _780478) ^ [_1667061, _1667063, _1667065] : [class_Lattices_Olattice(_1667061), -(c_Big__Operators_Olattice__class_OSup__fin(_1667061, hAPP(c_List_Oset(_1667061), hAPP(hAPP(c_List_Olist_OCons(_1667061), _1667063), _1667065))) = hAPP(c_List_Ofoldl(_1667061, _1667061, c_Lattices_Osemilattice__sup__class_Osup(_1667061), _1667063), _1667065))], (44141 ^ _780478) ^ [_1663891, _1663893, _1663895, _1663897] : [-(hAPP(c_List_Orotate(_1663891, _1663893), hAPP(c_List_Orotate(_1663891, _1663895), _1663897)) = hAPP(c_List_Orotate(_1663891, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1663893), _1663895)), _1663897))], (20814 ^ _780478) ^ [_1168243, _1168245, _1168247] : [class_Rings_Olinordered__semidom(_1168243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168243), c_Groups_Ozero__class_Ozero(_1168243)), _1168245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168243), c_Groups_Ozero__class_Ozero(_1168243)), hAPP(hAPP(c_Power_Opower__class_Opower(_1168243), _1168245), _1168247))))], (13482 ^ _780478) ^ [_1020883, _1020885, _1020887] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1020883), _1020885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1020883, tc_HOL_Obool)), _1020887), _1020885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1020883), _1020887)), hAPP(c_Finite__Set_Ocard(_1020883), _1020885))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1020883, tc_HOL_Obool)), _1020887), _1020885)))], (38845 ^ _780478) ^ [_1530882, _1530884, _1530886, _1530888, _1530890, _1530892] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530882, _1530884)), hAPP(hAPP(c_Product__Type_OPair(_1530882, _1530884), _1530886), _1530888)), hAPP(hAPP(c_Product__Type_OSigma(_1530882, _1530884), _1530890), _1530892))), 38848 ^ _780478 : [(38851 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530884), _1530888), hAPP(_1530892, _1530886))))], (38849 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1530882), _1530886), _1530890)))]]], (45215 ^ _780478) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (43167 ^ _780478) ^ [_1641106, _1641108, _1641110] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641106), tc_List_Olist(_1641106))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641106), tc_List_Olist(_1641106)), c_List_Olist_ONil(_1641106)), _1641108)), c_List_Olistrel1(_1641106, _1641110)))], (23417 ^ _780478) ^ [_1215883, _1215885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1215883), _1215885)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1215883), _1215885)))], (3102 ^ _780478) ^ [_826542, _826544, _826546, _826548] : [-(c_List_Olistrel1(_826548, _826544) = c_List_Olistrel1(_826546, _826542)), _826548 = _826546, _826544 = _826542], (29449 ^ _780478) ^ [_1327303, _1327305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1327303)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1327305, _1327303)), _1327303)))], (42215 ^ _780478) ^ [_1618396, _1618398, _1618400, _1618402] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618396) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1618398), hAPP(hAPP(c_List_Olist_OCons(_1618398), _1618400), _1618402)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1618396)) = _1618400)], (20526 ^ _780478) ^ [_1163250, _1163252, _1163254, _1163256] : [class_Rings_Olinordered__ring__strict(_1163250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163250), _1163252), _1163254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163250), _1163256), c_Groups_Ozero__class_Ozero(_1163250))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163250), _1163254), _1163256)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163250), _1163252), _1163256))))], (47562 ^ _780478) ^ [_1737711, _1737713, _1737715] : [hBOOL(hAPP(c_List_Odistinct(_1737711), _1737713)), -(hBOOL(hAPP(c_List_Odistinct(_1737711), c_List_Oinsert(_1737711, _1737715, _1737713))))], (37563 ^ _780478) ^ [_1497299, _1497301, _1497303, _1497305] : [c_Equiv__Relations_Oequivp(_1497299, _1497301), hBOOL(hAPP(hAPP(_1497301, _1497303), _1497305)), -(hBOOL(hAPP(hAPP(_1497301, _1497305), _1497303)))], (42469 ^ _780478) ^ [_1625976, _1625978, _1625980, _1625982] : [-(hAPP(c_List_Oset(tc_prod(_1625976, _1625978)), hAPP(hAPP(c_List_Ozip(_1625976, _1625978), _1625980), _1625982)) = hAPP(c_Set_OCollect(tc_prod(_1625976, _1625978)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1625976, _1625978)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1625976, _1625978), 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(_1625976, _1625978)), 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(_1625976, _1625978)), 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(_1625976, _1625978), tc_fun(tc_Nat_Onat, tc_prod(_1625976, _1625978)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1625976, _1625978), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1625976, _1625978)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1625976, _1625978)), c_COMBB(tc_prod(_1625976, _1625978), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1625978, tc_prod(_1625976, _1625978)), hAPP(hAPP(c_COMBB(_1625976, tc_fun(_1625978, tc_prod(_1625976, _1625978)), tc_Nat_Onat), c_Product__Type_OPair(_1625976, _1625978)), hAPP(c_List_Onth(_1625976), _1625980))), hAPP(c_List_Onth(_1625978), _1625982)))))), 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(_1625976)), _1625980)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625978)), _1625982)))))))], (22365 ^ _780478) ^ [_1196421, _1196423, _1196425] : [class_Orderings_Oord(_1196421), 22368 ^ _780478 : [(22375 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196421), _1196423), _1196425)), -(hBOOL(hAPP(hAPP(c_member(_1196421), _1196423), hAPP(c_SetInterval_Oord__class_OlessThan(_1196421), _1196425))))], (22369 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1196421), _1196423), hAPP(c_SetInterval_Oord__class_OlessThan(_1196421), _1196425))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1196421), _1196423), _1196425)))]]], (21310 ^ _780478) ^ [_1176243, _1176245] : [-(_1176243 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1176243), _1176245) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1176243), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1176245)))], (39305 ^ _780478) ^ [_1543558, _1543560, _1543562, _1543564, _1543566] : [c_Relation_Orefl__on(_1543558, _1543560, _1543562), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543558, _1543558)), hAPP(hAPP(c_Product__Type_OPair(_1543558, _1543558), _1543564), _1543566)), _1543562)), -(hBOOL(hAPP(hAPP(c_member(_1543558), _1543564), _1543560)))], (23317 ^ _780478) ^ [_1214246, _1214248] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1214246), _1214248) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1214246), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214248)))], (52217 ^ _780478) ^ [_1832378, _1832380] : [-(class_Enum_Oenum(tc_prod(_1832378, _1832380))), class_Enum_Oenum(_1832378), class_Enum_Oenum(_1832380)], (41138 ^ _780478) ^ [_1587920, _1587922, _1587924, _1587926, _1587928] : [c_Relation_Osingle__valued(_1587920, _1587920, _1587922), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587920, _1587920)), hAPP(hAPP(c_Product__Type_OPair(_1587920, _1587920), _1587924), _1587926)), c_Transitive__Closure_Ortrancl(_1587920, _1587922))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1587920, _1587920)), hAPP(hAPP(c_Product__Type_OPair(_1587920, _1587920), _1587924), _1587928)), c_Transitive__Closure_Ortrancl(_1587920, _1587922))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587920, _1587920)), hAPP(hAPP(c_Product__Type_OPair(_1587920, _1587920), _1587926), _1587928)), c_Transitive__Closure_Ortrancl(_1587920, _1587922)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587920, _1587920)), hAPP(hAPP(c_Product__Type_OPair(_1587920, _1587920), _1587928), _1587926)), c_Transitive__Closure_Ortrancl(_1587920, _1587922))))], (47377 ^ _780478) ^ [_1733872, _1733874, _1733876, _1733878] : [-(hBOOL(hAPP(_1733872, _1733874))), -(c_List_OdropWhile(_1733876, _1733872, hAPP(hAPP(c_List_Olist_OCons(_1733876), _1733874), _1733878)) = hAPP(hAPP(c_List_Olist_OCons(_1733876), _1733874), _1733878))], (41439 ^ _780478) ^ [_1595973, _1595975, _1595977, _1595979, _1595981] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595973, _1595973)), hAPP(hAPP(c_Product__Type_OPair(_1595973, _1595973), _1595975), _1595977)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595973, _1595973), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1595979)), _1595981))), 41443 ^ _780478 : [(41446 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595973, _1595973)), hAPP(hAPP(c_Product__Type_OPair(_1595973, _1595973), 41442 ^ [_1595973, _1595975, _1595977, _1595979, _1595981]), _1595977)), _1595981)))], (41444 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595973, _1595973)), hAPP(hAPP(c_Product__Type_OPair(_1595973, _1595973), _1595975), 41442 ^ [_1595973, _1595975, _1595977, _1595979, _1595981])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1595973, _1595973), tc_HOL_Obool), _1595979), _1595981))))]]], (43103 ^ _780478) ^ [_1639981, _1639983] : [-(c_List_Olist_Olist__size(_1639981, _1639983, c_List_Olist_ONil(_1639981)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50979 ^ _780478) ^ [_1813676, _1813678] : [class_Rings_Ocomm__semiring__1(_1813676), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813676), _1813678), c_Groups_Ozero__class_Ozero(_1813676))))], (29908 ^ _780478) ^ [_1335600, _1335602, _1335604] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1335600, _1335602)), _1335604) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1335600), _1335604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1335602), _1335604)))], (48249 ^ _780478) ^ [_1753022, _1753024, _1753026, _1753028] : [c_List_Olist__all(_1753022, _1753024, hAPP(hAPP(c_List_Olist_OCons(_1753022), _1753026), _1753028)), 48252 ^ _780478 : [(48255 ^ _780478) ^ [] : [-(c_List_Olist__all(_1753022, _1753024, _1753028))], (48253 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1753024, _1753026)))]]], (42477 ^ _780478) ^ [_1626450, _1626452, _1626454] : [_1626450 = _1626452, 42480 ^ _780478 : [(42483 ^ _780478) ^ [_1626606] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1626454, _1626454)), _1626606), hAPP(c_List_Oset(tc_prod(_1626454, _1626454)), hAPP(hAPP(c_List_Ozip(_1626454, _1626454), _1626450), _1626452)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1626454, _1626454, tc_HOL_Obool), c_fequal), _1626606)))], (42481 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626454)), _1626450) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626454)), _1626452))]]], (36347 ^ _780478) ^ [_1471943, _1471945, _1471947, _1471949, _1471951] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471943, _1471945, tc_HOL_Obool), _1471947), hAPP(hAPP(c_Product__Type_OPair(_1471943, _1471945), _1471949), _1471951))), -(hBOOL(hAPP(hAPP(_1471947, _1471949), _1471951)))], (51629 ^ _780478) ^ [_1825417, _1825419] : [class_Rings_Ocomm__semiring__1(_1825417), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1825417), c_Groups_Ozero__class_Ozero(_1825417)), _1825419)), -(_1825419 = c_Groups_Ozero__class_Ozero(_1825417))], (37043 ^ _780478) ^ [_1485016, _1485018, _1485020] : [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), _1485016), _1485018))), -(hBOOL(hAPP(hAPP(_1485020, _1485016), _1485018))), 37050 ^ _780478 : [(37053 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37049 ^ [_1485016, _1485018, _1485020]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1485020, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37048 ^ [_1485016, _1485018, _1485020])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37049 ^ [_1485016, _1485018, _1485020]))))], (37059 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1485020, 37048 ^ [_1485016, _1485018, _1485020]), 37049 ^ [_1485016, _1485018, _1485020]))], (37051 ^ _780478) ^ [] : [-(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), 37048 ^ [_1485016, _1485018, _1485020]), 37049 ^ [_1485016, _1485018, _1485020]))))]]], (4486 ^ _780478) ^ [_848556, _848558] : [_848558 = _848556, -(c_Lazy__Sequence_Oyield(_848558) = c_Lazy__Sequence_Oyield(_848556))], (48441 ^ _780478) ^ [_1757219, _1757221, _1757223] : [-(hAPP(c_New__DSequence_Opos__single(_1757219, _1757221), _1757223) = hAPP(c_Lazy__Sequence_Osingle(_1757219), _1757221))], (788 ^ _780478) ^ [_792324, _792326, _792328, _792330] : [-(c_Relation_Otrans(_792328, _792324)), c_Relation_Otrans(_792330, _792326), _792330 = _792328, _792326 = _792324], (24663 ^ _780478) ^ [_1238866, _1238868, _1238870, _1238872] : [_1238866 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1238868), _1238870)), _1238872), -(_1238868 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1238866), _1238868) = _1238870), 24670 ^ _780478 : [(24673 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238872), _1238868))], (24671 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238868)))]], 24678 ^ _780478 : [(24681 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1238868), _1238872)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1238872), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24679 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238868))]]], (15403 ^ _780478) ^ [_1058004, _1058006] : [class_Groups_Omonoid__mult(_1058004), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1058004), _1058006), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1058006)], (6172 ^ _780478) ^ [_879179, _879181, _879183] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_879179), _879183)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_879179), hAPP(hAPP(c_Set_Oinsert(_879179), _879181), _879183))))], (7122 ^ _780478) ^ [_899344, _899346, _899348, _899350] : [class_Orderings_Oord(_899344), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899344), _899346), _899348)), _899348 = _899350, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899344), _899346), _899350)))], (39035 ^ _780478) ^ [_1537097, _1537099] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1537097, _1537099, tc_prod(_1537097, _1537099)), c_Product__Type_OPair(_1537097, _1537099)) = c_Fun_Oid(tc_prod(_1537097, _1537099)))], (5923 ^ _780478) ^ [_874625, _874627, _874629, _874631] : [_874625 = _874627, 5926 ^ _780478 : [(5933 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874629), _874627), _874631)), -(hBOOL(hAPP(hAPP(c_member(_874629), _874625), _874631)))], (5927 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874629), _874625), _874631)), -(hBOOL(hAPP(hAPP(c_member(_874629), _874627), _874631)))]]], (51231 ^ _780478) ^ [_1818634, _1818636, _1818638, _1818640, _1818642] : [class_Rings_Ocomm__semiring__1(_1818634), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818634), _1818636), _1818638)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818634), _1818640), _1818642)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1818634), _1818636), _1818640)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1818634), _1818638), _1818642))))], (25465 ^ _780478) ^ [_1253247] : [hBOOL(hAPP(_1253247, 25466 ^ [_1253247])), 25469 ^ _780478 : [(25470 ^ _780478) ^ [_1253341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1253341)), -(hBOOL(hAPP(_1253247, hAPP(c_Int_Onat, _1253341))))]]], (12722 ^ _780478) ^ [_1005575, _1005577, _1005579] : [class_Lattices_Osemilattice__sup(_1005575), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005575), _1005577), _1005579) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1005575), _1005579), _1005577))], (5979 ^ _780478) ^ [_875544, _875546, _875548, _875550] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_875544), _875546), _875548), _875550)), -(_875546 = _875550), -(hBOOL(hAPP(_875548, _875550)))], (27310 ^ _780478) ^ [_1286047, _1286049] : [c_Nat__Transfer_Ois__nat(_1286047), c_Nat__Transfer_Onat__set(_1286049), 27317 ^ _780478 : [(27324 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1286047)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1286049))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1286047), _1286049)))], (27318 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1286047), _1286049)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1286047)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1286049))))]]], (12752 ^ _780478) ^ [_1006202, _1006204, _1006206, _1006208] : [class_Lattices_Olattice(_1006202), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006202), _1006204), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006202), _1006206), _1006208)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006202), _1006206), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006202), _1006204), _1006208)))], (29061 ^ _780478) ^ [_1319458, _1319460, _1319462] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1319458, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1319458, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1319458), _1319460)), hAPP(c_Set_OPow(_1319458), _1319462))), hAPP(c_Set_OPow(_1319458), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319458, tc_HOL_Obool)), _1319460), _1319462)))))], (43686 ^ _780478) ^ [_1652860, _1652862, _1652864, _1652866, _1652868] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652860), tc_List_Olist(_1652860))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652860), tc_List_Olist(_1652860)), _1652862), _1652864)), c_List_Olexord(_1652860, _1652866))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652860), tc_List_Olist(_1652860))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652860), tc_List_Olist(_1652860)), hAPP(hAPP(c_List_Oappend(_1652860), _1652868), _1652862)), hAPP(hAPP(c_List_Oappend(_1652860), _1652868), _1652864))), c_List_Olexord(_1652860, _1652866))))], (33825 ^ _780478) ^ [_1419497, _1419499] : [class_Int_Onumber__ring(_1419497), 33828 ^ _780478 : [(33835 ^ _780478) ^ [] : [c_Int_Oiszero(_1419497, hAPP(c_Int_Onumber__class_Onumber__of(_1419497), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1419499)))), -(c_Groups_Ozero__class_Ozero(_1419497) = hAPP(c_Int_Onumber__class_Onumber__of(_1419497), _1419499))], (33829 ^ _780478) ^ [] : [c_Groups_Ozero__class_Ozero(_1419497) = hAPP(c_Int_Onumber__class_Onumber__of(_1419497), _1419499), -(c_Int_Oiszero(_1419497, hAPP(c_Int_Onumber__class_Onumber__of(_1419497), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1419499)))))]]], (50070 ^ _780478) ^ [_1792571, _1792573, _1792575, _1792577] : [hAPP(c_Set_Oimage(_1792571, _1792573, _1792575), c_Orderings_Otop__class_Otop(tc_fun(_1792571, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1792573, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1792571, _1792573, _1792575), hAPP(c_Set_Oimage(_1792573, _1792571, c_Hilbert__Choice_Oinv__into(_1792571, _1792573, c_Orderings_Otop__class_Otop(tc_fun(_1792571, tc_HOL_Obool)), _1792575)), _1792577)) = _1792577)], (52235 ^ _780478) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (36140 ^ _780478) ^ [_1467520, _1467522, _1467524, _1467526, _1467528] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1467520, _1467522), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1467524), _1467526))), -(_1467522 = 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), _1467528), _1467520), _1467522), 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), _1467528), _1467524)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1467528), _1467526)), _1467522))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1467528), _1467526), _1467522)))))], (12113 ^ _780478) ^ [_993316, _993318, _993320] : [class_Orderings_Olinorder(_993316), hBOOL(hAPP(c_Finite__Set_Ofinite(_993316), _993318)), 12120 ^ _780478 : [(12127 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_993316, tc_HOL_Obool)), _993318), hAPP(hAPP(c_Set_Oinsert(_993316), _993320), c_Orderings_Obot__class_Obot(tc_fun(_993316, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_993316, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_993316, c_Orderings_Oord__class_Omax(_993316), hAPP(hAPP(c_Set_Oinsert(_993316), _993320), _993318)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_993316), _993320), c_Big__Operators_Olattice_OSup__fin(_993316, c_Orderings_Oord__class_Omax(_993316), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_993316, tc_HOL_Obool)), _993318), hAPP(hAPP(c_Set_Oinsert(_993316), _993320), c_Orderings_Obot__class_Obot(tc_fun(_993316, tc_HOL_Obool)))))))], (12121 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_993316, tc_HOL_Obool)), _993318), hAPP(hAPP(c_Set_Oinsert(_993316), _993320), c_Orderings_Obot__class_Obot(tc_fun(_993316, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_993316, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_993316, c_Orderings_Oord__class_Omax(_993316), hAPP(hAPP(c_Set_Oinsert(_993316), _993320), _993318)) = _993320)]]], (42005 ^ _780478) ^ [_1612513, _1612515, _1612517, _1612519] : [c_List_Olistrelp(_1612513, hAPP(hAPP(c_COMBC(_1612513, tc_fun(tc_prod(_1612513, _1612513), tc_HOL_Obool), tc_fun(_1612513, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612513, tc_fun(tc_fun(tc_prod(_1612513, _1612513), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1612513, _1612513), tc_HOL_Obool), tc_fun(_1612513, tc_HOL_Obool)), _1612513), c_COMBC(_1612513, tc_fun(tc_prod(_1612513, _1612513), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1612513, tc_prod(_1612513, _1612513)), tc_fun(_1612513, tc_fun(tc_fun(tc_prod(_1612513, _1612513), tc_HOL_Obool), tc_HOL_Obool)), _1612513), hAPP(c_COMBB(tc_prod(_1612513, _1612513), tc_fun(tc_fun(tc_prod(_1612513, _1612513), tc_HOL_Obool), tc_HOL_Obool), _1612513), c_member(tc_prod(_1612513, _1612513)))), c_Product__Type_OPair(_1612513, _1612513)))), _1612515), _1612517, _1612519), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612513), tc_List_Olist(_1612513))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612513), tc_List_Olist(_1612513)), _1612517), _1612519)), c_List_Olistrel(_1612513, _1612515))))], (27986 ^ _780478) ^ [_1298088, _1298090, _1298092] : [-(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)), _1298088)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1298090, _1298092)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1298090), _1298088), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1298092), _1298088)))], (16679 ^ _780478) ^ [_1085602, _1085604, _1085606] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1085602), _1085604)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085602), _1085606)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1085602), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1085602, tc_HOL_Obool)), _1085604), _1085606))), hAPP(c_Finite__Set_Ocard(_1085602), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1085602, tc_HOL_Obool)), _1085604), _1085606))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1085602), _1085604)), hAPP(c_Finite__Set_Ocard(_1085602), _1085606)))], (3428 ^ _780478) ^ [_831599, _831601, _831603, _831605] : [-(c_List_OremoveAll(_831605, _831601) = c_List_OremoveAll(_831603, _831599)), _831605 = _831603, _831601 = _831599], (15587 ^ _780478) ^ [_1061875, _1061877, _1061879, _1061881] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1061875, tc_HOL_Obool)), _1061877), _1061879), _1061881)), 15590 ^ _780478 : [(15593 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1061879, _1061881)))], (15591 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1061877, _1061881)))]]], (44835 ^ _780478) ^ [_1678829, _1678831, _1678833, _1678835, _1678837, _1678839] : [-(hAPP(hAPP(c_List_Omap(_1678829, _1678831), _1678833), hAPP(hAPP(c_List_Omap(_1678835, _1678829), _1678837), _1678839)) = hAPP(hAPP(c_List_Omap(_1678835, _1678831), hAPP(c_Fun_Ocomp(_1678829, _1678831, _1678835, _1678833), _1678837)), _1678839))], (46370 ^ _780478) ^ [_1713712, _1713714, _1713716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713712), _1713714)), _1713716)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1713712, _1713716)), _1713714) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1713712), _1713714))], (17219 ^ _780478) ^ [_1097512, _1097514, _1097516, _1097518] : [class_Complete__Lattice_Ocomplete__lattice(_1097512), -(_1097514 = c_Orderings_Obot__class_Obot(tc_fun(_1097516, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097516, _1097512), _1097514), hAPP(c_COMBK(_1097512, _1097516), _1097518)) = _1097518)], (50020 ^ _780478) ^ [_1791578, _1791580, _1791582, _1791584, _1791586, _1791588] : [c_Fun_Oinj__on(_1791578, _1791580, _1791582, _1791584), hBOOL(hAPP(hAPP(c_member(_1791578), _1791586), _1791584)), hAPP(_1791582, _1791586) = _1791588, -(hAPP(c_Hilbert__Choice_Oinv__into(_1791578, _1791580, _1791584, _1791582), _1791588) = _1791586)], (6630 ^ _780478) ^ [_889434, _889436, _889438, _889440, _889442, _889444] : [c_Finite__Set_Ofolding__image__simple(_889434, _889436, _889438, _889440, _889442, _889444), -(hAPP(_889444, c_Orderings_Obot__class_Obot(tc_fun(_889436, tc_HOL_Obool))) = _889440)], (38232 ^ _780478) ^ [_1514882, _1514884] : [c_Wellfounded_Owf(_1514882, _1514884), -(c_Wellfounded_Owf(tc_fun(_1514882, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1514882, _1514884)))], (27409 ^ _780478) ^ [_1287682, _1287684] : [c_Nat__Transfer_Ois__nat(_1287682), c_Nat__Transfer_Ois__nat(_1287684), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1287682), _1287684)))], (47270 ^ _780478) ^ [_1731495, _1731497, _1731499, _1731501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731495), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1731497)), c_List_OtakeWhile(_1731497, _1731499, _1731501)))), -(hAPP(hAPP(c_List_Onth(_1731497), c_List_OtakeWhile(_1731497, _1731499, _1731501)), _1731495) = hAPP(hAPP(c_List_Onth(_1731497), _1731501), _1731495))], (29007 ^ _780478) ^ [_1318038, _1318040] : [hAPP(c_Set_OPow(_1318038), _1318040) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1318038, tc_HOL_Obool), tc_HOL_Obool))], (4890 ^ _780478) ^ [_855030, _855032, _855034, _855036] : [-(c_Complete__Lattice_OSup__class_OSup(_855036, _855032) = c_Complete__Lattice_OSup__class_OSup(_855034, _855030)), _855036 = _855034, _855032 = _855030], (39057 ^ _780478) ^ [_1537526, _1537528, _1537530, _1537532, _1537534, _1537536] : [class_Groups_Ocomm__monoid__mult(_1537526), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537528), _1537530)), 39067 ^ _780478 : [(39070 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1537532), hAPP(_1537534, 39066 ^ [_1537526, _1537528, _1537530, _1537532, _1537534, _1537536])))], (39068 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1537528), 39066 ^ [_1537526, _1537528, _1537530, _1537532, _1537534, _1537536]), _1537530)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1537528, _1537526), hAPP(hAPP(c_COMBS(_1537528, tc_fun(_1537532, tc_HOL_Obool), _1537526), hAPP(hAPP(c_COMBB(tc_fun(_1537532, _1537526), tc_fun(tc_fun(_1537532, tc_HOL_Obool), _1537526), _1537528), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1537532, _1537526)), _1537536)), _1537534)), _1537530) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1537528, _1537532), _1537526), hAPP(c_Product__Type_Oprod_Oprod__case(_1537528, _1537532, _1537526), _1537536)), hAPP(hAPP(c_Product__Type_OSigma(_1537528, _1537532), _1537530), _1537534)))], (952 ^ _780478) ^ [_794742, _794744, _794746, _794748, _794750, _794752, _794754, _794756, _794758, _794760, _794762, _794764] : [-(c_Equiv__Relations_Ocongruent2(_794762, _794758, _794754, _794750, _794746, _794742)), c_Equiv__Relations_Ocongruent2(_794764, _794760, _794756, _794752, _794748, _794744), _794764 = _794762, _794760 = _794758, _794756 = _794754, _794752 = _794750, _794748 = _794746, _794744 = _794742], (24455 ^ _780478) ^ [_1234867, _1234869, _1234871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234867), 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)), _1234869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234869), _1234871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234867), _1234869)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1234867), _1234871))))], (44676 ^ _780478) ^ [_1674363, _1674365, _1674367, _1674369] : [-(_1674363 = c_List_Olist_ONil(_1674365)), -(c_List_Olast(_1674367, hAPP(hAPP(c_List_Omap(_1674365, _1674367), _1674369), _1674363)) = hAPP(_1674369, c_List_Olast(_1674365, _1674363)))], (27970 ^ _780478) ^ [_1297664, _1297666] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1297664, _1297666)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1297664), hAPP(c_Nat_OSuc, _1297666)))], (31815 ^ _780478) ^ [_1381420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1381420), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1381420)))], (11075 ^ _780478) ^ [_973881, _973883, _973885] : [hBOOL(hAPP(hAPP(c_member(_973881), _973883), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_973881, tc_HOL_Obool)), _973885))), hBOOL(hAPP(hAPP(c_member(_973881), _973883), _973885))], (5248 ^ _780478) ^ [_860681, _860683, _860685, _860687] : [-(c_Transitive__Closure_Ortrancl(_860687, _860683) = c_Transitive__Closure_Ortrancl(_860685, _860681)), _860687 = _860685, _860683 = _860681], (14531 ^ _780478) ^ [_1040192, _1040194, _1040196] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040192), _1040194)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1040192), _1040196)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040194), _1040196))], (512 ^ _780478) ^ [_788168, _788170, _788172, _788174, _788176, _788178] : [-(c_Finite__Set_Ofun__left__comm__idem(_788176, _788172, _788168)), c_Finite__Set_Ofun__left__comm__idem(_788178, _788174, _788170), _788178 = _788176, _788174 = _788172, _788170 = _788168], (12221 ^ _780478) ^ [_995559, _995561, _995563] : [class_Orderings_Olinorder(_995559), hAPP(_995561, hAPP(hAPP(c_Orderings_Oord__class_Omin(_995559), 12226 ^ [_995559, _995561, _995563]), 12227 ^ [_995559, _995561, _995563])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_995559), hAPP(_995561, 12226 ^ [_995559, _995561, _995563])), hAPP(_995561, 12227 ^ [_995559, _995561, _995563])), hBOOL(hAPP(c_Finite__Set_Ofinite(_995559), _995563)), -(_995563 = c_Orderings_Obot__class_Obot(tc_fun(_995559, tc_HOL_Obool))), -(hAPP(_995561, c_Big__Operators_Olattice_OInf__fin(_995559, c_Orderings_Oord__class_Omin(_995559), _995563)) = c_Big__Operators_Olattice_OInf__fin(_995559, c_Orderings_Oord__class_Omin(_995559), hAPP(c_Set_Oimage(_995559, _995559, _995561), _995563)))], (19362 ^ _780478) ^ [_1143142, _1143144] : [class_Groups_Ogroup__add(_1143142), 19365 ^ _780478 : [(19372 ^ _780478) ^ [] : [_1143144 = c_Groups_Ozero__class_Ozero(_1143142), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1143142), _1143144) = c_Groups_Ozero__class_Ozero(_1143142))], (19366 ^ _780478) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1143142), _1143144) = c_Groups_Ozero__class_Ozero(_1143142), -(_1143144 = c_Groups_Ozero__class_Ozero(_1143142))]]], (30785 ^ _780478) ^ [_1352381, _1352383, _1352385] : [class_Fields_Olinordered__field__inverse__zero(_1352381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352381), c_Groups_Ozero__class_Ozero(_1352381)), _1352383)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352381), hAPP(c_Groups_Oabs__class_Oabs(_1352381), _1352385)), _1352383) = hAPP(c_Groups_Oabs__class_Oabs(_1352381), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352381), _1352385), _1352383)))], (44053 ^ _780478) ^ [_1662415, _1662417, _1662419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662415), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662417)), _1662419))), -(hAPP(hAPP(c_List_Oappend(_1662417), hAPP(hAPP(c_List_Otake(_1662417), _1662415), _1662419)), hAPP(hAPP(c_List_Olist_OCons(_1662417), hAPP(c_List_Ohd(_1662417), hAPP(hAPP(c_List_Odrop(_1662417), _1662415), _1662419))), c_List_Olist_ONil(_1662417))) = hAPP(hAPP(c_List_Otake(_1662417), hAPP(c_Nat_OSuc, _1662415)), _1662419))], (21598 ^ _780478) ^ [_1181627, _1181629, _1181631, _1181633] : [class_Rings_Olinordered__semiring__strict(_1181627), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181627), _1181629), _1181631)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1181627), _1181629), _1181633))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181627), c_Groups_Ozero__class_Ozero(_1181627)), _1181629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181627), _1181631), _1181633)))], (37832 ^ _780478) ^ [_1503438, _1503440] : [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)), _1503438), _1503440)), 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)), _1503438), 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)), _1503440), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (23895 ^ _780478) ^ [_1224790, _1224792, _1224794] : [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), _1224790), _1224792)), _1224794))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224794), _1224790)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224792)))], (7030 ^ _780478) ^ [_897894, _897896, _897898] : [-(c_Fun_Oinj__on(_897894, _897896, _897898, c_Orderings_Obot__class_Obot(tc_fun(_897894, tc_HOL_Obool))))], (11353 ^ _780478) ^ [_979218, _979220] : [_979220 = c_Orderings_Obot__class_Obot(tc_fun(_979218, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_979218, tc_HOL_Obool)), _979220), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_979218, tc_HOL_Obool)), _979220))))], (37622 ^ _780478) ^ [_1498508, _1498510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1498508), _1498510)), -(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), _1498508), _1498510)), c_Wellfounded_Oless__than)))], (42935 ^ _780478) ^ [_1636995, _1636997, _1636999] : [hBOOL(hAPP(c_List_Odistinct(_1636995), _1636997)), -(hAPP(c_List_Oset(_1636995), c_List_Oremove1(_1636995, _1636999, _1636997)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1636995, tc_HOL_Obool)), hAPP(c_List_Oset(_1636995), _1636997)), hAPP(hAPP(c_Set_Oinsert(_1636995), _1636999), c_Orderings_Obot__class_Obot(tc_fun(_1636995, tc_HOL_Obool)))))], (25679 ^ _780478) ^ [_1256919] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256919))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52441 ^ _780478) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P_H)), v_c0)), v_Q_H)), v_F)), -(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P)), v_c0)), v_Q)), v_F)))], (37762 ^ _780478) ^ [_1501357, _1501359, _1501361, _1501363] : [_1501357 = _1501359, hBOOL(hAPP(hAPP(c_member(_1501361), _1501357), _1501363)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1501361, _1501361)), hAPP(hAPP(c_Product__Type_OPair(_1501361, _1501361), _1501357), _1501359)), c_Relation_OId__on(_1501361, _1501363))))], (25148 ^ _780478) ^ [_1247671, _1247673, _1247675, _1247677] : [c_Sum__Type_OPlus(_1247671, _1247673, _1247675, _1247677) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1247671, _1247673), tc_HOL_Obool)), 25151 ^ _780478 : [(25154 ^ _780478) ^ [] : [-(_1247677 = c_Orderings_Obot__class_Obot(tc_fun(_1247673, tc_HOL_Obool)))], (25152 ^ _780478) ^ [] : [-(_1247675 = c_Orderings_Obot__class_Obot(tc_fun(_1247671, tc_HOL_Obool)))]]], (36046 ^ _780478) ^ [_1465313, _1465315, _1465317, _1465319, _1465321] : [c_Equiv__Relations_Oequiv(_1465313, _1465315, _1465317), hBOOL(hAPP(hAPP(c_member(_1465313), _1465319), _1465315)), hBOOL(hAPP(hAPP(c_member(_1465313), _1465321), _1465315)), 36057 ^ _780478 : [(36064 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1465313, _1465313)), hAPP(hAPP(c_Product__Type_OPair(_1465313, _1465313), _1465319), _1465321)), _1465317)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1465313), hAPP(hAPP(c_Set_Oinsert(_1465313), _1465319), c_Orderings_Obot__class_Obot(tc_fun(_1465313, tc_HOL_Obool)))), _1465317) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1465313), hAPP(hAPP(c_Set_Oinsert(_1465313), _1465321), c_Orderings_Obot__class_Obot(tc_fun(_1465313, tc_HOL_Obool)))), _1465317))], (36058 ^ _780478) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1465313), hAPP(hAPP(c_Set_Oinsert(_1465313), _1465319), c_Orderings_Obot__class_Obot(tc_fun(_1465313, tc_HOL_Obool)))), _1465317) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1465313), hAPP(hAPP(c_Set_Oinsert(_1465313), _1465321), c_Orderings_Obot__class_Obot(tc_fun(_1465313, tc_HOL_Obool)))), _1465317), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1465313, _1465313)), hAPP(hAPP(c_Product__Type_OPair(_1465313, _1465313), _1465319), _1465321)), _1465317)))]]], (43165 ^ _780478) ^ [_1641038, _1641040, _1641042] : [-(hAPP(hAPP(c_List_Otake(_1641038), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1641038), _1641040), _1641042)) = hAPP(hAPP(c_List_Olist_OCons(_1641038), _1641040), c_List_Olist_ONil(_1641038)))], (40514 ^ _780478) ^ [_1572801, _1572803] : [-(c_Transitive__Closure_Otrancl(_1572801, c_Transitive__Closure_Ortrancl(_1572801, _1572803)) = c_Transitive__Closure_Ortrancl(_1572801, _1572803))], (34777 ^ _780478) ^ [_1436102] : [class_Rings_Osemiring__1(_1436102), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1436102), c_Groups_Oone__class_Oone(_1436102)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1436102))], (48588 ^ _780478) ^ [_1760804, _1760806, _1760808, _1760810] : [48590 ^ _780478 : [(48593 ^ _780478) ^ [] : [hBOOL(hAPP(_1760810, 48589 ^ [_1760804, _1760806, _1760808, _1760810]))], (48591 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760804), 48589 ^ [_1760804, _1760806, _1760808, _1760810]), hAPP(c_List_Oset(_1760804), c_List_Oreplicate(_1760804, _1760806, _1760808)))))]], -(hBOOL(hAPP(_1760810, _1760808))), -(_1760806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2842 ^ _780478) ^ [_822548, _822550] : [_822550 = _822548, -(c_Relation_OField(_822550) = c_Relation_OField(_822548))], (12758 ^ _780478) ^ [_1006345, _1006347, _1006349, _1006351] : [class_Lattices_Osemilattice__sup(_1006345), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006345), _1006347), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006345), _1006349), _1006351)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006345), _1006349), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1006345), _1006347), _1006351)))], (39155 ^ _780478) ^ [_1540183, _1540185, _1540187, _1540189] : [-(c_Product__Type_Oapsnd(_1540183, _1540185, _1540187, _1540189) = c_Product__Type_Omap__pair(_1540187, _1540187, _1540183, _1540185, c_Fun_Oid(_1540187), _1540189))], (33592 ^ _780478) ^ [_1414035, _1414037] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414035), c_Int_OPls))), 33595 ^ _780478 : [(33602 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414037), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414035)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414037)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1414035), _1414037)))], (33596 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1414037), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414035)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414037)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414035))]]], (49064 ^ _780478) ^ [_1770962, _1770964] : [-(c_Lazy__Sequence_Oappend(_1770962, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770962), _1770964) = _1770964)], (5364 ^ _780478) ^ [_862475, _862477, _862479, _862481, _862483, _862485, _862487, _862489, _862491, _862493] : [-(c_New__DSequence_Opos__map(_862493, _862489, _862485, _862481, _862477) = c_New__DSequence_Opos__map(_862491, _862487, _862483, _862479, _862475)), _862493 = _862491, _862489 = _862487, _862485 = _862483, _862481 = _862479, _862477 = _862475], (23357 ^ _780478) ^ [_1214982] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1214982)), _1214982) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6089 ^ _780478) ^ [_877429, _877431, _877433, _877435, _877437, _877439] : [hBOOL(hAPP(hAPP(c_member(_877429), _877431), _877433)), _877435 = hAPP(_877437, _877431), -(hBOOL(hAPP(hAPP(c_member(_877439), _877435), hAPP(c_Set_Oimage(_877429, _877439, _877437), _877433))))], (30917 ^ _780478) ^ [_1354891, _1354893, _1354895, _1354897] : [-(_1354891 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1354893, tc_HOL_Obool), tc_HOL_Obool))), 30923 ^ _780478 : [(30926 ^ _780478) ^ [] : [c_Fun_Oinj__on(_1354893, _1354895, _1354897, 30922 ^ [_1354891, _1354893, _1354895, _1354897])], (30924 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1354893, tc_HOL_Obool)), 30922 ^ [_1354891, _1354893, _1354895, _1354897]), _1354891)))]], -(c_Fun_Oinj__on(_1354893, _1354895, _1354897, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1354893, tc_HOL_Obool), _1354891)))], (27815 ^ _780478) ^ [_1295032, _1295034] : [27817 ^ _780478 : [(27820 ^ _780478) ^ [] : [hBOOL(hAPP(_1295034, 27816 ^ [_1295032, _1295034]))], (27818 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 27816 ^ [_1295032, _1295034]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1295032))))]], 27821 ^ _780478 : [(27822 ^ _780478) ^ [_1295187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1295187), _1295032)), -(hBOOL(hAPP(_1295034, _1295187)))]]], (8838 ^ _780478) ^ [_933154, _933156, _933158] : [class_Orderings_Oorder(_933154), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933154), _933156), _933158)), _933156 = _933158], (46477 ^ _780478) ^ [_1715955, _1715957, _1715959] : [class_Orderings_Olinorder(_1715955), c_List_Olinorder__class_Osorted(_1715955, _1715957), -(c_List_Olinorder__class_Osorted(_1715955, hAPP(hAPP(c_List_Otake(_1715955), _1715959), _1715957)))], (45829 ^ _780478) ^ [_1700558, _1700560, _1700562] : [-(hBOOL(hAPP(hAPP(c_member(_1700558), _1700560), hAPP(c_List_Oset(_1700558), _1700562)))), -(c_List_Oremdups(_1700558, hAPP(hAPP(c_List_Olist_OCons(_1700558), _1700560), _1700562)) = hAPP(hAPP(c_List_Olist_OCons(_1700558), _1700560), c_List_Oremdups(_1700558, _1700562)))], (18812 ^ _780478) ^ [_1133696, _1133698, _1133700] : [class_Lattices_Olattice(_1133696), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133696), _1133698)), -(_1133698 = c_Orderings_Obot__class_Obot(tc_fun(_1133696, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1133696), _1133700)), -(_1133700 = c_Orderings_Obot__class_Obot(tc_fun(_1133696, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1133696, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1133696, tc_HOL_Obool)), _1133698), _1133700)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1133696), c_Big__Operators_Olattice__class_OInf__fin(_1133696, _1133698)), c_Big__Operators_Olattice__class_OInf__fin(_1133696, _1133700)))], (46246 ^ _780478) ^ [_1711607, _1711609] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1711607), _1711609))), -(c_List_Oupt(_1711607, hAPP(c_Nat_OSuc, _1711609)) = c_List_Olist_ONil(tc_Nat_Onat))], (25651 ^ _780478) ^ [_1256401, _1256403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1256401), hAPP(c_Int_Onat, _1256403))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1256401)), _1256403)))], (33330 ^ _780478) ^ [_1409937] : [class_Int_Onumber__ring(_1409937), -(hAPP(c_Int_Onumber__class_Onumber__of(_1409937), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1409937))], (34509 ^ _780478) ^ [_1431225, _1431227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1431225)), c_Int_OBit1(_1431227))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1431225), _1431227)))], (14078 ^ _780478) ^ [_1032060, _1032062, _1032064] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1032060), _1032062)), _1032064) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032060), _1032064)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1032062), _1032064)))], (42103 ^ _780478) ^ [_1615445, _1615447, _1615449, _1615451] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615445)), hAPP(hAPP(c_List_Olist_OCons(_1615445), _1615447), _1615449)), c_List_Olists(_1615445, _1615451)))), hBOOL(hAPP(hAPP(c_member(_1615445), _1615447), _1615451)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1615445)), _1615449), c_List_Olists(_1615445, _1615451)))], (1614 ^ _780478) ^ [_803517, _803519] : [-(class_Rings_Olinordered__semidom(_803517)), _803519 = _803517, class_Rings_Olinordered__semidom(_803519)], (36212 ^ _780478) ^ [_1468934, _1468936, _1468938, _1468940, _1468942, _1468944] : [hBOOL(hAPP(hAPP(_1468934, _1468936), _1468938)), hBOOL(hAPP(hAPP(_1468940, _1468936), _1468938)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1468942, tc_fun(_1468944, tc_HOL_Obool))), _1468934), _1468940), _1468936), _1468938)))], (7246 ^ _780478) ^ [_901288, _901290, _901292] : [class_Orderings_Olinorder(_901288), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901288), _901290), _901292))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901288), _901292), _901290)))], (33971 ^ _780478) ^ [_1422029] : [class_Rings_Osemiring__1(_1422029), c_Int_Oiszero(_1422029, c_Groups_Oone__class_Oone(_1422029))], (35373 ^ _780478) ^ [_1447050] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447050), c_Int_OMin) = c_Int_Opred(_1447050))], (27098 ^ _780478) ^ [_1282663, _1282665] : [c_Nat__Transfer_Onat__set(_1282663), c_Nat__Transfer_Onat__set(_1282665), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1282663), _1282665) = 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), _1282663)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1282665))))], (29500 ^ _780478) ^ [_1328223, _1328225, _1328227] : [class_Divides_Osemiring__div(_1328223), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328223), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328223), _1328225), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1328223), _1328227), _1328225))), c_Divides_Odiv__class_Omod(_1328223, _1328227, _1328225)) = _1328227)], (45393 ^ _780478) ^ [_1691082, _1691084, _1691086, _1691088, _1691090] : [c_List_Olist__all2(_1691082, _1691084, _1691086, _1691088, _1691090), 45396 ^ _780478 : [(45399 ^ _780478) ^ [_1691248] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1691082, _1691084)), _1691248), hAPP(c_List_Oset(tc_prod(_1691082, _1691084)), hAPP(hAPP(c_List_Ozip(_1691082, _1691084), _1691088), _1691090)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1691082, _1691084, tc_HOL_Obool), _1691086), _1691248)))], (45397 ^ _780478) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691082)), _1691088) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691084)), _1691090))]]], (29494 ^ _780478) ^ [_1328090, _1328092, _1328094] : [class_Divides_Osemiring__div(_1328090), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328090), c_Divides_Odiv__class_Omod(_1328090, _1328092, _1328094)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328090), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1328090), _1328092), _1328094)), _1328094)) = _1328092)], (29313 ^ _780478) ^ [_1324741, _1324743] : [class_Divides_Osemiring__div(_1324741), -(c_Divides_Odiv__class_Omod(_1324741, _1324743, c_Groups_Ozero__class_Ozero(_1324741)) = _1324743)], (44823 ^ _780478) ^ [_1678558, _1678560, _1678562, _1678564] : [-(_1678558 = c_List_Olist_ONil(_1678560)), -(hAPP(c_List_Ohd(_1678562), hAPP(hAPP(c_List_Omap(_1678560, _1678562), _1678564), _1678558)) = hAPP(_1678564, hAPP(c_List_Ohd(_1678560), _1678558)))], (31238 ^ _780478) ^ [_1362160, _1362162, _1362164, _1362166] : [hBOOL(hAPP(hAPP(c_member(_1362160), _1362162), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1362160, tc_HOL_Obool)), _1362164), hAPP(c_Set_OCollect(_1362160), _1362166)))), 31241 ^ _780478 : [(31244 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1362166, _1362162)))], (31242 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1362160), _1362162), _1362164)))]]], (3288 ^ _780478) ^ [_829473, _829475] : [_829475 = _829473, -(c_Random_Orange(_829475) = c_Random_Orange(_829473))], (6280 ^ _780478) ^ [_881431, _881433, _881435] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_881431, _881433, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_881431)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_881431), _881435), c_Com_Ocom_OSKIP), _881435)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_881431), tc_HOL_Obool)))))], (24098 ^ _780478) ^ [_1229049, _1229051] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1229049), _1229051))), -(c_Nat__Transfer_Otsub(_1229051, _1229049) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31154 ^ _780478) ^ [_1360297, _1360299, _1360301] : [hBOOL(hAPP(hAPP(c_member(_1360297), _1360299), hAPP(c_Set_OCollect(_1360297), _1360301))), -(hBOOL(hAPP(_1360301, _1360299)))], (17564 ^ _780478) ^ [_1106882, _1106884, _1106886, _1106888, _1106890] : [-(_1106882 = c_Orderings_Obot__class_Obot(tc_fun(_1106884, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106886, tc_HOL_Obool)), _1106888), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106884, tc_fun(_1106886, tc_HOL_Obool)), _1106882), _1106890)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1106884, tc_fun(_1106886, tc_HOL_Obool)), _1106882), hAPP(hAPP(c_COMBB(tc_fun(_1106886, tc_HOL_Obool), tc_fun(_1106886, tc_HOL_Obool), _1106884), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1106886, tc_HOL_Obool)), _1106888)), _1106890)))], (13258 ^ _780478) ^ [_1016121, _1016123, _1016125] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1016121), _1016123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016121, tc_HOL_Obool)), _1016125), _1016123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1016121), _1016125)), hAPP(c_Finite__Set_Ocard(_1016121), _1016123))))], (6688 ^ _780478) ^ [_890729, _890731] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_890729, _890731)], (44037 ^ _780478) ^ [_1661901, _1661903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661901)), _1661903)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1661901), _1661903) = _1661903)], (41198 ^ _780478) ^ [_1589395, _1589397, _1589399] : [c_Wellfounded_Owf(_1589395, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589395, _1589395), tc_HOL_Obool), _1589397), _1589399)), -(c_Wellfounded_Owf(_1589395, _1589399))], (40824 ^ _780478) ^ [_1579611, _1579613, _1579615] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1579611, _1579611), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1579611, _1579611), _1579613)), c_Transitive__Closure_Ortrancl(_1579611, _1579613)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1579611, _1579611), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1579611, _1579611)), hAPP(hAPP(c_Product__Type_OPair(_1579611, _1579611), _1579615), _1579615)), c_Transitive__Closure_Otrancl(_1579611, _1579613)))], (27713 ^ _780478) ^ [_1292628, _1292630] : [class_Rings_Oring__1(_1292628), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1292630)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1292628), hAPP(c_Int_Onat, _1292630)) = hAPP(c_Int_Oring__1__class_Oof__int(_1292628), _1292630))], (9398 ^ _780478) ^ [_941467, _941469, _941471, _941473] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_941467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941467), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941467), _941469), _941471)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_941467), _941473), _941471))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_941467), _941469), _941473)))], (37748 ^ _780478) ^ [_1500982] : [-(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)), _1500982), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (28320 ^ _780478) ^ [_1304644] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1304644)) = hAPP(c_Nat_OSuc, _1304644))], (29524 ^ _780478) ^ [_1328823, _1328825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1328823), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1328825), _1328823)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1328823, _1328825) = _1328823)], (26774 ^ _780478) ^ [_1276486, _1276488, _1276490, _1276492] : [class_Fields_Olinordered__field(_1276486), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276486), c_Groups_Ozero__class_Ozero(_1276486)), _1276488)), 26781 ^ _780478 : [(26788 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276486), _1276490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276486), _1276492), _1276488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276486), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276486), _1276490), _1276488)), _1276492)))], (26782 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276486), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276486), _1276490), _1276488)), _1276492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276486), _1276490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1276486), _1276492), _1276488))))]]], (32324 ^ _780478) ^ [_1391267, _1391269] : [class_Int_Onumber__ring(_1391267), -(hBOOL(hAPP(hAPP(c_member(_1391267), hAPP(c_Int_Onumber__class_Onumber__of(_1391267), _1391269)), c_Int_Oring__1__class_OInts(_1391267))))], (49500 ^ _780478) ^ [_1781713, _1781715] : [-(c_Equiv__Relations_Oequivp(_1781713, _1781715)), c_Predicate_Oreflp(_1781713, _1781715), c_Predicate_Osymp(_1781713, _1781715), c_Predicate_Otransp(_1781713, _1781715)], (33915 ^ _780478) ^ [_1421158, _1421160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1421158)), c_Int_OBit1(_1421160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421158), _1421160)))], (45179 ^ _780478) ^ [_1686043] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1686043)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (35876 ^ _780478) ^ [_1461478, _1461480] : [class_Rings_Osemiring__1(_1461478), -(hBOOL(hAPP(hAPP(c_member(_1461478), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1461478), _1461480)), c_Nat_Osemiring__1__class_ONats(_1461478))))], (38251 ^ _780478) ^ [_1515237, _1515239, _1515241, _1515243, _1515245, _1515247, _1515249] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1515237, _1515239, _1515241, _1515243, _1515245), _1515247), _1515249))), 38252 ^ _780478 : [(38253 ^ _780478) ^ [_1515308] : [hBOOL(hAPP(hAPP(_1515243, _1515247), _1515308)), hBOOL(hAPP(hAPP(_1515245, _1515308), _1515249))]]], (39349 ^ _780478) ^ [_1544802, _1544804] : [c_Relation_Orefl__on(_1544802, c_Orderings_Otop__class_Otop(tc_fun(_1544802, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1544802, _1544802)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544802, _1544802, tc_HOL_Obool), _1544804))), -(c_Predicate_Oreflp(_1544802, _1544804))], (38293 ^ _780478) ^ [_1515983, _1515985, _1515987, _1515989] : [c_Wellfounded_Owf(_1515983, _1515985), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515983, _1515983)), hAPP(hAPP(c_Product__Type_OPair(_1515983, _1515983), _1515987), _1515989)), _1515985)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515983, _1515983)), hAPP(hAPP(c_Product__Type_OPair(_1515983, _1515983), _1515989), _1515987)), _1515985))], (34897 ^ _780478) ^ [_1438240, _1438242] : [class_Rings_Olinordered__idom(_1438240), 34900 ^ _780478 : [(34907 ^ _780478) ^ [] : [-(_1438242 = c_Groups_Ozero__class_Ozero(_1438240)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1438240), c_Groups_Ozero__class_Ozero(_1438240)), hAPP(hAPP(c_Power_Opower__class_Opower(_1438240), _1438242), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34901 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1438240), c_Groups_Ozero__class_Ozero(_1438240)), hAPP(hAPP(c_Power_Opower__class_Opower(_1438240), _1438242), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1438242 = c_Groups_Ozero__class_Ozero(_1438240)]]], (15061 ^ _780478) ^ [_1051518, _1051520, _1051522] : [class_Lattices_Olattice(_1051518), hBOOL(hAPP(c_Finite__Set_Ofinite(_1051518), _1051520)), hBOOL(hAPP(hAPP(c_member(_1051518), _1051522), _1051520)), 15072 ^ _780478 : [(15079 ^ _780478) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051518, tc_HOL_Obool)), _1051520), hAPP(hAPP(c_Set_Oinsert(_1051518), _1051522), c_Orderings_Obot__class_Obot(tc_fun(_1051518, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1051518, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1051518, _1051520) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1051518), _1051522), c_Big__Operators_Olattice__class_OSup__fin(_1051518, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051518, tc_HOL_Obool)), _1051520), hAPP(hAPP(c_Set_Oinsert(_1051518), _1051522), c_Orderings_Obot__class_Obot(tc_fun(_1051518, tc_HOL_Obool)))))))], (15073 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1051518, tc_HOL_Obool)), _1051520), hAPP(hAPP(c_Set_Oinsert(_1051518), _1051522), c_Orderings_Obot__class_Obot(tc_fun(_1051518, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1051518, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1051518, _1051520) = _1051522)]]], (33688 ^ _780478) ^ [_1415939, _1415941] : [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(_1415941))), 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), _1415939)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415939)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415941))))], (39315 ^ _780478) ^ [_1543753, _1543755, _1543757, _1543759, _1543761] : [c_Relation_Orefl__on(_1543753, _1543755, _1543757), hBOOL(hAPP(hAPP(c_member(tc_prod(_1543753, _1543753)), hAPP(hAPP(c_Product__Type_OPair(_1543753, _1543753), _1543759), _1543761)), _1543757)), -(hBOOL(hAPP(hAPP(c_member(_1543753), _1543761), _1543755)))], (29874 ^ _780478) ^ [_1335065, _1335067] : [class_Groups_Osgn__if(_1335065), 29877 ^ _780478 : [(29884 ^ _780478) ^ [] : [-(_1335067 = c_Groups_Ozero__class_Ozero(_1335065)), 29887 ^ _780478 : [(29894 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335065), c_Groups_Ozero__class_Ozero(_1335065)), _1335067))), -(c_Groups_Osgn__class_Osgn(_1335065, _1335067) = hAPP(c_Groups_Ouminus__class_Ouminus(_1335065), c_Groups_Oone__class_Oone(_1335065)))], (29888 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335065), c_Groups_Ozero__class_Ozero(_1335065)), _1335067)), -(c_Groups_Osgn__class_Osgn(_1335065, _1335067) = c_Groups_Oone__class_Oone(_1335065))]]], (29878 ^ _780478) ^ [] : [_1335067 = c_Groups_Ozero__class_Ozero(_1335065), -(c_Groups_Osgn__class_Osgn(_1335065, _1335067) = c_Groups_Ozero__class_Ozero(_1335065))]]], (5785 ^ _780478) ^ [_872011, _872013, _872015, _872017] : [c_Hoare__Mirabelle_Ohoare__derivs(_872011, _872013, _872015), c_Hoare__Mirabelle_Ohoare__derivs(_872011, _872017, _872013), -(c_Hoare__Mirabelle_Ohoare__derivs(_872011, _872017, _872015))], (40806 ^ _780478) ^ [_1579380, _1579382] : [_1579380 = _1579382, -(c_Random_Oinc__shift(_1579380, _1579382) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (24813 ^ _780478) ^ [_1241486, _1241488, _1241490] : [class_Orderings_Oorder(_1241486), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241486), _1241488), _1241490)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1241486, _1241490, _1241488) = c_Orderings_Obot__class_Obot(tc_fun(_1241486, tc_HOL_Obool)))], (36942 ^ _780478) ^ [_1483163, _1483165] : [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), _1483163), _1483165))), 36945 ^ _780478 : [(36952 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1483165), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36955 ^ _780478 : [(36964 ^ _780478) ^ [] : [-(c_Nitpick_Onorm__frac(_1483163, _1483165) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1483163), _1483165)), 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), _1483163))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1483165)))), -(_1483163 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1483165 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36956 ^ _780478) ^ [] : [36957 ^ _780478 : [(36960 ^ _780478) ^ [] : [_1483165 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36958 ^ _780478) ^ [] : [_1483163 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1483163, _1483165) = 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)))]]], (36946 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1483165), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1483163, _1483165) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1483163), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1483165)))]]], (25045 ^ _780478) ^ [_1245684, _1245686, _1245688, _1245690] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1245684, _1245686)), c_Sum__Type_OPlus(_1245684, _1245686, _1245688, _1245690))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1245686), _1245690)))], (18496 ^ _780478) ^ [_1127031, _1127033, _1127035, _1127037] : [-(_1127031 = c_Orderings_Obot__class_Obot(tc_fun(_1127033, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1127033, tc_fun(_1127035, tc_HOL_Obool)), _1127031), hAPP(c_COMBK(tc_fun(_1127035, tc_HOL_Obool), _1127033), _1127037)) = _1127037)], (52065 ^ _780478) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (23405 ^ _780478) ^ [_1215690] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1215690), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1215690)], (45607 ^ _780478) ^ [_1695962, _1695964, _1695966, _1695968, _1695970, _1695972, _1695974, _1695976] : [c_List_Olist__all2(_1695962, _1695964, _1695966, _1695968, _1695970), hBOOL(hAPP(hAPP(_1695966, _1695972), _1695974)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1695976), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1695964)), _1695970))), -(c_List_Olist__all2(_1695962, _1695964, _1695966, hAPP(hAPP(c_List_Olist__update(_1695962, _1695968), _1695976), _1695972), hAPP(hAPP(c_List_Olist__update(_1695964, _1695970), _1695976), _1695974)))], (30769 ^ _780478) ^ [_1352095, _1352097] : [class_Groups_Oordered__ab__group__add__abs(_1352095), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352095), _1352097), c_Groups_Ozero__class_Ozero(_1352095))), -(hAPP(c_Groups_Oabs__class_Oabs(_1352095), _1352097) = hAPP(c_Groups_Ouminus__class_Ouminus(_1352095), _1352097))], (30059 ^ _780478) ^ [_1338204, _1338206] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1338204), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1338206), _1338204)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1338206), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1338206, _1338204)))], (22757 ^ _780478) ^ [] : [-(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))], (49810 ^ _780478) ^ [_1787555, _1787557, _1787559] : [c_Equiv__Relations_Oequiv(_1787555, _1787557, _1787559), 49813 ^ _780478 : [(49818 ^ _780478) ^ [] : [-(c_Relation_Otrans(_1787555, _1787559))], (49816 ^ _780478) ^ [] : [-(c_Relation_Osym(_1787555, _1787559))], (49814 ^ _780478) ^ [] : [-(c_Relation_Orefl__on(_1787555, _1787557, _1787559))]]], (34467 ^ _780478) ^ [_1430494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1430494), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1430494)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52299 ^ _780478) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (30021 ^ _780478) ^ [_1337485, _1337487] : [class_Rings_Olinordered__idom(_1337485), 30024 ^ _780478 : [(30031 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337485), c_Groups_Ozero__class_Ozero(_1337485)), _1337487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337485), c_Groups_Ozero__class_Ozero(_1337485)), c_Groups_Osgn__class_Osgn(_1337485, _1337487))))], (30025 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337485), c_Groups_Ozero__class_Ozero(_1337485)), c_Groups_Osgn__class_Osgn(_1337485, _1337487))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337485), c_Groups_Ozero__class_Ozero(_1337485)), _1337487)))]]], (31744 ^ _780478) ^ [_1380206, _1380208, _1380210, _1380212] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1380206, tc_HOL_Obool)), _1380208), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1380206), _1380210), _1380212))), 31748 ^ _780478 : [(31751 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1380206), 31747 ^ [_1380206, _1380208, _1380210, _1380212]), _1380210)))], (31749 ^ _780478) ^ [] : [-(_1380208 = hAPP(c_Relation_OImage(_1380206, _1380206, _1380212), hAPP(hAPP(c_Set_Oinsert(_1380206), 31747 ^ [_1380206, _1380208, _1380210, _1380212]), c_Orderings_Obot__class_Obot(tc_fun(_1380206, tc_HOL_Obool)))))]]], (19426 ^ _780478) ^ [_1144107] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1144107)], (12964 ^ _780478) ^ [_1010187, _1010189, _1010191, _1010193] : [class_Lattices_Osemilattice__sup(_1010187), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010187), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1010187), _1010189), _1010191)), _1010193)), 12971 ^ _780478 : [(12974 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010187), _1010191), _1010193)))], (12972 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1010187), _1010189), _1010193)))]]], (44594 ^ _780478) ^ [_1672814, _1672816, _1672818] : [-(c_List_Olast(_1672814, hAPP(hAPP(c_List_Oappend(_1672814), _1672816), hAPP(hAPP(c_List_Olist_OCons(_1672814), _1672818), c_List_Olist_ONil(_1672814)))) = _1672818)], (52229 ^ _780478) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (29153 ^ _780478) ^ [_1321424, _1321426, _1321428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1321424), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 29156 ^ _780478 : [(29157 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1321426, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1321428), _1321424)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1321428, _1321424))), 29160 ^ _780478 : [(29161 ^ _780478) ^ [_1321634, _1321636] : [-(hBOOL(hAPP(hAPP(_1321426, _1321636), _1321634))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1321424), _1321634)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1321634), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1321428 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1321424), _1321636)), _1321634)]]], (29175 ^ _780478) ^ [] : [29178 ^ _780478 : [(29181 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 29177 ^ [_1321424, _1321426, _1321428]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29183 ^ _780478) ^ [] : [-(_1321428 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1321424), 29176 ^ [_1321424, _1321426, _1321428])), 29177 ^ [_1321424, _1321426, _1321428]))], (29185 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1321426, 29176 ^ [_1321424, _1321426, _1321428]), 29177 ^ [_1321424, _1321426, _1321428]))], (29179 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1321424), 29177 ^ [_1321424, _1321426, _1321428])))]], -(hBOOL(hAPP(hAPP(_1321426, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1321428), _1321424)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1321428, _1321424))))]]], (13346 ^ _780478) ^ [_1017974, _1017976, _1017978, _1017980] : [-(hBOOL(hAPP(hAPP(c_member(_1017974), hAPP(_1017976, _1017978)), hAPP(c_Set_Oimage(_1017980, _1017974, _1017976), c_Orderings_Otop__class_Otop(tc_fun(_1017980, tc_HOL_Obool))))))], (17576 ^ _780478) ^ [_1107215, _1107217, _1107219, _1107221, _1107223] : [-(_1107215 = c_Orderings_Obot__class_Obot(tc_fun(_1107217, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1107217, tc_fun(_1107219, tc_HOL_Obool)), _1107215), hAPP(hAPP(c_COMBC(_1107217, tc_fun(_1107219, tc_HOL_Obool), tc_fun(_1107219, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1107219, tc_HOL_Obool), tc_fun(tc_fun(_1107219, tc_HOL_Obool), tc_fun(_1107219, tc_HOL_Obool)), _1107217), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1107219, tc_HOL_Obool))), _1107221)), _1107223)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1107219, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1107217, tc_fun(_1107219, tc_HOL_Obool)), _1107215), _1107221)), _1107223))], (50192 ^ _780478) ^ [_1795640, _1795642, _1795644, _1795646, _1795648, _1795650] : [class_Groups_Ocomm__monoid__mult(_1795640), hBOOL(hAPP(c_Finite__Set_Ofinite(_1795642), _1795644)), 50202 ^ _780478 : [(50205 ^ _780478) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795646), hAPP(_1795648, 50201 ^ [_1795640, _1795642, _1795644, _1795646, _1795648, _1795650])))], (50203 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795642), 50201 ^ [_1795640, _1795642, _1795644, _1795646, _1795648, _1795650]), _1795644)))]], 50209 ^ _780478 : [(50213 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795642), 50211 ^ [_1795640, _1795642, _1795644, _1795646, _1795648, _1795650]), _1795644)))], (50215 ^ _780478) ^ [] : [50208 ^ [_1795640, _1795642, _1795644, _1795646, _1795648, _1795650] = 50211 ^ [_1795640, _1795642, _1795644, _1795646, _1795648, _1795650]], (50217 ^ _780478) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1795646, tc_HOL_Obool)), hAPP(_1795648, 50208 ^ [_1795640, _1795642, _1795644, _1795646, _1795648, _1795650])), hAPP(_1795648, 50211 ^ [_1795640, _1795642, _1795644, _1795646, _1795648, _1795650])) = c_Orderings_Obot__class_Obot(tc_fun(_1795646, tc_HOL_Obool))], (50210 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795642), 50208 ^ [_1795640, _1795642, _1795644, _1795646, _1795648, _1795650]), _1795644)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1795640, _1795646, c_Groups_Otimes__class_Otimes(_1795640)), _1795650), c_Groups_Oone__class_Oone(_1795640)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1795642, tc_fun(_1795646, tc_HOL_Obool)), _1795644), _1795648)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1795640, _1795642, c_Groups_Otimes__class_Otimes(_1795640)), hAPP(hAPP(c_COMBB(tc_fun(_1795646, tc_HOL_Obool), _1795640, _1795642), hAPP(hAPP(c_Finite__Set_Ofold__image(_1795640, _1795646, c_Groups_Otimes__class_Otimes(_1795640)), _1795650), c_Groups_Oone__class_Oone(_1795640))), _1795648)), c_Groups_Oone__class_Oone(_1795640)), _1795644))], (14975 ^ _780478) ^ [_1049646, _1049648, _1049650, _1049652, _1049654, _1049656] : [hBOOL(hAPP(hAPP(c_member(_1049646), _1049648), c_SetInterval_Oord_OatLeastLessThan(_1049646, _1049650, _1049652, _1049654, _1049656))), 14978 ^ _780478 : [(14981 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1049652, _1049648), _1049656)))], (14979 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(_1049650, _1049654), _1049648)))]]], (27421 ^ _780478) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (13224 ^ _780478) ^ [_1015219, _1015221, _1015223, _1015225] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1015219, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1015219, tc_fun(_1015219, tc_HOL_Obool), tc_HOL_Obool), c_member(_1015219)), _1015221)), hAPP(hAPP(c_COMBC(_1015219, tc_fun(_1015219, tc_HOL_Obool), tc_HOL_Obool), c_member(_1015219)), _1015223)), _1015225)), -(hBOOL(hAPP(hAPP(c_member(_1015219), _1015225), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1015219, tc_HOL_Obool)), _1015221), _1015223))))], (5170 ^ _780478) ^ [_859478, _859480, _859482, _859484, _859486, _859488] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_859488, _859484, _859480) = c_SetInterval_Oord__class_OatLeastAtMost(_859486, _859482, _859478)), _859488 = _859486, _859484 = _859482, _859480 = _859478], (47548 ^ _780478) ^ [_1737548, _1737550, _1737552] : [-(hBOOL(hAPP(hAPP(c_member(_1737548), _1737550), hAPP(c_List_Oset(_1737548), _1737552)))), -(c_List_Oinsert(_1737548, _1737550, _1737552) = hAPP(hAPP(c_List_Olist_OCons(_1737548), _1737550), _1737552))], (44829 ^ _780478) ^ [_1678622, _1678624, _1678626, _1678628, _1678630] : [-(hAPP(hAPP(c_List_Odrop(_1678622), _1678624), hAPP(hAPP(c_List_Omap(_1678626, _1678622), _1678628), _1678630)) = hAPP(hAPP(c_List_Omap(_1678626, _1678622), _1678628), hAPP(hAPP(c_List_Odrop(_1678626), _1678624), _1678630)))], (16242 ^ _780478) ^ [_1075407, _1075409, _1075411, _1075413, _1075415] : [c_Fun_Oinj__on(_1075407, _1075409, _1075411, _1075413), c_Fun_Oinj__on(_1075407, _1075409, _1075411, _1075415), -(c_Fun_Oinj__on(_1075407, _1075409, _1075411, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075407, tc_HOL_Obool)), _1075413), _1075415)))], (17426 ^ _780478) ^ [_1103146, _1103148, _1103150, _1103152, _1103154] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103146, tc_HOL_Obool)), _1103148), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103150, tc_fun(_1103146, tc_HOL_Obool)), _1103152), _1103154)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1103150, tc_fun(_1103146, tc_HOL_Obool)), _1103152), hAPP(hAPP(c_COMBB(tc_fun(_1103146, tc_HOL_Obool), tc_fun(_1103146, tc_HOL_Obool), _1103150), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1103146, tc_HOL_Obool)), _1103148)), _1103154)))], (6334 ^ _780478) ^ [_882605, _882607, _882609] : [hAPP(hAPP(c_COMBC(_882605, tc_fun(_882605, tc_HOL_Obool), tc_HOL_Obool), c_member(_882605)), _882607) = hAPP(hAPP(c_COMBC(_882605, tc_fun(_882605, tc_HOL_Obool), tc_HOL_Obool), c_member(_882605)), _882609), -(_882607 = _882609)], (23233 ^ _780478) ^ [_1212878, _1212880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1212878), _1212880)), -(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)), _1212878)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212880))))], (1264 ^ _780478) ^ [_799142, _799144] : [-(class_Int_Oring__char__0(_799142)), _799144 = _799142, class_Int_Oring__char__0(_799144)], (35193 ^ _780478) ^ [_1443839] : [-(_1443839 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 35196 ^ _780478 : [(35203 ^ _780478) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1443839, 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, _1443839) = 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), _1443839), 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)))], (35197 ^ _780478) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1443839, 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, _1443839) = 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), _1443839), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (43263 ^ _780478) ^ [_1643087, _1643089, _1643091] : [-(_1643087 = c_List_Olist_ONil(_1643089)), -(hBOOL(hAPP(hAPP(c_member(_1643089), hAPP(c_Product__Type_Ofst(_1643089, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1643089, _1643087), _1643091))), hAPP(c_List_Oset(_1643089), _1643087))))], (8738 ^ _780478) ^ [_931579, _931581, _931583, _931585] : [class_Orderings_Opreorder(_931579), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931579), _931581), _931583)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931579), _931583), _931585)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931579), _931581), _931585)))], (17470 ^ _780478) ^ [_1104843, _1104845, _1104847, _1104849, _1104851] : [_1104843 = c_Orderings_Obot__class_Obot(tc_fun(_1104845, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1104847), _1104849), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1104845, tc_fun(_1104847, tc_HOL_Obool)), _1104843), _1104851)) = hAPP(hAPP(c_Set_Oinsert(_1104847), _1104849), c_Orderings_Obot__class_Obot(tc_fun(_1104847, tc_HOL_Obool))))], (28927 ^ _780478) ^ [_1316298, _1316300, _1316302, _1316304, _1316306] : [class_Groups_Ocomm__monoid__add(_1316298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316300), _1316302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1316300, tc_HOL_Obool)), _1316304), _1316302)), 28941 ^ _780478 : [(28944 ^ _780478) ^ [] : [hAPP(_1316306, 28940 ^ [_1316298, _1316300, _1316302, _1316304, _1316306]) = c_Groups_Ozero__class_Ozero(_1316298)], (28942 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1316300), 28940 ^ [_1316298, _1316300, _1316302, _1316304, _1316306]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316300, tc_HOL_Obool)), _1316302), _1316304))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316300, _1316298), _1316306), _1316302) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1316300, _1316298), _1316306), _1316304))], (45183 ^ _780478) ^ [] : [-(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))], (30659 ^ _780478) ^ [_1349755, _1349757] : [class_Rings_Olinordered__idom(_1349755), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349755), c_Groups_Osgn__class_Osgn(_1349755, _1349757)), hAPP(c_Groups_Oabs__class_Oabs(_1349755), _1349757)) = _1349757)], (45135 ^ _780478) ^ [_1685325] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1685325)) = _1685325)], (13602 ^ _780478) ^ [_1023381, _1023383, _1023385, _1023387, _1023389] : [c_Finite__Set_Ofolding__one__idem(_1023381, _1023383, _1023385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023381), _1023387)), -(_1023387 = c_Orderings_Obot__class_Obot(tc_fun(_1023381, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1023381), _1023389)), -(_1023389 = c_Orderings_Obot__class_Obot(tc_fun(_1023381, tc_HOL_Obool))), -(hAPP(_1023385, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1023381, tc_HOL_Obool)), _1023387), _1023389)) = hAPP(hAPP(_1023383, hAPP(_1023385, _1023387)), hAPP(_1023385, _1023389)))], (51409 ^ _780478) ^ [_1821729, _1821731] : [c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_COMBS(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_Nat_Onat), c_COMBS(tc_Nat_Onat, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat), c_fNot)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))), _1821729, _1821731), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821729), _1821731)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1821731), _1821729)))], (20198 ^ _780478) ^ [_1157245, _1157247] : [class_Groups_Olinordered__ab__group__add(_1157245), 20201 ^ _780478 : [(20208 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157245), c_Groups_Ozero__class_Ozero(_1157245)), _1157247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157245), c_Groups_Ozero__class_Ozero(_1157245)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157245), _1157247), _1157247))))], (20202 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157245), c_Groups_Ozero__class_Ozero(_1157245)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1157245), _1157247), _1157247))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157245), c_Groups_Ozero__class_Ozero(_1157245)), _1157247)))]]], (16510 ^ _780478) ^ [_1081946, _1081948, _1081950, _1081952, _1081954] : [c_Fun_Oinj__on(_1081946, _1081948, _1081950, c_Orderings_Otop__class_Otop(tc_fun(_1081946, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1081946, _1081948, _1081950), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1081946, tc_HOL_Obool)), _1081952), _1081954)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1081948, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1081946, _1081948, _1081950), _1081952)), hAPP(c_Set_Oimage(_1081946, _1081948, _1081950), _1081954)))], (38112 ^ _780478) ^ [_1511559, _1511561, _1511563, _1511565, _1511567, _1511569, _1511571] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1511559, _1511561, _1511563, hAPP(hAPP(c_COMBC(_1511559, tc_fun(tc_prod(_1511559, _1511561), tc_HOL_Obool), tc_fun(_1511561, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511561, tc_fun(tc_fun(tc_prod(_1511559, _1511561), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511559, _1511561), tc_HOL_Obool), tc_fun(_1511561, tc_HOL_Obool)), _1511559), c_COMBC(_1511561, tc_fun(tc_prod(_1511559, _1511561), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511561, tc_prod(_1511559, _1511561)), tc_fun(_1511561, tc_fun(tc_fun(tc_prod(_1511559, _1511561), tc_HOL_Obool), tc_HOL_Obool)), _1511559), hAPP(c_COMBB(tc_prod(_1511559, _1511561), tc_fun(tc_fun(tc_prod(_1511559, _1511561), tc_HOL_Obool), tc_HOL_Obool), _1511561), c_member(tc_prod(_1511559, _1511561)))), c_Product__Type_OPair(_1511559, _1511561)))), _1511565), hAPP(hAPP(c_COMBC(_1511561, tc_fun(tc_prod(_1511561, _1511563), tc_HOL_Obool), tc_fun(_1511563, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511563, tc_fun(tc_fun(tc_prod(_1511561, _1511563), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1511561, _1511563), tc_HOL_Obool), tc_fun(_1511563, tc_HOL_Obool)), _1511561), c_COMBC(_1511563, tc_fun(tc_prod(_1511561, _1511563), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511563, tc_prod(_1511561, _1511563)), tc_fun(_1511563, tc_fun(tc_fun(tc_prod(_1511561, _1511563), tc_HOL_Obool), tc_HOL_Obool)), _1511561), hAPP(c_COMBB(tc_prod(_1511561, _1511563), tc_fun(tc_fun(tc_prod(_1511561, _1511563), tc_HOL_Obool), tc_HOL_Obool), _1511563), c_member(tc_prod(_1511561, _1511563)))), c_Product__Type_OPair(_1511561, _1511563)))), _1511567)), _1511569), _1511571)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1511559, _1511563)), hAPP(hAPP(c_Product__Type_OPair(_1511559, _1511563), _1511569), _1511571)), hAPP(hAPP(c_Relation_Orel__comp(_1511559, _1511561, _1511563), _1511565), _1511567))))], (42587 ^ _780478) ^ [_1629113, _1629115, _1629117] : [class_Groups_Omonoid__add(_1629113), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1629113), hAPP(hAPP(c_List_Olist_OCons(_1629113), _1629115), _1629117)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1629113), _1629115), hAPP(c_List_Omonoid__add__class_Olistsum(_1629113), _1629117)))], (23791 ^ _780478) ^ [_1222930, _1222932, _1222934] : [class_Orderings_Oorder(_1222930), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222930, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1222930), _1222932)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1222930, _1222932), _1222934)) = c_Orderings_Obot__class_Obot(tc_fun(_1222930, tc_HOL_Obool)))], (18317 ^ _780478) ^ [_1123204, _1123206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1123204)), _1123206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123204), _1123206)))], (13238 ^ _780478) ^ [_1015695, _1015697, _1015699, _1015701] : [c_Fun_Oinj__on(_1015695, _1015697, _1015699, c_Orderings_Otop__class_Otop(tc_fun(_1015695, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1015695, tc_fun(_1015701, _1015697), hAPP(hAPP(c_COMBB(_1015697, tc_fun(_1015701, _1015697), _1015695), c_COMBK(_1015697, _1015701)), _1015699), c_Orderings_Otop__class_Otop(tc_fun(_1015695, tc_HOL_Obool))))], (44197 ^ _780478) ^ [_1665057, _1665059, _1665061] : [-(_1665057 = c_List_Olist_ONil(_1665059)), -(hAPP(hAPP(c_List_Otake(_1665059), hAPP(c_Nat_OSuc, _1665061)), _1665057) = hAPP(hAPP(c_List_Olist_OCons(_1665059), hAPP(c_List_Ohd(_1665059), _1665057)), hAPP(hAPP(c_List_Otake(_1665059), _1665061), hAPP(c_List_Otl(_1665059), _1665057))))], (24993 ^ _780478) ^ [_1244654, _1244656, _1244658] : [class_Groups_Oordered__ab__group__add(_1244654), -(hAPP(c_Set_Oimage(_1244654, _1244654, c_Groups_Ouminus__class_Ouminus(_1244654)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244654, _1244656), _1244658)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1244654, hAPP(c_Groups_Ouminus__class_Ouminus(_1244654), _1244658), hAPP(c_Groups_Ouminus__class_Ouminus(_1244654), _1244656)))], (6204 ^ _780478) ^ [_879834, _879836, _879838, _879840, _879842] : [-(hAPP(c_Set_Oimage(_879834, _879836, _879838), hAPP(hAPP(c_Set_Oinsert(_879834), _879840), _879842)) = hAPP(hAPP(c_Set_Oinsert(_879836), hAPP(_879838, _879840)), hAPP(c_Set_Oimage(_879834, _879836, _879838), _879842)))], (33514 ^ _780478) ^ [_1412793, _1412795] : [class_Int_Onumber__ring(_1412793), class_Rings_Olinordered__idom(_1412793), 33521 ^ _780478 : [(33528 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412795), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412793), hAPP(c_Int_Onumber__class_Onumber__of(_1412793), _1412795)), c_Groups_Ozero__class_Ozero(_1412793))))], (33522 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412793), hAPP(c_Int_Onumber__class_Onumber__of(_1412793), _1412795)), c_Groups_Ozero__class_Ozero(_1412793))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412795), c_Int_OPls)))]]], (48387 ^ _780478) ^ [_1755786, _1755788, _1755790, _1755792, _1755794] : [-(_1755786 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1755788, _1755790, _1755792, _1755794), _1755786) = c_Lazy__Sequence_Ohb__bind(_1755788, _1755790, hAPP(_1755792, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1755786), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1755788, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1755790))), _1755794), _1755786)))], (23465 ^ _780478) ^ [_1216730, _1216732] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1216730), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1216732)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1216730), _1216732)))], (34363 ^ _780478) ^ [_1428738, _1428740] : [c_Int_OBit1(_1428738) = c_Int_OBit0(_1428740)], (2672 ^ _780478) ^ [_819859, _819861, _819863, _819865, _819867, _819869] : [-(c_Predicate_ODomainP(_819869, _819865, _819861) = c_Predicate_ODomainP(_819867, _819863, _819859)), _819869 = _819867, _819865 = _819863, _819861 = _819859], (43069 ^ _780478) ^ [_1639387, _1639389] : [_1639389 = c_List_Olist_ONil(_1639387), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639387)), _1639389) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21372 ^ _780478) ^ [_1177318, _1177320, _1177322] : [class_Groups_Oordered__comm__monoid__add(_1177318), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1177318), c_Groups_Ozero__class_Ozero(_1177318)), _1177320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177318), c_Groups_Ozero__class_Ozero(_1177318)), _1177322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1177318), c_Groups_Ozero__class_Ozero(_1177318)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1177318), _1177320), _1177322))))], (24373 ^ _780478) ^ [_1233559, _1233561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233559)), 24376 ^ _780478 : [(24385 ^ _780478) ^ [] : [-(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), _1233559), _1233561)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233561), _1233559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233561))], (24377 ^ _780478) ^ [] : [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), _1233559), _1233561))), 24380 ^ _780478 : [(24383 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233561)))], (24381 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1233561), _1233559)))]]]]], (7724 ^ _780478) ^ [_910952, _910954, _910956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_910952), tc_HOL_Obool)), _910954), _910956)), -(c_Hoare__Mirabelle_Ohoare__derivs(_910952, _910956, _910954))], (15663 ^ _780478) ^ [_1063408, _1063410, _1063412, _1063414] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063408, tc_HOL_Obool)), _1063410), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063408, tc_HOL_Obool)), _1063412), _1063414)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063408, tc_HOL_Obool)), _1063412), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063408, tc_HOL_Obool)), _1063410), _1063414)))], (44492 ^ _780478) ^ [_1671267, _1671269, _1671271] : [class_Orderings_Olinorder(_1671267), hBOOL(hAPP(hAPP(c_member(_1671267), _1671269), hAPP(c_List_Oset(_1671267), _1671271))), -(c_List_Olinorder__class_Oinsort__insert__key(_1671267, _1671267, c_COMBI(_1671267), _1671269, _1671271) = _1671271)], (23363 ^ _780478) ^ [_1215056, _1215058] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215056), _1215058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1215058), _1215056)))], (25305 ^ _780478) ^ [_1250861, _1250863, _1250865, _1250867] : [class_Rings_Odivision__ring(_1250861), -(_1250863 = c_Groups_Ozero__class_Ozero(_1250861)), 25312 ^ _780478 : [(25319 ^ _780478) ^ [] : [_1250865 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250861), _1250867), _1250863), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250861), _1250865), _1250863) = _1250867)], (25313 ^ _780478) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1250861), _1250865), _1250863) = _1250867, -(_1250865 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1250861), _1250867), _1250863))]]], (12674 ^ _780478) ^ [_1004729, _1004731, _1004733, _1004735] : [hBOOL(hAPP(_1004729, _1004731)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004733, tc_HOL_Obool)), _1004735), _1004729), _1004731)))], (16240 ^ _780478) ^ [_1075323, _1075325, _1075327, _1075329] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075323, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075323, tc_HOL_Obool)), _1075325), _1075327)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075323, tc_HOL_Obool)), _1075329), _1075327)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1075323, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1075323, tc_HOL_Obool)), _1075325), _1075327)), _1075329))], (9668 ^ _780478) ^ [_946732, _946734, _946736, _946738, _946740, _946742] : [class_Rings_Oordered__ring(_946732), 9671 ^ _780478 : [(9678 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946732), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946732), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946732), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_946732), _946734), _946740)), _946736)), _946738)), _946742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946732), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946732), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946732), _946734), _946736)), _946738)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946732), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946732), _946740), _946736)), _946742))))], (9672 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946732), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946732), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946732), _946734), _946736)), _946738)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946732), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946732), _946740), _946736)), _946742))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_946732), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_946732), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_946732), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_946732), _946734), _946740)), _946736)), _946738)), _946742)))]]], (20692 ^ _780478) ^ [_1166158, _1166160] : [class_Rings_Olinordered__idom(_1166158), 20695 ^ _780478 : [(20702 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166158), _1166160), c_Groups_Ozero__class_Ozero(_1166158))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166158), _1166160), hAPP(c_Groups_Ouminus__class_Ouminus(_1166158), _1166160))))], (20696 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166158), _1166160), hAPP(c_Groups_Ouminus__class_Ouminus(_1166158), _1166160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166158), _1166160), c_Groups_Ozero__class_Ozero(_1166158))))]]], (16705 ^ _780478) ^ [_1086332, _1086334, _1086336, _1086338, _1086340, _1086342] : [hBOOL(hAPP(hAPP(c_member(_1086332), _1086334), _1086336)), 16708 ^ _780478 : [(16715 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1086332), _1086338), _1086336))), -(hAPP(c_Set_Ovimage(_1086340, _1086332, hAPP(hAPP(c_COMBC(_1086340, _1086332, _1086332), hAPP(hAPP(c_COMBC(_1086340, _1086332, tc_fun(_1086332, _1086332)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1086332, tc_fun(_1086332, _1086332)), _1086340), c_If(_1086332)), hAPP(hAPP(c_COMBC(_1086340, tc_fun(_1086340, tc_HOL_Obool), tc_HOL_Obool), c_member(_1086340)), _1086342))), _1086334)), _1086338)), _1086336) = _1086342)], (16709 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1086332), _1086338), _1086336)), -(hAPP(c_Set_Ovimage(_1086340, _1086332, hAPP(hAPP(c_COMBC(_1086340, _1086332, _1086332), hAPP(hAPP(c_COMBC(_1086340, _1086332, tc_fun(_1086332, _1086332)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1086332, tc_fun(_1086332, _1086332)), _1086340), c_If(_1086332)), hAPP(hAPP(c_COMBC(_1086340, tc_fun(_1086340, tc_HOL_Obool), tc_HOL_Obool), c_member(_1086340)), _1086342))), _1086334)), _1086338)), _1086336) = c_Orderings_Otop__class_Otop(tc_fun(_1086340, tc_HOL_Obool)))]]], (49730 ^ _780478) ^ [_1786338, _1786340] : [-(c_Relation_Osym(_1786338, c_Relation_OId__on(_1786338, _1786340)))], (38541 ^ _780478) ^ [_1521755, _1521757, _1521759] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1521755, _1521757)), _1521759)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1521757), hAPP(c_Relation_ORange(_1521755, _1521757), _1521759))))], (41681 ^ _780478) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2560 ^ _780478) ^ [_818159, _818161, _818163, _818165, _818167, _818169] : [-(c_Wellfounded_Omlex__prod(_818169, _818165, _818161) = c_Wellfounded_Omlex__prod(_818167, _818163, _818159)), _818169 = _818167, _818165 = _818163, _818161 = _818159], (25078 ^ _780478) ^ [_1246304, _1246306, _1246308] : [-(hBOOL(hAPP(_1246304, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1246306), _1246308)))), 25079 ^ _780478 : [(25086 ^ _780478) ^ [_1246472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246308), _1246472)), _1246306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246308), hAPP(c_Nat_OSuc, _1246472)))), hBOOL(hAPP(_1246304, _1246472))], (25080 ^ _780478) ^ [] : [_1246308 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1246304, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (42137 ^ _780478) ^ [_1616377, _1616379, _1616381, _1616383] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616377), tc_List_Olist(_1616377))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616377), tc_List_Olist(_1616377)), _1616379), _1616381)), c_List_Olistrel(_1616377, _1616383)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616377)), _1616379) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616377)), _1616381), 42143 ^ _780478 : [(42146 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1616377, _1616377)), hAPP(hAPP(c_Product__Type_OPair(_1616377, _1616377), hAPP(hAPP(c_List_Onth(_1616377), _1616379), 42142 ^ [_1616377, _1616379, _1616381, _1616383])), hAPP(hAPP(c_List_Onth(_1616377), _1616381), 42142 ^ [_1616377, _1616379, _1616381, _1616383]))), _1616383))], (42144 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42142 ^ [_1616377, _1616379, _1616381, _1616383]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616377)), _1616379))))]]], (36463 ^ _780478) ^ [_1474261, _1474263] : [c_Nitpick_Orefl_H(_1474261, _1474263), 36466 ^ _780478 : [(36467 ^ _780478) ^ [_1474339] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1474261, _1474261)), hAPP(hAPP(c_Product__Type_OPair(_1474261, _1474261), _1474339), _1474339)), _1474263)))]]], (6876 ^ _780478) ^ [_894377, _894379, _894381, _894383, _894385] : [c_Fun_Oinj__on(_894377, _894379, _894381, hAPP(hAPP(c_Set_Oinsert(_894377), _894383), _894385)), 6879 ^ _780478 : [(6882 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_894379), hAPP(_894381, _894383)), hAPP(c_Set_Oimage(_894377, _894379, _894381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894377, tc_HOL_Obool)), _894385), hAPP(hAPP(c_Set_Oinsert(_894377), _894383), c_Orderings_Obot__class_Obot(tc_fun(_894377, tc_HOL_Obool)))))))], (6880 ^ _780478) ^ [] : [-(c_Fun_Oinj__on(_894377, _894379, _894381, _894385))]]], (27577 ^ _780478) ^ [_1290381] : [c_Nat__Transfer_Ois__nat(_1290381), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1290381)))], (31652 ^ _780478) ^ [_1377532, _1377534, _1377536] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1377532), _1377534), _1377536) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1377532, tc_HOL_Obool), tc_HOL_Obool)), -(_1377534 = c_Orderings_Obot__class_Obot(tc_fun(_1377532, tc_HOL_Obool)))], (8146 ^ _780478) ^ [_919795, _919797, _919799, _919801] : [class_Groups_Ocancel__ab__semigroup__add(_919795), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919795), _919797), _919799) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919795), _919797), _919801), -(_919799 = _919801)], (32124 ^ _780478) ^ [_1387157, _1387159, _1387161, _1387163, _1387165] : [c_Com_Ocom_OSemi(_1387157, _1387159) = c_Com_Ocom_OLocal(_1387161, _1387163, _1387165)], (19076 ^ _780478) ^ [_1138941, _1138943] : [class_Groups_Ozero(_1138941), 19079 ^ _780478 : [(19086 ^ _780478) ^ [] : [_1138943 = c_Groups_Ozero__class_Ozero(_1138941), -(c_Groups_Ozero__class_Ozero(_1138941) = _1138943)], (19080 ^ _780478) ^ [] : [c_Groups_Ozero__class_Ozero(_1138941) = _1138943, -(_1138943 = c_Groups_Ozero__class_Ozero(_1138941))]]], (31726 ^ _780478) ^ [_1379688, _1379690, _1379692, _1379694, _1379696, _1379698] : [-(hAPP(c_Relation_OImage(_1379688, _1379690, _1379692), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379694, tc_fun(_1379688, tc_HOL_Obool)), _1379696), _1379698)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1379694, tc_fun(_1379690, tc_HOL_Obool)), _1379696), hAPP(hAPP(c_COMBB(tc_fun(_1379688, tc_HOL_Obool), tc_fun(_1379690, tc_HOL_Obool), _1379694), c_Relation_OImage(_1379688, _1379690, _1379692)), _1379698)))], (15099 ^ _780478) ^ [_1052359, _1052361] : [class_Rings_Ocomm__semiring__1(_1052359), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1052359), _1052361), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1052361)], (46615 ^ _780478) ^ [_1718049, _1718051, _1718053, _1718055] : [class_Orderings_Olinorder(_1718049), -(c_List_Olinorder__class_Osorted(_1718049, hAPP(hAPP(c_List_Omap(_1718051, _1718049), _1718053), c_List_Olinorder__class_Osort__key(_1718051, _1718049, _1718053, _1718055))))], (50179 ^ _780478) ^ [_1795314, _1795316, _1795318, _1795320, _1795322] : [c_Fun_Oinj__on(_1795314, _1795316, _1795318, c_Orderings_Otop__class_Otop(tc_fun(_1795314, tc_HOL_Obool))), 50185 ^ _780478 : [(50188 ^ _780478) ^ [] : [hBOOL(hAPP(_1795320, hAPP(c_Hilbert__Choice_Oinv__into(_1795314, _1795316, c_Orderings_Otop__class_Otop(tc_fun(_1795314, tc_HOL_Obool)), _1795318), 50184 ^ [_1795314, _1795316, _1795318, _1795320, _1795322])))], (50186 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795316), 50184 ^ [_1795314, _1795316, _1795318, _1795320, _1795322]), hAPP(c_Set_Oimage(_1795314, _1795316, _1795318), c_Orderings_Otop__class_Otop(tc_fun(_1795314, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1795320, _1795322)))], (15765 ^ _780478) ^ [_1065544, _1065546, _1065548, _1065550] : [class_Lattices_Osemilattice__inf(_1065544), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065544), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065544), _1065546), _1065548)), _1065550) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065544), _1065546), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1065544), _1065548), _1065550)))], (4286 ^ _780478) ^ [_845308, _845310] : [_845310 = _845308, -(c_List_Oappend(_845310) = c_List_Oappend(_845308))], (22787 ^ _780478) ^ [_1204706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204706)), -(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), _1204706))))], (36512 ^ _780478) ^ [_1475053, _1475055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475053)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1475055)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1475053, _1475055), c_Divides_OposDivAlg(_1475053, _1475055))))], (12574 ^ _780478) ^ [_1002500, _1002502] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002500, tc_HOL_Obool)), _1002502), _1002502) = _1002502)], (42397 ^ _780478) ^ [_1622972, _1622974, _1622976] : [hBOOL(hAPP(hAPP(c_member(_1622972), _1622974), hAPP(c_List_Oset(_1622972), _1622976))), -(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(_1622972)), _1622976))))], (34427 ^ _780478) ^ [_1429770, _1429772] : [_1429770 = _1429772, -(c_Int_OBit0(_1429770) = c_Int_OBit0(_1429772))], (38124 ^ _780478) ^ [_1512835, _1512837, _1512839] : [c_Wellfounded_Owf(_1512835, _1512837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1512835, _1512835), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1512835, _1512835, _1512835), _1512837), _1512839)), _1512837)), -(c_FunDef_Oreduction__pair(_1512835, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1512835, _1512835), tc_HOL_Obool), tc_fun(tc_prod(_1512835, _1512835), tc_HOL_Obool)), _1512837), _1512839)))], (18648 ^ _780478) ^ [_1130605, _1130607, _1130609, _1130611, _1130613] : [-(_1130605 = c_Orderings_Obot__class_Obot(tc_fun(_1130607, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130607, tc_fun(_1130609, tc_HOL_Obool)), _1130605), hAPP(hAPP(c_COMBC(_1130607, tc_fun(_1130609, tc_HOL_Obool), tc_fun(_1130609, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1130609, tc_HOL_Obool), tc_fun(tc_fun(_1130609, tc_HOL_Obool), tc_fun(_1130609, tc_HOL_Obool)), _1130607), c_Groups_Ominus__class_Ominus(tc_fun(_1130609, tc_HOL_Obool))), _1130611)), _1130613)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1130609, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1130607, tc_fun(_1130609, tc_HOL_Obool)), _1130605), _1130611)), _1130613))], (52283 ^ _780478) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (48840 ^ _780478) ^ [_1765583, _1765585] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1765583)), _1765585) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1765583, tc_Lazy__Sequence_Olazy__sequence(_1765583)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1765583, tc_Lazy__Sequence_Olazy__sequence(_1765583), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1765583), tc_Nat_Onat), _1765583), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1765583), 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(_1765583)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1765583)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1765583), _1765585)))], (37959 ^ _780478) ^ [_1507745, _1507747, _1507749, _1507751, _1507753, _1507755, _1507757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507745, _1507747), tc_HOL_Obool)), _1507749), _1507751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507747, _1507753), tc_HOL_Obool)), _1507755), _1507757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1507745, _1507753), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1507745, _1507747, _1507753), _1507749), _1507755)), hAPP(hAPP(c_Relation_Orel__comp(_1507745, _1507747, _1507753), _1507751), _1507757))))], (12580 ^ _780478) ^ [_1002645, _1002647, _1002649, _1002651] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002645, tc_HOL_Obool)), _1002647), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002645, tc_HOL_Obool)), _1002649), _1002651)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002645, tc_HOL_Obool)), _1002649), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1002645, tc_HOL_Obool)), _1002647), _1002651)))], (45109 ^ _780478) ^ [_1684578, _1684580, _1684582, _1684584] : [class_Groups_Ocomm__monoid__add(_1684578), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1684578), _1684580), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1684582, _1684584))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1684578), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1684578), _1684580), c_List_Oupto(_1684582, _1684584))))], (49381 ^ _780478) ^ [_1778367, _1778369, _1778371, _1778373] : [class_Complete__Lattice_Ocomplete__lattice(_1778367), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1778369, _1778367), _1778371), _1778373) = c_Complete__Lattice_OSup__class_OSup(_1778367, hAPP(c_Set_OCollect(_1778367), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778369, _1778367), tc_HOL_Obool), tc_HOL_Obool, _1778367), c_HOL_OEx(tc_fun(_1778369, _1778367))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1778369, _1778367), tc_HOL_Obool), tc_fun(tc_fun(_1778369, _1778367), tc_HOL_Obool), _1778367), hAPP(c_COMBS(tc_fun(_1778369, _1778367), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1778369, _1778367)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1778369, _1778367), tc_fun(tc_fun(_1778369, _1778367), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1778369, _1778367))), _1778371)))), hAPP(hAPP(c_COMBC(_1778367, tc_fun(tc_fun(_1778369, _1778367), _1778367), tc_fun(tc_fun(_1778369, _1778367), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1778367, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1778369, _1778367), _1778367), tc_fun(tc_fun(_1778369, _1778367), tc_HOL_Obool)), _1778367), c_COMBB(_1778367, tc_HOL_Obool, tc_fun(_1778369, _1778367))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1778369, _1778367), _1778369, _1778367), c_COMBI(tc_fun(_1778369, _1778367))), _1778373)))))))], (26168 ^ _780478) ^ [_1265693, _1265695, _1265697] : [class_Fields_Olinordered__field__inverse__zero(_1265693), 26171 ^ _780478 : [(26186 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265693), c_Groups_Ozero__class_Ozero(_1265693)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265693), _1265695), _1265697)))), 26187 ^ _780478 : [(26194 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265693), _1265695), c_Groups_Ozero__class_Ozero(_1265693))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265693), _1265697), c_Groups_Ozero__class_Ozero(_1265693)))], (26188 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265693), c_Groups_Ozero__class_Ozero(_1265693)), _1265695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265693), c_Groups_Ozero__class_Ozero(_1265693)), _1265697))]]], (26172 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265693), c_Groups_Ozero__class_Ozero(_1265693)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265693), _1265695), _1265697))), 26177 ^ _780478 : [(26180 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265693), c_Groups_Ozero__class_Ozero(_1265693)), _1265697)))], (26178 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265693), c_Groups_Ozero__class_Ozero(_1265693)), _1265695)))]], 26181 ^ _780478 : [(26184 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265693), _1265697), c_Groups_Ozero__class_Ozero(_1265693))))], (26182 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1265693), _1265695), c_Groups_Ozero__class_Ozero(_1265693))))]]]]], (18452 ^ _780478) ^ [_1126071, _1126073] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1126071)), _1126073) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1126073), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1126071), _1126073)))], (670 ^ _780478) ^ [_790585, _790587, _790589, _790591, _790593, _790595] : [-(c_List_Olist__ex1(_790593, _790589, _790585)), c_List_Olist__ex1(_790595, _790591, _790587), _790595 = _790593, _790591 = _790589, _790587 = _790585], (21189 ^ _780478) ^ [_1174296, _1174298, _1174300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174296), _1174298)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174300), _1174296)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1174300), _1174298))))], (51023 ^ _780478) ^ [_1814411, _1814413, _1814415, _1814417, _1814419] : [class_Groups_Ocomm__monoid__mult(_1814411), class_Rings_Odvd(_1814411), hBOOL(hAPP(c_Finite__Set_Ofinite(_1814413), _1814415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1814413, tc_HOL_Obool)), _1814417), _1814415)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814411), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1814413, _1814411), _1814419), _1814417)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1814413, _1814411), _1814419), _1814415))))], (41231 ^ _780478) ^ [_1590219, _1590221, _1590223] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590219, _1590219), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1590221)), _1590223) = hAPP(hAPP(c_Relation_Orel__comp(_1590219, _1590219, _1590219), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1590219, _1590219), tc_HOL_Obool), _1590221), _1590223)), _1590223))], (23691 ^ _780478) ^ [_1220885, _1220887, _1220889, _1220891, _1220893] : [class_Groups_Ocomm__monoid__add(_1220885), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220887), _1220889)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220889), _1220891)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220885), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220885), _1220893), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220887), _1220889))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220885), _1220893), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220889), _1220891))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220885), _1220893), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220887), _1220891)))], (8156 ^ _780478) ^ [_919962, _919964, _919966, _919968] : [class_Groups_Ocancel__semigroup__add(_919962), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919962), _919964), _919966) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_919962), _919964), _919968), -(_919966 = _919968)], (6696 ^ _780478) ^ [_890895, _890897, _890899, _890901] : [c_Com_Ocom_OSemi(_890895, _890897) = c_Com_Ocom_OWhile(_890899, _890901)], (34563 ^ _780478) ^ [_1432164, _1432166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432164), _1432166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1432164)), c_Int_OBit0(_1432166))))], (28624 ^ _780478) ^ [_1310519, _1310521, _1310523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1310519)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1310521), _1310523)), 28631 ^ _780478 : [(28632 ^ _780478) ^ [_1310709] : [28634 ^ _780478 : [(28640 ^ _780478) ^ [] : [-(_1310709 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 28636 ^ [_1310519, _1310521, _1310523, _1310709]), 28633 ^ [_1310519, _1310521, _1310523, _1310709]))], (28638 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28636 ^ [_1310519, _1310521, _1310523, _1310709]), _1310523)))], (28635 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28633 ^ [_1310519, _1310521, _1310523, _1310709]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1310519))))]], -(_1310709 = _1310521), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1310709), _1310519) = _1310521]]], (23735 ^ _780478) ^ [_1221800, _1221802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221800)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221802))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1221800), _1221802)))], (45789 ^ _780478) ^ [_1699843, _1699845, _1699847, _1699849] : [_1699843 = _1699845, -(hAPP(c_List_OremoveAll(_1699847, _1699843), hAPP(hAPP(c_List_Olist_OCons(_1699847), _1699845), _1699849)) = hAPP(c_List_OremoveAll(_1699847, _1699843), _1699849))], (18420 ^ _780478) ^ [_1125134, _1125136] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1125134), _1125136)), hAPP(c_Nat_OSuc, _1125134))))], (37728 ^ _780478) ^ [_1500566, _1500568, _1500570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1500566, _1500566), tc_HOL_Obool)), _1500568), _1500570)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1500566, tc_HOL_Obool)), hAPP(c_Relation_OField(_1500566), _1500568)), hAPP(c_Relation_OField(_1500566), _1500570))))], (48503 ^ _780478) ^ [_1758498, _1758500, _1758502] : [-(c_Predicate_Oconversep(_1758498, _1758500, c_Predicate_Oconversep(_1758500, _1758498, _1758502)) = _1758502)], (28340 ^ _780478) ^ [_1304985, _1304987, _1304989] : [class_Orderings_Oord(_1304985), 28343 ^ _780478 : [(28350 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304985), _1304989), _1304987)), -(hBOOL(hAPP(hAPP(c_member(_1304985), _1304987), hAPP(c_SetInterval_Oord__class_OatLeast(_1304985), _1304989))))], (28344 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1304985), _1304987), hAPP(c_SetInterval_Oord__class_OatLeast(_1304985), _1304989))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304985), _1304989), _1304987)))]]], (30877 ^ _780478) ^ [_1354212, _1354214] : [30878 ^ _780478 : [(30881 ^ _780478) ^ [] : [_1354214 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30879 ^ _780478) ^ [] : [-(_1354212 = 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), _1354212)), _1354214))))], (7479 ^ _780478) ^ [_906148, _906150, _906152, _906154, _906156, _906158] : [c_Fun_Oinj__on(_906148, _906150, _906152, _906154), hAPP(_906152, _906156) = hAPP(_906152, _906158), hBOOL(hAPP(hAPP(c_member(_906148), _906156), _906154)), hBOOL(hAPP(hAPP(c_member(_906148), _906158), _906154)), -(_906156 = _906158)], (2974 ^ _780478) ^ [_824530, _824532] : [_824532 = _824530, -(c_Nitpick_Onum(_824532) = c_Nitpick_Onum(_824530))], (22570 ^ _780478) ^ [_1200879, _1200881] : [-(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, _1200879)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1200881))))], (26202 ^ _780478) ^ [_1266283, _1266285, _1266287] : [class_Fields_Olinordered__field__inverse__zero(_1266283), 26205 ^ _780478 : [(26220 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266283), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266283), _1266285), _1266287)), c_Groups_Ozero__class_Ozero(_1266283)))), 26221 ^ _780478 : [(26228 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266283), _1266285), c_Groups_Ozero__class_Ozero(_1266283))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266283), c_Groups_Ozero__class_Ozero(_1266283)), _1266287))], (26222 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266283), c_Groups_Ozero__class_Ozero(_1266283)), _1266285)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266283), _1266287), c_Groups_Ozero__class_Ozero(_1266283)))]]], (26206 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266283), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266283), _1266285), _1266287)), c_Groups_Ozero__class_Ozero(_1266283))), 26211 ^ _780478 : [(26214 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266283), _1266287), c_Groups_Ozero__class_Ozero(_1266283))))], (26212 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266283), c_Groups_Ozero__class_Ozero(_1266283)), _1266285)))]], 26215 ^ _780478 : [(26218 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266283), c_Groups_Ozero__class_Ozero(_1266283)), _1266287)))], (26216 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1266283), _1266285), c_Groups_Ozero__class_Ozero(_1266283))))]]]]], (21330 ^ _780478) ^ [_1176557, _1176559, _1176561] : [class_Groups_Oordered__comm__monoid__add(_1176557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176557), _1176559), c_Groups_Ozero__class_Ozero(_1176557))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176557), _1176561), c_Groups_Ozero__class_Ozero(_1176557))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176557), _1176559), _1176561)), c_Groups_Ozero__class_Ozero(_1176557))))], (40732 ^ _780478) ^ [_1578049, _1578051, _1578053, _1578055] : [c_Wellfounded_Oacyclic(_1578049, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1578049, _1578049)), hAPP(hAPP(c_Product__Type_OPair(_1578049, _1578049), _1578051), _1578053)), _1578055)), 40735 ^ _780478 : [(40738 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578049, _1578049)), hAPP(hAPP(c_Product__Type_OPair(_1578049, _1578049), _1578053), _1578051)), c_Transitive__Closure_Ortrancl(_1578049, _1578055)))], (40736 ^ _780478) ^ [] : [-(c_Wellfounded_Oacyclic(_1578049, _1578055))]]], (37885 ^ _780478) ^ [_1504782, _1504784, _1504786, _1504788] : [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), _1504782), _1504784)), 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), _1504786), _1504788)), 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), _1504782), _1504788)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1504786), _1504784))))], (24429 ^ _780478) ^ [_1234446, _1234448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1234446), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24432 ^ _780478 : [(24439 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234448), 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), _1234448), _1234446))))], (24433 ^ _780478) ^ [] : [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), _1234448), _1234446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1234448), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (40762 ^ _780478) ^ [_1578701, _1578703, _1578705, _1578707, _1578709] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578701, _1578701)), hAPP(hAPP(c_Product__Type_OPair(_1578701, _1578701), _1578703), _1578705)), c_Transitive__Closure_Ortrancl(_1578701, _1578707))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1578701, _1578701), tc_HOL_Obool)), _1578707), hAPP(hAPP(c_Product__Type_OSigma(_1578701, _1578701), _1578709), hAPP(c_COMBK(tc_fun(_1578701, tc_HOL_Obool), _1578701), _1578709)))), -(_1578703 = _1578705), -(hBOOL(hAPP(hAPP(c_member(_1578701), _1578703), _1578709)))], (2858 ^ _780478) ^ [_822782, _822784, _822786, _822788] : [-(c_Relation_ORange(_822788, _822784) = c_Relation_ORange(_822786, _822782)), _822788 = _822786, _822784 = _822782], (37451 ^ _780478) ^ [_1494170, _1494172, _1494174, _1494176, _1494178, _1494180] : [-(c_Product__Type_Oprod_Oprod__rec(_1494170, _1494172, _1494174, _1494176, hAPP(hAPP(c_Product__Type_OPair(_1494170, _1494172), _1494178), _1494180)) = hAPP(hAPP(_1494176, _1494178), _1494180))], (13981 ^ _780478) ^ [_1030431] : [13983 ^ _780478 : [(13986 ^ _780478) ^ [_1030541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 13982 ^ [_1030431, _1030541]), _1030541))], (13984 ^ _780478) ^ [_1030507] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 13982 ^ [_1030431, _1030507]), _1030431)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1030431)))], (16496 ^ _780478) ^ [_1081611, _1081613, _1081615, _1081617, _1081619, _1081621] : [c_Fun_Oinj__on(_1081611, _1081613, _1081615, _1081617), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081611, tc_HOL_Obool)), _1081619), _1081617)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1081611, tc_HOL_Obool)), _1081621), _1081617)), -(hAPP(c_Set_Oimage(_1081611, _1081613, _1081615), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1081611, tc_HOL_Obool)), _1081619), _1081621)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1081613, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1081611, _1081613, _1081615), _1081619)), hAPP(c_Set_Oimage(_1081611, _1081613, _1081615), _1081621)))], (23148 ^ _780478) ^ [_1211416, _1211418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1211416), _1211418)), -(_1211418 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1211416), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23151 ^ [_1211416, _1211418])))], (52365 ^ _780478) ^ [_1833986, _1833988] : [hBOOL(_1833986), hBOOL(_1833988), -(hBOOL(hAPP(hAPP(c_fconj, _1833986), _1833988)))], (45546 ^ _780478) ^ [_1694490, _1694492, _1694494] : [-(c_Enum_Oproduct(_1694490, _1694492, c_List_Olist_ONil(_1694490), _1694494) = c_List_Olist_ONil(tc_prod(_1694490, _1694492)))], (26494 ^ _780478) ^ [_1271416, _1271418, _1271420, _1271422] : [class_Fields_Ofield__inverse__zero(_1271416), 26497 ^ _780478 : [(26498 ^ _780478) ^ [] : [_1271418 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271416), _1271420), _1271422), 26501 ^ _780478 : [(26508 ^ _780478) ^ [] : [_1271422 = c_Groups_Ozero__class_Ozero(_1271416), -(_1271418 = c_Groups_Ozero__class_Ozero(_1271416))], (26502 ^ _780478) ^ [] : [-(_1271422 = c_Groups_Ozero__class_Ozero(_1271416)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271416), _1271418), _1271422) = _1271420)]]], (26514 ^ _780478) ^ [] : [-(_1271418 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271416), _1271420), _1271422)), 26517 ^ _780478 : [(26520 ^ _780478) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271416), _1271418), _1271422) = _1271420], (26518 ^ _780478) ^ [] : [_1271422 = c_Groups_Ozero__class_Ozero(_1271416)]], 26521 ^ _780478 : [(26524 ^ _780478) ^ [] : [_1271418 = c_Groups_Ozero__class_Ozero(_1271416)], (26522 ^ _780478) ^ [] : [-(_1271422 = c_Groups_Ozero__class_Ozero(_1271416))]]]]], (48527 ^ _780478) ^ [_1759666, _1759668, _1759670] : [-(_1759666 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1759668), c_List_Oreplicate(_1759668, _1759666, _1759670)) = c_List_Oreplicate(_1759668, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1759666), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1759670))], (37859 ^ _780478) ^ [] : [-(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))], (28416 ^ _780478) ^ [_1306316, _1306318] : [class_Orderings_Olinorder(_1306316), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1306316, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1306316), _1306318)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1306316), _1306318))], (11005 ^ _780478) ^ [_972502, _972504, _972506] : [class_Groups_Ogroup__add(_972502), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972502), hAPP(c_Groups_Ouminus__class_Ouminus(_972502), _972504)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972502), _972504), _972506)) = _972506)], (46382 ^ _780478) ^ [_1713957, _1713959] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1713957), hAPP(c_List_Onth(_1713957), _1713959)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713957)), _1713959))) = _1713959)], (28975 ^ _780478) ^ [_1317327, _1317329] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1317327), hAPP(c_Nat_OSuc, _1317329)) = 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)), _1317329)), _1317327))], (19290 ^ _780478) ^ [_1142080, _1142082] : [class_Groups_Ogroup__add(_1142080), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142080), _1142082), c_Groups_Ozero__class_Ozero(_1142080)) = _1142082)], (49066 ^ _780478) ^ [_1770993, _1770995, _1770997, _1770999] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1770993, _1770995, _1770997, _1770999, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1770995)) = _1770997)], (9880 ^ _780478) ^ [_951834, _951836, _951838] : [class_Rings_Ocomm__semiring__1(_951834), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951834), _951836), _951838) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_951834), _951838), _951836))], (39558 ^ _780478) ^ [_1549595, _1549597, _1549599, _1549601] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1549595, tc_fun(_1549597, tc_HOL_Obool)), _1549599), _1549601) = hAPP(c_Set_OCollect(_1549597), hAPP(hAPP(c_COMBB(tc_fun(_1549595, tc_HOL_Obool), tc_HOL_Obool, _1549597), c_HOL_OAll(_1549595)), hAPP(hAPP(c_COMBB(tc_fun(_1549595, tc_HOL_Obool), tc_fun(_1549595, tc_HOL_Obool), _1549597), hAPP(c_COMBS(_1549595, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1549595), c_fimplies), hAPP(hAPP(c_COMBC(_1549595, tc_fun(_1549595, tc_HOL_Obool), tc_HOL_Obool), c_member(_1549595)), _1549599)))), hAPP(hAPP(c_COMBC(_1549597, tc_fun(_1549595, tc_fun(_1549597, tc_HOL_Obool)), tc_fun(_1549595, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1549597, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1549595, tc_fun(_1549597, tc_HOL_Obool)), tc_fun(_1549595, tc_HOL_Obool)), _1549597), c_COMBB(tc_fun(_1549597, tc_HOL_Obool), tc_HOL_Obool, _1549595)), c_member(_1549597))), _1549601)))))], (47712 ^ _780478) ^ [_1741516, _1741518] : [class_Enum_Oenum(_1741516), 47715 ^ _780478 : [(47723 ^ _780478) ^ [] : [47724 ^ _780478 : [(47725 ^ _780478) ^ [_1741696] : [hBOOL(hAPP(_1741518, _1741696))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1741516), _1741518)))], (47716 ^ _780478) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1741516), _1741518)), -(hBOOL(hAPP(_1741518, 47719 ^ [_1741516, _1741518])))]]], (42432 ^ _780478) ^ [_1623882, _1623884, _1623886] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1623882), _1623884)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1623882)), hAPP(c_Set_OCollect(tc_List_Olist(_1623882)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1623882), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1623882)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623882), tc_fun(_1623882, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1623882, tc_HOL_Obool), tc_fun(tc_fun(_1623882, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1623882)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1623882, tc_HOL_Obool))), c_List_Oset(_1623882))), _1623884))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1623882), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1623882)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1623882)))), _1623886))))))], (16412 ^ _780478) ^ [_1079710, _1079712] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079710, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1079710, tc_HOL_Obool)), _1079712)), _1079712) = c_Orderings_Obot__class_Obot(tc_fun(_1079710, tc_HOL_Obool)))], (14389 ^ _780478) ^ [_1037499, _1037501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1037499), _1037501)), _1037499))], (48435 ^ _780478) ^ [_1757108, _1757110] : [-(c_List_Osplice(_1757108, c_List_Olist_ONil(_1757108), _1757110) = _1757110)], (1978 ^ _780478) ^ [_809040, _809042, _809044, _809046, _809048, _809050, _809052, _809054, _809056, _809058] : [-(c_Fun_Ooverride__on(_809058, _809054, _809050, _809046, _809042) = c_Fun_Ooverride__on(_809056, _809052, _809048, _809044, _809040)), _809058 = _809056, _809054 = _809052, _809050 = _809048, _809046 = _809044, _809042 = _809040], (46168 ^ _780478) ^ [_1708810, _1708812] : [-(c_List_Oconcat(tc_List_Olist(_1708810), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1708810), tc_List_Olist(tc_List_Olist(_1708810))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1708810)), _1708810, c_List_Olist_ONil(tc_List_Olist(_1708810)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1708810), tc_List_Olist(tc_List_Olist(_1708810))), _1708810), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708810), tc_List_Olist(tc_List_Olist(_1708810)), tc_List_Olist(tc_List_Olist(_1708810))), c_List_Olist_OCons(tc_List_Olist(_1708810))), c_List_Olist_ONil(tc_List_Olist(_1708810)))))), _1708812)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1708810), tc_List_Olist(_1708810)), c_List_Otl(_1708810)), hAPP(c_List_Ofilter(tc_List_Olist(_1708810), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1708810)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708810), tc_List_Olist(_1708810), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1708810)))), _1708812)))], (43281 ^ _780478) ^ [_1643771, _1643773, _1643775] : [class_Orderings_Olinorder(_1643771), hBOOL(hAPP(c_Finite__Set_Ofinite(_1643771), _1643773)), -(c_List_Olinorder__class_Osorted__list__of__set(_1643771, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1643771, tc_HOL_Obool)), _1643773), hAPP(hAPP(c_Set_Oinsert(_1643771), _1643775), c_Orderings_Obot__class_Obot(tc_fun(_1643771, tc_HOL_Obool))))) = c_List_Oremove1(_1643771, _1643775, c_List_Olinorder__class_Osorted__list__of__set(_1643771, _1643773)))], (5596 ^ _780478) ^ [_866169, _866171, _866173, _866175] : [-(tc_Nitpick_Opair__box(_866175, _866171) = tc_Nitpick_Opair__box(_866173, _866169)), _866175 = _866173, _866171 = _866169], (14391 ^ _780478) ^ [_1037544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1037544), _1037544))], (6346 ^ _780478) ^ [_882881, _882883, _882885, _882887] : [c_Finite__Set_Ofolding__one(_882881, _882883, _882885), hBOOL(hAPP(c_Finite__Set_Ofinite(_882881), _882887)), -(_882887 = c_Orderings_Obot__class_Obot(tc_fun(_882881, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_882881), hAPP(hAPP(_882883, 6359 ^ [_882881, _882883, _882885, _882887]), 6360 ^ [_882881, _882883, _882885, _882887])), hAPP(hAPP(c_Set_Oinsert(_882881), 6359 ^ [_882881, _882883, _882885, _882887]), hAPP(hAPP(c_Set_Oinsert(_882881), 6360 ^ [_882881, _882883, _882885, _882887]), c_Orderings_Obot__class_Obot(tc_fun(_882881, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_882881), hAPP(_882885, _882887)), _882887)))], (34681 ^ _780478) ^ [_1434289, _1434291] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1434289)), c_Int_OBit1(_1434291)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1434289)), _1434291)))], (29025 ^ _780478) ^ [_1318475, _1318477, _1318479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1318475, tc_HOL_Obool)), _1318477), _1318479)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1318475, tc_HOL_Obool)), _1318477), hAPP(c_Set_OPow(_1318475), _1318479))))], (14555 ^ _780478) ^ [_1040647, _1040649, _1040651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040647), _1040649)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1040647), _1040651)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040649), _1040647)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040651), _1040647)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1040649), _1040651))], (23881 ^ _780478) ^ [_1224561, _1224563, _1224565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224561)), _1224561 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224563), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1224561), _1224565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224563), _1224561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1224565)))], (23126 ^ _780478) ^ [_1211020, _1211022, _1211024] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211020), _1211022))), 23129 ^ _780478 : [(23136 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211024), _1211022))), -(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)), _1211020)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1211024), _1211022)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23130 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211024), _1211022)), -(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)), _1211020)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1211024), _1211022)) = 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))))]]], (6394 ^ _780478) ^ [_884291, _884293, _884295, _884297, _884299] : [c_Finite__Set_Ofolding__one__idem(_884291, _884293, _884295), hAPP(_884297, hAPP(hAPP(_884293, 6399 ^ [_884291, _884293, _884295, _884297, _884299]), 6400 ^ [_884291, _884293, _884295, _884297, _884299])) = hAPP(hAPP(_884293, hAPP(_884297, 6399 ^ [_884291, _884293, _884295, _884297, _884299])), hAPP(_884297, 6400 ^ [_884291, _884293, _884295, _884297, _884299])), hBOOL(hAPP(c_Finite__Set_Ofinite(_884291), _884299)), -(_884299 = c_Orderings_Obot__class_Obot(tc_fun(_884291, tc_HOL_Obool))), -(hAPP(_884297, hAPP(_884295, _884299)) = hAPP(_884295, hAPP(c_Set_Oimage(_884291, _884291, _884297), _884299)))], (38669 ^ _780478) ^ [_1525070, _1525072, _1525074, _1525076] : [38670 ^ _780478 : [(38671 ^ _780478) ^ [_1525145] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1525070, _1525074)), hAPP(hAPP(c_Product__Type_OPair(_1525070, _1525074), _1525072), _1525145)), _1525076))]], -(hBOOL(hAPP(hAPP(c_member(_1525070), _1525072), hAPP(c_Relation_ODomain(_1525070, _1525074), _1525076))))], (14641 ^ _780478) ^ [_1042241, _1042243, _1042245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1042241), _1042243)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042245), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1042243), _1042241)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1042245), _1042243)), _1042241))], (43247 ^ _780478) ^ [_1642837, _1642839] : [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), _1642837), _1642839))), 43250 ^ _780478 : [(43257 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1642837), _1642839))), -(c_List_Oupto(_1642837, _1642839) = c_List_Olist_ONil(tc_Int_Oint))], (43251 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1642837), _1642839)), -(c_List_Oupto(_1642837, _1642839) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1642837), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1642837), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1642839)))]]], (45418 ^ _780478) ^ [_1691778, _1691780, _1691782, _1691784, _1691786, _1691788, _1691790] : [c_List_Olist__all2(_1691778, _1691780, _1691782, hAPP(hAPP(c_List_Omap(_1691784, _1691778), _1691786), _1691788), _1691790), -(c_List_Olist__all2(_1691784, _1691780, hAPP(hAPP(c_COMBB(_1691778, tc_fun(_1691780, tc_HOL_Obool), _1691784), _1691782), _1691786), _1691788, _1691790))], (37557 ^ _780478) ^ [_1497210, _1497212, _1497214] : [c_Equiv__Relations_Oequivp(_1497210, _1497212), -(hBOOL(hAPP(hAPP(_1497212, _1497214), _1497214)))], (52281 ^ _780478) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (38726 ^ _780478) ^ [_1527129, _1527131, _1527133, _1527135, _1527137, _1527139] : [hBOOL(hAPP(hAPP(c_member(_1527129), _1527131), _1527133)), 38729 ^ _780478 : [(38736 ^ _780478) ^ [] : [_1527137 = _1527139, -(hAPP(hAPP(c_Product__Type_OSigma(_1527135, _1527129), _1527137), hAPP(c_COMBK(tc_fun(_1527129, tc_HOL_Obool), _1527135), _1527133)) = hAPP(hAPP(c_Product__Type_OSigma(_1527135, _1527129), _1527139), hAPP(c_COMBK(tc_fun(_1527129, tc_HOL_Obool), _1527135), _1527133)))], (38730 ^ _780478) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1527135, _1527129), _1527137), hAPP(c_COMBK(tc_fun(_1527129, tc_HOL_Obool), _1527135), _1527133)) = hAPP(hAPP(c_Product__Type_OSigma(_1527135, _1527129), _1527139), hAPP(c_COMBK(tc_fun(_1527129, tc_HOL_Obool), _1527135), _1527133)), -(_1527137 = _1527139)]]], (2274 ^ _780478) ^ [_813720, _813722, _813724, _813726, _813728, _813730] : [-(c_Com_Ocom_OLocal(_813730, _813726, _813722) = c_Com_Ocom_OLocal(_813728, _813724, _813720)), _813730 = _813728, _813726 = _813724, _813722 = _813720], (22331 ^ _780478) ^ [_1195858] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195858))))], (36070 ^ _780478) ^ [_1465867, _1465869, _1465871, _1465873, _1465875, _1465877, _1465879] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1465867, _1465869), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1465871), _1465873))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1465875, _1465869), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1465877), _1465879))), -(_1465869 = 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), _1465867), _1465875), _1465869), 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), _1465871), _1465877)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1465873), _1465879)), _1465869))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1465873), _1465879), _1465869)))))], (35175 ^ _780478) ^ [_1443489, _1443491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1443489)), -(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)))), _1443491)), 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)))), _1443489)) = 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, _1443491, _1443489))))], (34793 ^ _780478) ^ [_1436383, _1436385, _1436387] : [class_Groups_Omonoid__mult(_1436383), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1436383), _1436385), 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)))), _1436387)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1436383), hAPP(hAPP(c_Power_Opower__class_Opower(_1436383), _1436385), _1436387)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (2098 ^ _780478) ^ [_811000, _811002, _811004, _811006, _811008, _811010] : [-(c_SetInterval_Oord_OlessThan(_811010, _811006, _811002) = c_SetInterval_Oord_OlessThan(_811008, _811004, _811000)), _811010 = _811008, _811006 = _811004, _811002 = _811000], (45717 ^ _780478) ^ [_1698582, _1698584] : [-(hBOOL(hAPP(c_List_Odistinct(_1698582), c_List_Oremdups(_1698582, _1698584))))], (39518 ^ _780478) ^ [_1548326, _1548328, _1548330] : [hBOOL(hAPP(c_Predicate_OPowp(_1548326, _1548328), _1548330)), 39521 ^ _780478 : [(39522 ^ _780478) ^ [_1548410] : [hBOOL(hAPP(hAPP(c_member(_1548326), _1548410), _1548330)), -(hBOOL(hAPP(_1548328, _1548410)))]]], (48286 ^ _780478) ^ [_1753720, _1753722, _1753724] : [c_List_Olist__all(_1753720, _1753722, _1753724), 48289 ^ _780478 : [(48290 ^ _780478) ^ [_1753801] : [hBOOL(hAPP(hAPP(c_member(_1753720), _1753801), hAPP(c_List_Oset(_1753720), _1753724))), -(hBOOL(hAPP(_1753722, _1753801)))]]], (49610 ^ _780478) ^ [_1783765, _1783767] : [49613 ^ _780478 : [(49618 ^ _780478) ^ [] : [49611 ^ [_1783765, _1783767] = 49612 ^ [_1783765, _1783767]], (49616 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783765, _1783765)), hAPP(hAPP(c_Product__Type_OPair(_1783765, _1783765), 49612 ^ [_1783765, _1783767]), 49611 ^ [_1783765, _1783767])), _1783767)))], (49614 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783765, _1783765)), hAPP(hAPP(c_Product__Type_OPair(_1783765, _1783765), 49611 ^ [_1783765, _1783767]), 49612 ^ [_1783765, _1783767])), _1783767)))]], -(c_Relation_Oantisym(_1783765, _1783767))], (43634 ^ _780478) ^ [_1651437, _1651439, _1651441, _1651443] : [-(hAPP(hAPP(c_List_Onth(_1651437), hAPP(hAPP(c_List_Oappend(_1651437), _1651439), hAPP(hAPP(c_List_Olist_OCons(_1651437), _1651441), _1651443))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651437)), _1651439)) = _1651441)], (8460 ^ _780478) ^ [_925921, _925923, _925925, _925927, _925929, _925931, _925933] : [c_Finite__Set_Ofun__left__comm(_925921, _925923, _925925), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_925921, _925923, _925925, _925927, _925929), _925931)), hBOOL(hAPP(hAPP(c_member(_925921), _925933), _925929)), 8472 ^ _780478 : [(8475 ^ _780478) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_925921, _925923, _925925, _925927, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_925921, tc_HOL_Obool)), _925929), hAPP(hAPP(c_Set_Oinsert(_925921), _925933), c_Orderings_Obot__class_Obot(tc_fun(_925921, tc_HOL_Obool))))), 8471 ^ [_925921, _925923, _925925, _925927, _925929, _925931, _925933])))], (8473 ^ _780478) ^ [] : [-(_925931 = hAPP(hAPP(_925925, _925933), 8471 ^ [_925921, _925923, _925925, _925927, _925929, _925931, _925933]))]]], (52121 ^ _780478) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (25061 ^ _780478) ^ [_1246000, _1246002, _1246004] : [hBOOL(hAPP(_1246000, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1246002), _1246004))), 25066 ^ _780478 : [(25069 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1246000, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25067 ^ _780478) ^ [] : [-(_1246004 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25071 ^ _780478 : [(25076 ^ _780478) ^ [] : [-(hBOOL(hAPP(_1246000, 25070 ^ [_1246000, _1246002, _1246004])))], (25074 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1246002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246004), hAPP(c_Nat_OSuc, 25070 ^ [_1246000, _1246002, _1246004])))))], (25072 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1246004), 25070 ^ [_1246000, _1246002, _1246004])), _1246002)))]]], (33430 ^ _780478) ^ [_1411420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1411420), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411420) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5036 ^ _780478) ^ [_857319, _857321, _857323, _857325, _857327, _857329, _857331, _857333, _857335, _857337] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_857337, _857333, _857329, _857325, _857321) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_857335, _857331, _857327, _857323, _857319)), _857337 = _857335, _857333 = _857331, _857329 = _857327, _857325 = _857323, _857321 = _857319], (33414 ^ _780478) ^ [_1411166, _1411168] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1411166), _1411168), hAPP(c_Int_Onumber__class_Onumber__of(_1411166), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1411166)), class_Fields_Ofield__inverse__zero(_1411166), class_Int_Onumber__ring(_1411166)], (28426 ^ _780478) ^ [] : [-(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)))], (28184 ^ _780478) ^ [_1302165, _1302167, _1302169, _1302171] : [class_Orderings_Olinorder(_1302165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302165), _1302167), _1302169)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1302165), _1302169), _1302171)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302165, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1302165, _1302167, _1302169)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1302165, _1302169, _1302171)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1302165, _1302167), _1302171))], (40562 ^ _780478) ^ [_1573954, _1573956, _1573958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1573954, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1573954, _1573954, _1573956), _1573958)), _1573958)), -(hAPP(c_Relation_OImage(_1573954, _1573954, c_Transitive__Closure_Ortrancl(_1573954, _1573956)), _1573958) = _1573958)], (23967 ^ _780478) ^ [_1226110, _1226112] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1226110), _1226112))))], (9502 ^ _780478) ^ [_943427] : [class_Groups_Oab__semigroup__mult(_943427), -(c_Finite__Set_Ofun__left__comm(_943427, _943427, c_Groups_Otimes__class_Otimes(_943427)))], (27042 ^ _780478) ^ [_1281595, _1281597, _1281599, _1281601] : [class_Fields_Olinordered__field(_1281595), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281595), _1281597), c_Groups_Ozero__class_Ozero(_1281595))), 27049 ^ _780478 : [(27056 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281595), _1281601), _1281597)), _1281599)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281595), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281595), _1281599), _1281597)), _1281601)))], (27050 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281595), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281595), _1281599), _1281597)), _1281601)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281595), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281595), _1281601), _1281597)), _1281599)))]]], (14197 ^ _780478) ^ [_1034242, _1034244, _1034246] : [class_Rings_Ocomm__semiring__1(_1034242), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034242), _1034244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034242), _1034246), _1034244)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034242), _1034246), c_Groups_Oone__class_Oone(_1034242))), _1034244))], (45252 ^ _780478) ^ [_1687465, _1687467, _1687469, _1687471] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1687465)), _1687467), c_List_Olists(_1687465, _1687469))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1687465)), _1687467), c_List_Olists(_1687465, _1687471))), -(hBOOL(hAPP(c_List_Olistsp(_1687465, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1687465, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1687465, tc_fun(_1687465, tc_HOL_Obool), tc_HOL_Obool), c_member(_1687465)), _1687469)), hAPP(hAPP(c_COMBC(_1687465, tc_fun(_1687465, tc_HOL_Obool), tc_HOL_Obool), c_member(_1687465)), _1687471))), _1687467)))], (34411 ^ _780478) ^ [_1429493, _1429495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1429493), _1429495)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1429493)), c_Int_OBit0(_1429495))))], (5238 ^ _780478) ^ [_860532, _860534, _860536, _860538] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_860538, _860534) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_860536, _860532)), _860538 = _860536, _860534 = _860532], (33744 ^ _780478) ^ [_1417172, _1417174] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417172)), hAPP(c_Nat_OSuc, _1417174)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417172))), 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, _1417174))), 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)), _1417174)))))], (4026 ^ _780478) ^ [_841252, _841254, _841256, _841258, _841260, _841262, _841264, _841266] : [-(c_New__DSequence_Oneg__bind(_841266, _841262, _841258, _841254) = c_New__DSequence_Oneg__bind(_841264, _841260, _841256, _841252)), _841266 = _841264, _841262 = _841260, _841258 = _841256, _841254 = _841252], (44358 ^ _780478) ^ [_1668555, _1668557, _1668559] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668555), tc_List_Olist(_1668555))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668555), tc_List_Olist(_1668555)), c_List_Olist_ONil(_1668555)), _1668557)), c_List_Olexord(_1668555, _1668559))), -(_1668557 = hAPP(hAPP(c_List_Olist_OCons(_1668555), 44361 ^ [_1668555, _1668557, _1668559]), 44362 ^ [_1668555, _1668557, _1668559]))], (33284 ^ _780478) ^ [_1409256, _1409258] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1409256)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409256)), _1409258)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1409256))), _1409258))], (1914 ^ _780478) ^ [_807267, _807269] : [-(hBOOL(_807267)), _807269 = _807267, hBOOL(_807269)], (20840 ^ _780478) ^ [_1168714, _1168716, _1168718] : [class_Groups_Ocomm__monoid__add(_1168714), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168716, _1168714), _1168718), c_Orderings_Obot__class_Obot(tc_fun(_1168716, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1168714))], (27936 ^ _780478) ^ [_1297080, _1297082, _1297084, _1297086] : [class_Orderings_Oorder(_1297080), 27939 ^ _780478 : [(27948 ^ _780478) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1297080, _1297082, _1297084) = hAPP(hAPP(c_Set_Oinsert(_1297080), _1297086), c_Orderings_Obot__class_Obot(tc_fun(_1297080, tc_HOL_Obool)))), _1297082 = _1297084, _1297084 = _1297086], (27940 ^ _780478) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1297080, _1297082, _1297084) = hAPP(hAPP(c_Set_Oinsert(_1297080), _1297086), c_Orderings_Obot__class_Obot(tc_fun(_1297080, tc_HOL_Obool))), 27943 ^ _780478 : [(27946 ^ _780478) ^ [] : [-(_1297084 = _1297086)], (27944 ^ _780478) ^ [] : [-(_1297082 = _1297084)]]]]], (20570 ^ _780478) ^ [_1164071, _1164073, _1164075] : [class_Groups_Oordered__ab__group__add(_1164071), 20573 ^ _780478 : [(20580 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164071), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1164071), _1164073), _1164075)), c_Groups_Ozero__class_Ozero(_1164071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164071), _1164073), _1164075)))], (20574 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164071), _1164073), _1164075)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164071), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1164071), _1164073), _1164075)), c_Groups_Ozero__class_Ozero(_1164071))))]]], (25681 ^ _780478) ^ [_1256951, _1256953, _1256955] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1256951), _1256953), _1256955) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1256951), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1256951, tc_Int_Oint), _1256953), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1256955))), class_Groups_Ocomm__monoid__add(_1256951), class_Groups_Ocomm__monoid__mult(_1256951)], (34163 ^ _780478) ^ [_1425067] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1425067))) = 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)))), _1425067))], (17264 ^ _780478) ^ [_1098716, _1098718, _1098720, _1098722, _1098724] : [17266 ^ _780478 : [(17272 ^ _780478) ^ [] : [hBOOL(hAPP(_1098724, 17268 ^ [_1098716, _1098718, _1098720, _1098722, _1098724]))], (17270 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098716), 17268 ^ [_1098716, _1098718, _1098720, _1098722, _1098724]), hAPP(_1098722, 17265 ^ [_1098716, _1098718, _1098720, _1098722, _1098724]))))], (17267 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1098718), 17265 ^ [_1098716, _1098718, _1098720, _1098722, _1098724]), _1098720)))]], 17273 ^ _780478 : [(17274 ^ _780478) ^ [_1099026] : [hBOOL(hAPP(hAPP(c_member(_1098716), _1099026), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1098718, tc_fun(_1098716, tc_HOL_Obool)), _1098720), _1098722))), -(hBOOL(hAPP(_1098724, _1099026)))]]], (38752 ^ _780478) ^ [_1527909, _1527911, _1527913, _1527915] : [hAPP(hAPP(c_Product__Type_OSigma(_1527909, _1527911), _1527913), hAPP(c_COMBK(tc_fun(_1527911, tc_HOL_Obool), _1527909), _1527915)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1527909, _1527911), tc_HOL_Obool)), -(_1527913 = c_Orderings_Obot__class_Obot(tc_fun(_1527909, tc_HOL_Obool))), -(_1527915 = c_Orderings_Obot__class_Obot(tc_fun(_1527911, tc_HOL_Obool)))], (39496 ^ _780478) ^ [_1547943, _1547945] : [39498 ^ _780478 : [(39501 ^ _780478) ^ [] : [hBOOL(hAPP(_1547943, hAPP(c_Int_OAbs__Integ, 39497 ^ [_1547943, _1547945])))], (39499 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39497 ^ [_1547943, _1547945]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1547943, _1547945)))], (15822 ^ _780478) ^ [_1066792, _1066794, _1066796] : [class_Lattices_Osemilattice__inf(_1066792), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1066792), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066792), _1066794), _1066796)), _1066794)))], (15856 ^ _780478) ^ [_1067369, _1067371, _1067373, _1067375] : [class_Lattices_Osemilattice__inf(_1067369), 15859 ^ _780478 : [(15868 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067369), _1067371), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067369), _1067373), _1067375)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067369), _1067371), _1067373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067369), _1067371), _1067375))], (15860 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067369), _1067371), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1067369), _1067373), _1067375))), 15863 ^ _780478 : [(15866 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067369), _1067371), _1067375)))], (15864 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1067369), _1067371), _1067373)))]]]]], (35517 ^ _780478) ^ [_1449188, _1449190] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1449188), hAPP(c_Int_Onumber__class_Onumber__of(_1449188), c_Int_OMin)), _1449190) = hAPP(c_Groups_Ouminus__class_Ouminus(_1449188), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1449188), c_Groups_Oone__class_Oone(_1449188)), _1449190))), class_Fields_Ofield__inverse__zero(_1449188), class_Int_Onumber__ring(_1449188)], (23705 ^ _780478) ^ [_1221208, _1221210, _1221212, _1221214, _1221216] : [class_Groups_Oab__group__add(_1221208), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221210), _1221212)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221212), _1221214)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1221208), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1221208), _1221216), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221210), _1221214))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1221208), _1221216), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221210), _1221212))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1221208), _1221216), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1221212), _1221214)))], (23063 ^ _780478) ^ [_1209668, _1209670] : [class_Rings_Osemiring__1(_1209668), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209668), _1209670) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1209668, hAPP(hAPP(c_COMBC(_1209668, _1209668, _1209668), c_Groups_Oplus__class_Oplus(_1209668)), c_Groups_Oone__class_Oone(_1209668)), _1209670, c_Groups_Ozero__class_Ozero(_1209668)))], (51909 ^ _780478) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (48625 ^ _780478) ^ [_1761423, _1761425, _1761427, _1761429, _1761431] : [-(c_List_Oreplicate(_1761423, _1761425, _1761427) = c_List_Oreplicate(_1761423, _1761429, _1761431)), _1761425 = _1761429, 48630 ^ _780478 : [(48633 ^ _780478) ^ [] : [_1761427 = _1761431], (48631 ^ _780478) ^ [] : [_1761425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (50564 ^ _780478) ^ [_1803248, _1803250, _1803252, _1803254, _1803256, _1803258, _1803260] : [c_Fun_Obij__betw(_1803248, _1803250, _1803252, _1803254, _1803256), c_Fun_Obij__betw(_1803248, _1803250, _1803252, _1803258, _1803260), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1803250, tc_HOL_Obool)), _1803256), _1803260) = c_Orderings_Obot__class_Obot(tc_fun(_1803250, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1803248, _1803250, _1803252, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1803248, tc_HOL_Obool)), _1803254), _1803258), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1803250, tc_HOL_Obool)), _1803256), _1803260)))], (35153 ^ _780478) ^ [_1443050, _1443052] : [class_Rings_Oring__1(_1443050), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1443050), hAPP(c_Groups_Ouminus__class_Ouminus(_1443050), c_Groups_Oone__class_Oone(_1443050))), 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)))), _1443052))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1443050), c_Groups_Oone__class_Oone(_1443050)))], (21542 ^ _780478) ^ [_1180551, _1180553, _1180555, _1180557] : [class_Rings_Olinordered__semiring__strict(_1180551), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180551), _1180553), _1180555)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1180551), _1180557), _1180555))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180551), c_Groups_Ozero__class_Ozero(_1180551)), _1180555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180551), _1180553), _1180557)))], (52055 ^ _780478) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (49226 ^ _780478) ^ [_1775087, _1775089, _1775091] : [c_Relation_Otrans(_1775087, _1775089), c_Relation_Otrans(_1775087, _1775091), -(c_Relation_Otrans(_1775087, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1775087, _1775087), tc_HOL_Obool)), _1775089), _1775091)))], (16186 ^ _780478) ^ [_1073745, _1073747, _1073749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073745, tc_HOL_Obool)), _1073747), _1073749)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073745, tc_HOL_Obool)), _1073747), _1073749) = _1073747)], (7094 ^ _780478) ^ [_898912, _898914, _898916] : [class_Orderings_Oorder(_898912), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898912), _898914), _898916)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_898912), _898916), _898914)), -(_898914 = _898916)], (29375 ^ _780478) ^ [_1326002, _1326004, _1326006, _1326008] : [class_Divides_Osemiring__div(_1326002), -(c_Divides_Odiv__class_Omod(_1326002, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326002), _1326004), _1326006), _1326008) = c_Divides_Odiv__class_Omod(_1326002, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326002), _1326004), c_Divides_Odiv__class_Omod(_1326002, _1326006, _1326008)), _1326008))], (1174 ^ _780478) ^ [_798017, _798019] : [-(class_Rings_Oordered__ring__abs(_798017)), _798019 = _798017, class_Rings_Oordered__ring__abs(_798019)], (6248 ^ _780478) ^ [_880640, _880642, _880644] : [class_Orderings_Obot(_880640), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_880642, _880640)), _880644) = c_Orderings_Obot__class_Obot(_880640))], (52127 ^ _780478) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (21316 ^ _780478) ^ [_1176302, _1176304, _1176306] : [class_Groups_Oordered__comm__monoid__add(_1176302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1176302), _1176304), c_Groups_Ozero__class_Ozero(_1176302))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176302), _1176306), c_Groups_Ozero__class_Ozero(_1176302))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1176302), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1176302), _1176304), _1176306)), c_Groups_Ozero__class_Ozero(_1176302))))], (3400 ^ _780478) ^ [_831157, _831159, _831161, _831163, _831165, _831167] : [-(c_Finite__Set_Ofold(_831167, _831163, _831159) = c_Finite__Set_Ofold(_831165, _831161, _831157)), _831167 = _831165, _831163 = _831161, _831159 = _831157], (2544 ^ _780478) ^ [_817925, _817927] : [_817927 = _817925, -(c_Wellfounded_Omeasure(_817927) = c_Wellfounded_Omeasure(_817925))], (34121 ^ _780478) ^ [_1424476, _1424478] : [class_Int_Onumber__ring(_1424476), 34124 ^ _780478 : [(34131 ^ _780478) ^ [] : [c_Int_Oiszero(_1424476, hAPP(c_Int_Onumber__class_Onumber__of(_1424476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1424478), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1424476), _1424478) = c_Groups_Oone__class_Oone(_1424476))], (34125 ^ _780478) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1424476), _1424478) = c_Groups_Oone__class_Oone(_1424476), -(c_Int_Oiszero(_1424476, hAPP(c_Int_Onumber__class_Onumber__of(_1424476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1424478), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (30747 ^ _780478) ^ [_1351742, _1351744] : [class_Groups_Oordered__ab__group__add__abs(_1351742), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1351742), hAPP(c_Groups_Ouminus__class_Ouminus(_1351742), hAPP(c_Groups_Oabs__class_Oabs(_1351742), _1351744))), c_Groups_Ozero__class_Ozero(_1351742))))], (7287 ^ _780478) ^ [_902174, _902176, _902178, _902180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902174, tc_HOL_Obool)), _902176), _902178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902174, tc_HOL_Obool)), _902178), _902180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902174, tc_HOL_Obool)), _902176), _902180)))], (8629 ^ _780478) ^ [_929851, _929853, _929855] : [class_Orderings_Olinorder(_929851), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929851, tc_HOL_Obool)), _929853), _929855)), -(_929853 = c_Orderings_Obot__class_Obot(tc_fun(_929851, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_929851), _929855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929851), c_Big__Operators_Olinorder__class_OMax(_929851, _929853)), c_Big__Operators_Olinorder__class_OMax(_929851, _929855))))], (20030 ^ _780478) ^ [_1154047, _1154049, _1154051] : [class_Rings_Oordered__ring(_1154047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154047), _1154049), c_Groups_Ozero__class_Ozero(_1154047))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154047), _1154051), c_Groups_Ozero__class_Ozero(_1154047))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154047), c_Groups_Ozero__class_Ozero(_1154047)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154047), _1154049), _1154051))))], (27443 ^ _780478) ^ [_1288130, _1288132] : [c_Nat__Transfer_Ois__nat(_1288130), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1288130), _1288132)))], (50787 ^ _780478) ^ [_1807822, _1807824, _1807826, _1807828, _1807830] : [50789 ^ _780478 : [(50792 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1807826, tc_HOL_Obool)), _1807828), hAPP(_1807830, 50788 ^ [_1807822, _1807824, _1807826, _1807828, _1807830])))], (50790 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1807822), 50788 ^ [_1807822, _1807824, _1807826, _1807828, _1807830]), _1807824)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1807826, tc_HOL_Obool)), _1807828), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1807822, tc_fun(_1807826, tc_HOL_Obool)), _1807824), _1807830))))], (16396 ^ _780478) ^ [_1079112, _1079114, _1079116, _1079118] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079112, tc_HOL_Obool)), _1079114), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1079112, tc_HOL_Obool)), _1079116), _1079118)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1079112, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079112, tc_HOL_Obool)), _1079114), _1079116)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079112, tc_HOL_Obool)), _1079114), _1079118)))], (38901 ^ _780478) ^ [_1532332, _1532334, _1532336, _1532338, _1532340, _1532342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532332, _1532334), tc_HOL_Obool)), _1532336), hAPP(hAPP(c_Product__Type_OSigma(_1532332, _1532334), _1532338), hAPP(c_COMBK(tc_fun(_1532334, tc_HOL_Obool), _1532332), _1532340)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1532334, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1532332, _1532334, _1532336), _1532342)), _1532340)))], (51847 ^ _780478) ^ [_1828710, _1828712] : [class_Groups_Ouminus(_1828710), -(class_Groups_Ouminus(tc_fun(_1828712, _1828710)))], (48216 ^ _780478) ^ [_1752383, _1752385, _1752387] : [48218 ^ _780478 : [(48221 ^ _780478) ^ [] : [hBOOL(hAPP(_1752385, 48217 ^ [_1752383, _1752385, _1752387]))], (48219 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1752383), 48217 ^ [_1752383, _1752385, _1752387]), hAPP(c_List_Oset(_1752383), _1752387))))]], -(c_List_Olist__all(_1752383, _1752385, _1752387))], (44987 ^ _780478) ^ [_1682287, _1682289] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1682287)), hAPP(c_Code__Numeral_Oof__nat, _1682289)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1682287), _1682289)))], (31354 ^ _780478) ^ [_1365649, _1365651, _1365653, _1365655, _1365657, _1365659] : [class_Groups_Ocomm__monoid__add(_1365649), hBOOL(hAPP(c_Finite__Set_Ofinite(_1365651), _1365653)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365651, _1365649), hAPP(hAPP(c_COMBS(_1365651, _1365649, _1365649), hAPP(hAPP(c_COMBS(_1365651, _1365649, tc_fun(_1365649, _1365649)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1365649, tc_fun(_1365649, _1365649)), _1365651), c_If(_1365649)), _1365655)), _1365657)), _1365659)), _1365653) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1365649), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365651, _1365649), _1365657), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365651, tc_HOL_Obool)), _1365653), hAPP(c_Set_OCollect(_1365651), _1365655)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365651, _1365649), _1365659), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1365651, tc_HOL_Obool)), _1365653), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1365651, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1365651), _1365655))))))], (16040 ^ _780478) ^ [_1070831, _1070833] : [class_Lattices_Obounded__lattice__top(_1070831), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070831), c_Orderings_Otop__class_Otop(_1070831)), _1070833) = _1070833)], (48547 ^ _780478) ^ [_1760074, _1760076, _1760078] : [-(_1760074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1760076), c_List_Oreplicate(_1760076, _1760074, _1760078)) = _1760078)], (25876 ^ _780478) ^ [_1260146, _1260148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1260148)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1260146)), hAPP(c_Int_Onat, _1260148)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1260146), _1260148)))], (25391 ^ _780478) ^ [_1252155, _1252157, _1252159] : [class_Rings_Odivision__ring(_1252155), -(_1252157 = c_Groups_Ozero__class_Ozero(_1252155)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252155), hAPP(c_Groups_Ouminus__class_Ouminus(_1252155), _1252159)), hAPP(c_Groups_Ouminus__class_Ouminus(_1252155), _1252157)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1252155), _1252159), _1252157))], (38776 ^ _780478) ^ [_1528506, _1528508, _1528510, _1528512, _1528514, _1528516] : [class_Groups_Ocomm__monoid__mult(_1528506), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1528508, _1528506), hAPP(hAPP(c_COMBC(_1528508, tc_fun(_1528510, tc_HOL_Obool), _1528506), hAPP(hAPP(c_COMBB(tc_fun(_1528510, _1528506), tc_fun(tc_fun(_1528510, tc_HOL_Obool), _1528506), _1528508), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1528510, _1528506)), _1528512)), _1528514)), _1528516) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1528508, _1528510), _1528506), hAPP(c_Product__Type_Oprod_Oprod__case(_1528508, _1528510, _1528506), _1528512)), hAPP(hAPP(c_Product__Type_OSigma(_1528508, _1528510), _1528516), hAPP(c_COMBK(tc_fun(_1528510, tc_HOL_Obool), _1528508), _1528514))))], (27465 ^ _780478) ^ [_1288431, _1288433] : [class_Int_Oring__char__0(_1288431), 27468 ^ _780478 : [(27475 ^ _780478) ^ [] : [_1288433 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1288431) = hAPP(c_Int_Oring__1__class_Oof__int(_1288431), _1288433))], (27469 ^ _780478) ^ [] : [c_Groups_Ozero__class_Ozero(_1288431) = hAPP(c_Int_Oring__1__class_Oof__int(_1288431), _1288433), -(_1288433 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (5913 ^ _780478) ^ [_874460, _874462, _874464, _874466] : [_874460 = _874462, hBOOL(hAPP(hAPP(c_member(_874464), _874462), _874466)), -(hBOOL(hAPP(hAPP(c_member(_874464), _874460), _874466)))], (43670 ^ _780478) ^ [_1652412, _1652414, _1652416, _1652418, _1652420, _1652422] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652412), tc_List_Olist(_1652412))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652412), tc_List_Olist(_1652412)), hAPP(hAPP(c_List_Oappend(_1652412), _1652414), _1652420)), hAPP(hAPP(c_List_Oappend(_1652412), _1652416), _1652422))), c_List_Olistrel1(_1652412, _1652418)))), 43671 ^ _780478 : [(43678 ^ _780478) ^ [] : [_1652414 = _1652416, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652412), tc_List_Olist(_1652412))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652412), tc_List_Olist(_1652412)), _1652420), _1652422)), c_List_Olistrel1(_1652412, _1652418)))], (43672 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1652412), tc_List_Olist(_1652412))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1652412), tc_List_Olist(_1652412)), _1652414), _1652416)), c_List_Olistrel1(_1652412, _1652418))), _1652420 = _1652422]]], (23495 ^ _780478) ^ [_1217265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1217265), 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)), _1217265)), _1217265)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17209 ^ _780478) ^ [_1097303, _1097305, _1097307, _1097309, _1097311] : [class_Complete__Lattice_Ocomplete__lattice(_1097303), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1097305, tc_HOL_Obool)), _1097307), _1097309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097303), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097305, _1097303), _1097307), _1097311)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1097305, _1097303), _1097309), _1097311))))], (37875 ^ _780478) ^ [] : [-(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))))))], (406 ^ _780478) ^ [_786633, _786635, _786637, _786639, _786641, _786643] : [-(c_Relation_Ototal__on(_786641, _786637, _786633)), c_Relation_Ototal__on(_786643, _786639, _786635), _786643 = _786641, _786639 = _786637, _786635 = _786633], (48737 ^ _780478) ^ [_1763639, _1763641] : [-(c_Predicate_Opred__comp(_1763639, _1763639, _1763639, c_fequal, c_Predicate_Opred__comp(_1763639, _1763639, _1763639, _1763641, c_fequal)) = _1763641)], (16180 ^ _780478) ^ [_1073575, _1073577, _1073579, _1073581, _1073583] : [-(hAPP(c_Set_Ovimage(_1073575, _1073577, _1073579), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073577, tc_HOL_Obool)), _1073581), _1073583)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073575, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1073575, _1073577, _1073579), _1073581)), hAPP(c_Set_Ovimage(_1073575, _1073577, _1073579), _1073583)))], (52307 ^ _780478) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (556 ^ _780478) ^ [_788882, _788884, _788886, _788888, _788890, _788892] : [-(c_Finite__Set_Ofun__left__comm(_788890, _788886, _788882)), c_Finite__Set_Ofun__left__comm(_788892, _788888, _788884), _788892 = _788890, _788888 = _788886, _788884 = _788882], (19508 ^ _780478) ^ [_1145277] : [-(_1145277 = 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)), _1145277)))], (47578 ^ _780478) ^ [_1738015, _1738017, _1738019, _1738021] : [-(c_List_Omaps(_1738015, _1738017, _1738019, _1738021) = c_List_Oconcat(_1738017, hAPP(hAPP(c_List_Omap(_1738015, tc_List_Olist(_1738017)), _1738019), _1738021)))], (33484 ^ _780478) ^ [_1412296, _1412298] : [33485 ^ _780478 : [(33488 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412296), c_Int_OPls))], (33486 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412296), _1412298))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412296)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1412298))))], (38074 ^ _780478) ^ [_1510877, _1510879, _1510881, _1510883, _1510885, _1510887, _1510889] : [c_Typedef_Otype__definition(_1510877, _1510879, _1510881, _1510883, _1510885), 38077 ^ _780478 : [(38084 ^ _780478) ^ [] : [_1510887 = _1510889, -(hAPP(_1510881, _1510887) = hAPP(_1510881, _1510889))], (38078 ^ _780478) ^ [] : [hAPP(_1510881, _1510887) = hAPP(_1510881, _1510889), -(_1510887 = _1510889)]]], (39711 ^ _780478) ^ [_1553675, _1553677, _1553679, _1553681, _1553683, _1553685] : [-(hAPP(hAPP(c_Fun_Ocomp(_1553675, _1553677, _1553679, hAPP(c_COMBK(_1553677, _1553675), _1553681)), _1553683), _1553685) = _1553681)], (46009 ^ _780478) ^ [_1705298, _1705300, _1705302] : [hBOOL(hAPP(c_List_Odistinct(_1705298), _1705300)), -(hBOOL(hAPP(c_List_Odistinct(_1705298), hAPP(c_List_Ofilter(_1705298, _1705302), _1705300))))], (48337 ^ _780478) ^ [_1754727, _1754729] : [c_List_Olist__ex1(_1754727, _1754729, c_List_Olist_ONil(_1754727))], (1624 ^ _780478) ^ [_803642, _803644] : [-(class_Groups_Oab__semigroup__mult(_803642)), _803644 = _803642, class_Groups_Oab__semigroup__mult(_803644)], (51245 ^ _780478) ^ [_1818905, _1818907, _1818909, _1818911] : [class_Rings_Odvd(_1818905), _1818907 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1818905), _1818909), _1818911), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1818905), _1818909), _1818907)))], (46166 ^ _780478) ^ [_1708730, _1708732, _1708734] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708730)), hAPP(c_List_Ofilter(_1708730, _1708732), _1708734)) = 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(_1708730)), _1708734)))), hAPP(hAPP(c_COMBB(_1708730, tc_HOL_Obool, tc_Nat_Onat), _1708732), hAPP(c_List_Onth(_1708730), _1708734))))))], (25553 ^ _780478) ^ [_1254883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1254883), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1254883) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6990 ^ _780478) ^ [_897225, _897227, _897229, _897231, _897233, _897235] : [hBOOL(hAPP(hAPP(c_member(_897225), _897227), _897229)), -(hAPP(c_Fun_Ooverride__on(_897225, _897231, _897233, _897235, _897229), _897227) = hAPP(_897235, _897227))], (35209 ^ _780478) ^ [_1444099, _1444101] : [class_Rings_Oring__1(_1444099), 35212 ^ _780478 : [(35219 ^ _780478) ^ [] : [-(_1444101 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35222 ^ _780478 : [(35229 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1444101), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1444099), _1444101) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1444099), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1444099, _1444099)), tc_fun(tc_Int_Oint, _1444099)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1444099, _1444099), _1444099), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1444099, _1444099)), tc_fun(tc_Int_Oint, _1444099)), tc_Int_Oint), c_COMBB(tc_fun(_1444099, _1444099), _1444099, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1444099, tc_fun(tc_fun(_1444099, _1444099), _1444099), tc_Int_Oint), c_HOL_OLet(_1444099, _1444099)), c_Int_Oring__1__class_Oof__int(_1444099)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1444099, _1444099), tc_fun(_1444099, _1444099)), hAPP(hAPP(c_COMBB(tc_fun(_1444099, tc_fun(_1444099, _1444099)), tc_fun(tc_fun(_1444099, _1444099), tc_fun(_1444099, _1444099)), tc_Int_Oint), c_COMBS(_1444099, _1444099, _1444099)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1444099, _1444099), tc_fun(_1444099, tc_fun(_1444099, _1444099))), hAPP(hAPP(c_COMBB(tc_fun(_1444099, tc_fun(_1444099, _1444099)), tc_fun(tc_fun(_1444099, _1444099), tc_fun(_1444099, tc_fun(_1444099, _1444099))), tc_Int_Oint), c_COMBB(_1444099, tc_fun(_1444099, _1444099), _1444099)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1444099, tc_fun(_1444099, _1444099)), tc_Int_Oint), c_If(_1444099)), 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(_1444099, _1444099, _1444099), c_Groups_Oplus__class_Oplus(_1444099)), c_COMBI(_1444099))))), hAPP(hAPP(c_COMBC(_1444099, _1444099, _1444099), hAPP(hAPP(c_COMBB(_1444099, tc_fun(_1444099, _1444099), _1444099), c_Groups_Oplus__class_Oplus(_1444099)), hAPP(hAPP(c_COMBS(_1444099, _1444099, _1444099), c_Groups_Oplus__class_Oplus(_1444099)), c_COMBI(_1444099)))), c_Groups_Oone__class_Oone(_1444099))))), c_Divides_Odivmod__int(_1444101, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (35223 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1444101), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1444099), _1444101) = hAPP(c_Groups_Ouminus__class_Ouminus(_1444099), hAPP(c_Int_Oring__1__class_Oof__int(_1444099), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1444101))))]]], (35213 ^ _780478) ^ [] : [_1444101 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1444099), _1444101) = c_Groups_Ozero__class_Ozero(_1444099))]]], (22833 ^ _780478) ^ [_1205498, _1205500, _1205502] : [class_Rings_Olinordered__semidom(_1205498), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205500), _1205502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205498), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205498), _1205500)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1205498), _1205502))))], (15705 ^ _780478) ^ [_1064276, _1064278, _1064280, _1064282, _1064284] : [class_Lattices_Olattice(_1064276), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1064278, _1064276)), _1064280), _1064282), _1064284) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1064276), hAPP(_1064280, _1064284)), hAPP(_1064282, _1064284)))], (37523 ^ _780478) ^ [_1496545] : [-(c_Equiv__Relations_Oequivp(_1496545, c_fequal))], (6126 ^ _780478) ^ [_878211, _878213, _878215] : [hAPP(hAPP(c_Set_Oinsert(_878211), _878213), c_Orderings_Obot__class_Obot(tc_fun(_878211, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_878211), _878215), c_Orderings_Obot__class_Obot(tc_fun(_878211, tc_HOL_Obool))), -(_878213 = _878215)], (2766 ^ _780478) ^ [_821358, _821360, _821362, _821364, _821366, _821368] : [-(c_Hoare__Mirabelle_Opeek__and(_821368, _821364, _821360) = c_Hoare__Mirabelle_Opeek__and(_821366, _821362, _821358)), _821368 = _821366, _821364 = _821362, _821360 = _821358], (13400 ^ _780478) ^ [_1019143, _1019145] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019143, tc_HOL_Obool)), _1019145) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1019143, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1019143, tc_HOL_Obool))), _1019145))], (31753 ^ _780478) ^ [_1380443, _1380445] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1380443)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1380445)), hAPP(c_Int_Onat, _1380443)) = hAPP(c_Int_Onat, _1380445))], (51041 ^ _780478) ^ [_1814744, _1814746, _1814748, _1814750] : [class_Rings_Ocomm__ring(_1814744), class_Rings_Odvd(_1814744), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814744), _1814746), _1814748)), 51052 ^ _780478 : [(51059 ^ _780478) ^ [_1815170, _1815172] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814744), _1814746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1814744), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1814744), _1815172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814744), _1815170), _1814748))), _1814750))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814744), _1814746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1814744), _1815172), _1814750))))], (51053 ^ _780478) ^ [_1814997, _1814999] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814744), _1814746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1814744), _1814999), _1814750))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814744), _1814746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1814744), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1814744), _1814999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1814744), _1814997), _1814748))), _1814750))))]]], (39157 ^ _780478) ^ [_1540226, _1540228, _1540230, _1540232] : [-(c_Product__Type_Oapfst(_1540226, _1540228, _1540230, _1540232) = c_Product__Type_Omap__pair(_1540226, _1540228, _1540230, _1540230, _1540232, c_Fun_Oid(_1540230)))], (36650 ^ _780478) ^ [_1477412, _1477414] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1477412), _1477414)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1477412), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1477414)))], (21758 ^ _780478) ^ [_1184466, _1184468] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1184466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1184468)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1184466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1184466), _1184468))))], (29117 ^ _780478) ^ [_1320709, _1320711, _1320713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1320709)), 29120 ^ _780478 : [(29121 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1320711, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1320713), _1320709)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1320713, _1320709))), 29124 ^ _780478 : [(29125 ^ _780478) ^ [_1320910, _1320912] : [-(hBOOL(hAPP(hAPP(_1320711, _1320912), _1320910))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1320910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1320910), _1320709)), _1320713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1320709), _1320912)), _1320910)]]], (29139 ^ _780478) ^ [] : [29142 ^ _780478 : [(29145 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 29141 ^ [_1320709, _1320711, _1320713]), _1320709)))], (29147 ^ _780478) ^ [] : [-(_1320713 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1320709), 29140 ^ [_1320709, _1320711, _1320713])), 29141 ^ [_1320709, _1320711, _1320713]))], (29149 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(_1320711, 29140 ^ [_1320709, _1320711, _1320713]), 29141 ^ [_1320709, _1320711, _1320713]))], (29143 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29141 ^ [_1320709, _1320711, _1320713])))]], -(hBOOL(hAPP(hAPP(_1320711, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1320713), _1320709)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1320713, _1320709))))]]], (858 ^ _780478) ^ [_793289, _793291, _793293, _793295, _793297, _793299, _793301, _793303] : [-(c_Fun_Oinj__on(_793301, _793297, _793293, _793289)), c_Fun_Oinj__on(_793303, _793299, _793295, _793291), _793303 = _793301, _793299 = _793297, _793295 = _793293, _793291 = _793289], (8858 ^ _780478) ^ [_933460, _933462, _933464] : [class_Orderings_Opreorder(_933460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933460), _933462), _933464)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933460), _933464), _933462))], (52291 ^ _780478) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (38547 ^ _780478) ^ [_1521868, _1521870, _1521872] : [-(hAPP(c_Set_Oimage(tc_prod(_1521868, _1521870), _1521870, c_Product__Type_Osnd(_1521868, _1521870)), _1521872) = hAPP(c_Relation_ORange(_1521868, _1521870), _1521872))], (39793 ^ _780478) ^ [_1555484, _1555486, _1555488, _1555490, _1555492, _1555494, _1555496, _1555498, _1555500, _1555502] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1555484, _1555486), tc_prod(_1555488, _1555490), tc_prod(_1555492, _1555494), c_Product__Type_Omap__pair(_1555484, _1555488, _1555486, _1555490, _1555496, _1555498)), c_Product__Type_Omap__pair(_1555492, _1555484, _1555494, _1555486, _1555500, _1555502)) = c_Product__Type_Omap__pair(_1555492, _1555488, _1555494, _1555490, hAPP(c_Fun_Ocomp(_1555484, _1555488, _1555492, _1555496), _1555500), hAPP(c_Fun_Ocomp(_1555486, _1555490, _1555494, _1555498), _1555502)))], (35683 ^ _780478) ^ [_1456538, _1456540, _1456542, _1456544, _1456546, _1456548] : [c_Equiv__Relations_Ocongruent(_1456538, _1456540, _1456542, _1456544), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456538, _1456538)), hAPP(hAPP(c_Product__Type_OPair(_1456538, _1456538), _1456546), _1456548)), _1456542)), -(hAPP(_1456544, _1456546) = hAPP(_1456544, _1456548))], (35315 ^ _780478) ^ [_1446171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1446171)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446171), c_Int_OMin)))], (35385 ^ _780478) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (39622 ^ _780478) ^ [_1551782, _1551784, _1551786] : [-(hAPP(c_Fun_Ocomp(_1551782, _1551782, _1551784, c_Fun_Oid(_1551782)), _1551786) = _1551786)], (22781 ^ _780478) ^ [_1204621] : [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), _1204621))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204621)))], (20852 ^ _780478) ^ [_1168932, _1168934, _1168936, _1168938] : [class_Groups_Ocomm__monoid__add(_1168932), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1168934), _1168936))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168934, _1168932), _1168938), _1168936) = c_Groups_Ozero__class_Ozero(_1168932))], (50095 ^ _780478) ^ [_1793249, _1793251, _1793253, _1793255, _1793257, _1793259] : [hAPP(c_Set_Oimage(_1793249, _1793251, _1793253), _1793255) = _1793257, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1793251, tc_HOL_Obool)), _1793259), _1793257)), -(hAPP(c_Set_Oimage(_1793249, _1793251, _1793253), hAPP(c_Set_Oimage(_1793251, _1793249, c_Hilbert__Choice_Oinv__into(_1793249, _1793251, _1793255, _1793253)), _1793259)) = _1793259)], (41634 ^ _780478) ^ [_1600997, _1600999] : [-(c_Nitpick_Ouminus__frac(_1600997, _1600999) = c_Nitpick_OAbs__Frac(_1600997, 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(_1600997), _1600999))), hAPP(c_Nitpick_Odenom(_1600997), _1600999))))], (15011 ^ _780478) ^ [_1050365, _1050367, _1050369, _1050371, _1050373, _1050375] : [class_Groups_Ocomm__monoid__mult(_1050365), hBOOL(hAPP(c_Finite__Set_Ofinite(_1050367), _1050369)), 15018 ^ _780478 : [(15025 ^ _780478) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1050367), _1050371), _1050369))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1050367, _1050365), hAPP(hAPP(c_COMBC(_1050367, _1050365, _1050365), hAPP(hAPP(c_COMBS(_1050367, _1050365, tc_fun(_1050365, _1050365)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1050365, tc_fun(_1050365, _1050365)), _1050367), c_If(_1050365)), hAPP(hAPP(c_COMBC(_1050367, _1050367, tc_HOL_Obool), c_fequal), _1050371))), _1050373)), _1050375)), _1050369) = hAPP(hAPP(c_Power_Opower__class_Opower(_1050365), _1050375), hAPP(c_Finite__Set_Ocard(_1050367), _1050369)))], (15019 ^ _780478) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1050367), _1050371), _1050369)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1050367, _1050365), hAPP(hAPP(c_COMBC(_1050367, _1050365, _1050365), hAPP(hAPP(c_COMBS(_1050367, _1050365, tc_fun(_1050365, _1050365)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1050365, tc_fun(_1050365, _1050365)), _1050367), c_If(_1050365)), hAPP(hAPP(c_COMBC(_1050367, _1050367, tc_HOL_Obool), c_fequal), _1050371))), _1050373)), _1050375)), _1050369) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1050365), hAPP(_1050373, _1050371)), hAPP(hAPP(c_Power_Opower__class_Opower(_1050365), _1050375), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1050367), _1050369)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]]], input).
% 48.29/47.24  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q, v_x))), hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P)), v_c0)), v_Q)), v_F)))],start(52451 ^ 0)).
% 48.29/47.24  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q, v_x))), hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P)), v_c0)), v_Q)), v_F)))), c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P)), v_c0)), v_Q)), v_F))],extension(5795 ^ 1,bind([[_872154, _872156, _872158, _872160], [t_b, v_G, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q, v_x)), hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P)), v_c0)), v_Q)), v_F)]]))).
% 48.29/47.24  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool))))), c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P_H, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q_H, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool))))],extension(52431 ^ 2,bind([[_1834833], [v_x]]))).
% 48.29/47.24  ncf('1.1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b), hAPP(v_P_H, v_x)), hAPP(v_c0, v_x)), hAPP(v_Q_H, v_x))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b), tc_HOL_Obool)))))],extension(52447 ^ 3)).
% 48.29/47.24  ncf('1.1.2',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P)), v_c0)), v_Q)), v_F))), c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P_H)), v_c0)), v_Q_H)), v_F))],extension(52441 ^ 2)).
% 48.29/47.24  ncf('1.1.2.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_b, v_G, hAPP(c_Set_Oimage(t_a, tc_Hoare__Mirabelle_Otriple(t_b), hAPP(hAPP(c_COMBS(t_a, tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b)), hAPP(hAPP(c_COMBS(t_a, tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), hAPP(hAPP(c_COMBB(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(t_b, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(t_b))), t_a), c_Hoare__Mirabelle_Otriple_Otriple(t_b)), v_P_H)), v_c0)), v_Q_H)), v_F)))],extension(52449 ^ 3)).
% 48.29/47.24  %-----------------------------------------------------
% 48.29/47.24  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------