%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SCT165+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n016.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 11:51:38 EDT 2023

% Result   : Theorem 257.99s 248.87s
% Output   : Proof 257.99s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SCT165+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13  % Command  : nanocop.sh %s %d
% 0.13/0.35  % Computer : n016.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu May 18 15:53:56 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 257.99/248.87  
% 257.99/248.87  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 257.99/248.87  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 257.99/248.87  %-----------------------------------------------------
% 257.99/248.87  ncf(matrix, plain, [(3552 ^ _176355) ^ [_305832, _305834, _305836] : [_305832 = _305834, 3555 ^ _176355 : [(3556 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_305836, tc_HOL_Obool), _305832), _305834)))], (3558 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_305836, tc_HOL_Obool), _305834), _305832)))]]], (1663 ^ _176355) ^ [_235702, _235704, _235706, _235708] : [-(_235702 = _235704), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _235706), c_Arrow__Order__Mirabelle_OProf)), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _235708), c_Arrow__Order__Mirabelle_OProf)), 1679 ^ _176355 : [(1680 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _235702), _235704)), hAPP(_235706, 1676 ^ [_235702, _235704, _235706, _235708]))))], (1682 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _235704), _235702)), hAPP(_235708, 1676 ^ [_235702, _235704, _235706, _235708])))]], 1683 ^ _176355 : [(1684 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _235704), _235702)), hAPP(_235708, 1676 ^ [_235702, _235704, _235706, _235708]))))], (1686 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _235702), _235704)), hAPP(_235706, 1676 ^ [_235702, _235704, _235706, _235708])))]], 1687 ^ _176355 : [(1688 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _235702), _235704)), hAPP(v_F, _235706))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _235704), _235702)), hAPP(v_F, _235708))))], (1694 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _235704), _235702)), hAPP(v_F, _235708))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _235702), _235704)), hAPP(v_F, _235706))))]]], (6053 ^ _176355) ^ [_403973, _403975, _403977, _403979, _403981] : [c_Fun_Oinj__on(_403973, _403975, _403977, _403979), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_403973, tc_HOL_Obool), _403981), _403979)), -(c_Set_Oimage(_403975, _403973, c_Hilbert__Choice_Oinv__into(_403973, _403975, _403979, _403977), c_Set_Oimage(_403973, _403975, _403977, _403981)) = _403981)], (5158 ^ _176355) ^ [_367594, _367596] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _367594), hAPP(c_Nat_OSuc, _367596)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _367594), _367596)))], (1741 ^ _176355) ^ [_238732, _238734, _238736, _238738, _238740] : [-(_238732 = _238734), -(_238734 = _238736), -(_238732 = _238736), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _238738), c_Arrow__Order__Mirabelle_OProf)), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _238740), c_Arrow__Order__Mirabelle_OProf)), 1765 ^ _176355 : [(1766 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _238732), _238734)), hAPP(_238738, 1762 ^ [_238732, _238734, _238736, _238738, _238740]))))], (1768 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _238734), _238736)), hAPP(_238740, 1762 ^ [_238732, _238734, _238736, _238738, _238740])))]], 1769 ^ _176355 : [(1770 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _238734), _238736)), hAPP(_238740, 1762 ^ [_238732, _238734, _238736, _238738, _238740]))))], (1772 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _238732), _238734)), hAPP(_238738, 1762 ^ [_238732, _238734, _238736, _238738, _238740])))]], 1773 ^ _176355 : [(1774 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _238732), _238734)), hAPP(v_F, _238738))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _238734), _238736)), hAPP(v_F, _238740))))], (1780 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _238734), _238736)), hAPP(v_F, _238740))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _238732), _238734)), hAPP(v_F, _238738))))]]], (3346 ^ _176355) ^ [_296633, _296635, _296637, _296639, _296641] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_296633, _296635)), hAPP(hAPP(c_Product__Type_OPair(_296633, _296635), _296639), _296641)), _296637)), -(c_FunDef_Oin__rel(_296633, _296635, _296637, _296639, _296641))], (5898 ^ _176355) ^ [_397159, _397161] : [c_Finite__Set_Ofinite(_397159, c_Orderings_Otop__class_Otop(tc_fun(_397159, tc_HOL_Obool))), c_Fun_Oinj__on(_397159, _397159, _397161, c_Orderings_Otop__class_Otop(tc_fun(_397159, tc_HOL_Obool))), -(c_Set_Oimage(_397159, _397159, _397161, c_Orderings_Otop__class_Otop(tc_fun(_397159, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_397159, tc_HOL_Obool)))], (4 ^ _176355) ^ [_176606, _176608] : [_176608 = _176606, -(_176606 = _176608)], (5036 ^ _176355) ^ [_363165] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _363165)), _363165))], (6387 ^ _176355) ^ [_416326, _416328] : [-(class_Finite__Set_Ofinite(tc_sum(_416326, _416328))), class_Finite__Set_Ofinite(_416326), class_Finite__Set_Ofinite(_416328)], (925 ^ _176355) ^ [_208807] : [928 ^ _176355 : [(929 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _208807)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), v_n____), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (931 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), v_Lab____))]], 932 ^ _176355 : [(933 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _208807)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), v_n____), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (935 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), v_Lba____))]], 936 ^ _176355 : [(937 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _208807)), v_n____)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_e____)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop, hAPP(v_P____, _208807)), v_e____))))], (943 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _208807)), v_n____))), 946 ^ _176355 : [(947 ^ _176355) ^ [] : [hAPP(v_h____, _208807) = v_n____, -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_e____)), hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove, hAPP(v_P____, _208807)), v_c____), v_e____))))], (953 ^ _176355) ^ [] : [-(hAPP(v_h____, _208807) = v_n____), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_e____)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot, hAPP(v_P____, _208807)), v_e____))))]]]]], (1613 ^ _176355) ^ [_233578, _233580, _233582] : [hAPP(hAPP(c_COMBC(_233578, tc_fun(_233578, tc_HOL_Obool), tc_HOL_Obool), c_member(_233578)), _233580) = hAPP(hAPP(c_COMBC(_233578, tc_fun(_233578, tc_HOL_Obool), tc_HOL_Obool), c_member(_233578)), _233582), -(_233580 = _233582)], (4124 ^ _176355) ^ [_328964, _328966, _328968, _328970, _328972, _328974, _328976, _328978] : [c_Finite__Set_Ofolding__image__simple__idem(_328964, _328966, _328968, _328970, _328972, _328974), c_Finite__Set_Ofinite(_328966, _328976), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_328966, tc_HOL_Obool), _328978), _328976)), -(hAPP(hAPP(_328968, hAPP(_328974, _328978)), hAPP(_328974, _328976)) = hAPP(_328974, _328976))], (5351 ^ _176355) ^ [_374443, _374445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _374443), _374445)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _374443)), _374445)))], (5134 ^ _176355) ^ [_366614, _366616] : [5135 ^ _176355 : [(5136 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _366614), _366616))], (5138 ^ _176355) ^ [] : [_366614 = _366616]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _366614), hAPP(c_Nat_OSuc, _366616))))], (2003 ^ _176355) ^ [_248558, _248560, _248562] : [2004 ^ _176355 : [(2005 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_248558, tc_HOL_Obool)), _248560), _248562))], (2007 ^ _176355) ^ [] : [_248560 = _248562]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_248558, tc_HOL_Obool), _248560), _248562)))], (5932 ^ _176355) ^ [_398363, _398365, _398367, _398369, _398371] : [c_Fun_Oinj__on(_398363, _398365, _398367, c_Orderings_Otop__class_Otop(tc_fun(_398363, tc_HOL_Obool))), 5935 ^ _176355 : [(5936 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_398365), hAPP(_398367, _398369)), c_Set_Oimage(_398363, _398365, _398367, _398371))), -(hBOOL(hAPP(hAPP(c_member(_398363), _398369), _398371)))], (5942 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_398363), _398369), _398371)), -(hBOOL(hAPP(hAPP(c_member(_398365), hAPP(_398367, _398369)), c_Set_Oimage(_398363, _398365, _398367, _398371))))]]], (4356 ^ _176355) ^ [_338545, _338547, _338549, _338551] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_338545, tc_HOL_Obool), c_Set_Oinsert(_338545, _338547, _338549)), _338551))), hBOOL(hAPP(hAPP(c_member(_338545), _338547), _338551)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_338545, tc_HOL_Obool), _338549), _338551))], (3016 ^ _176355) ^ [_284469, _284471, _284473] : [class_Orderings_Olinorder(_284469), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_284469, _284471), _284473)), 3023 ^ _176355 : [(3024 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_284469), _284471), _284473))), -(_284471 = _284473)], (3030 ^ _176355) ^ [] : [_284471 = _284473, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_284469), _284471), _284473))]]], (2107 ^ _176355) ^ [_253752, _253754, _253756] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_253752, tc_HOL_Obool), _253754), _253756)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_253752, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_253752, tc_fun(_253752, tc_HOL_Obool), tc_HOL_Obool), c_member(_253752)), _253754)), hAPP(hAPP(c_COMBC(_253752, tc_fun(_253752, tc_HOL_Obool), tc_HOL_Obool), c_member(_253752)), _253756))))], (2928 ^ _176355) ^ [_281587, _281589, _281591] : [class_Orderings_Olinorder(_281587), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_281587), _281589), _281591))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_281587, _281591), _281589)))], (1435 ^ _176355) ^ [_226852, _226854] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226852), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _226852), _226854))))], (3550 ^ _176355) ^ [_305672, _305674] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_305672, tc_HOL_Obool), _305674), _305674)))], (5780 ^ _176355) ^ [_391671, _391673, _391675] : [hAPP(_391675, hAPP(c_Hilbert__Choice_Oinv__into(_391671, _391673, c_Orderings_Otop__class_Otop(tc_fun(_391671, tc_HOL_Obool)), _391675), 5781 ^ [_391671, _391673, _391675])) = 5781 ^ [_391671, _391673, _391675], -(c_Set_Oimage(_391671, _391673, _391675, c_Orderings_Otop__class_Otop(tc_fun(_391671, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_391673, tc_HOL_Obool)))], (2470 ^ _176355) ^ [_266108, _266110, _266112] : [class_Orderings_Olinorder(_266108), -(_266110 = _266112), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_266108), _266110), _266112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_266108), _266112), _266110)))], (3106 ^ _176355) ^ [_287378, _287380, _287382, _287384] : [class_Orderings_Opreorder(_287378), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_287378, _287380), _287382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_287378), _287382), _287384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_287378), _287380), _287384)))], (5070 ^ _176355) ^ [_364445, _364447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _364445), _364447)), -(hAPP(c_Nat_OSuc, _364445) = _364447), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _364445)), _364447)))], (1404 ^ _176355) ^ [_225570, _225572, _225574] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225570), _225572)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225570), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _225572), _225574))))], (2297 ^ _176355) ^ [_260348, _260350, _260352] : [class_Orderings_Opreorder(_260348), _260350 = _260352, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_260348, _260350), _260352)))], (3714 ^ _176355) ^ [_312741, _312743, _312745, _312747, _312749] : [c_Fun_Oinj__on(_312741, _312743, _312745, _312747), hBOOL(hAPP(hAPP(c_member(_312741), _312749), _312747)), -(hAPP(c_Hilbert__Choice_Oinv__into(_312741, _312743, _312747, _312745), hAPP(_312745, _312749)) = _312749)], (4442 ^ _176355) ^ [_342106] : [-(_342106 = 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)), _342106)))], (6431 ^ _176355) ^ [_418151, _418153] : [_418151 = _418153, -(hBOOL(hAPP(hAPP(c_fequal, _418151), _418153)))], (5228 ^ _176355) ^ [_370185] : [5229 ^ _176355 : [(5230 ^ _176355) ^ [_370258] : [_370185 = hAPP(c_Nat_OSuc, _370258)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _370185)))], (4460 ^ _176355) ^ [_342760, _342762] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _342760), _342762) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _342760 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _342762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4372 ^ _176355) ^ [_339165, _339167] : [-(c_Sum__Type_OPlus(_339165, _339167, c_Orderings_Otop__class_Otop(tc_fun(_339165, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_339167, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_339165, _339167), tc_HOL_Obool)))], (3974 ^ _176355) ^ [_323602, _323604, _323606] : [c_Finite__Set_Ofinite(_323602, _323604), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_323602, tc_HOL_Obool)), _323606), _323604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Finite__Set_Ocard(_323602, _323606)), c_Finite__Set_Ocard(_323602, _323604))))], (6345 ^ _176355) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (2852 ^ _176355) ^ [_279158, _279160, _279162] : [class_Orderings_Olinorder(_279158), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_279158, _279160), _279162))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_279158), _279162), _279160)))], (1326 ^ _176355) ^ [_222553, _222555] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _222553), _222555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _222553), _222555))), -(_222553 = _222555)], (550 ^ _176355) ^ [_194845, _194847] : [_194847 = _194845, -(c_Wellfounded_Ofinite__psubset(_194847) = c_Wellfounded_Ofinite__psubset(_194845))], (5557 ^ _176355) ^ [_382109, _382111, _382113] : [class_Rings_Ocomm__semiring__1(_382109), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_382109), _382111), _382113) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_382109), _382113), _382111))], (6081 ^ _176355) ^ [_405288, _405290, _405292, _405294] : [c_Fun_Oinj__on(_405288, _405290, _405292, c_Orderings_Otop__class_Otop(tc_fun(_405288, tc_HOL_Obool))), -(c_Set_Oimage(_405290, _405288, c_Hilbert__Choice_Oinv__into(_405288, _405290, c_Orderings_Otop__class_Otop(tc_fun(_405288, tc_HOL_Obool)), _405292), c_Set_Oimage(_405288, _405290, _405292, _405294)) = _405294)], (2053 ^ _176355) ^ [_250615, _250617] : [class_Orderings_Otop(_250615), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_250615, _250617), c_Orderings_Otop__class_Otop(_250615))))], (5024 ^ _176355) ^ [_362765, _362767] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362765), _362767))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _362767)), _362765)))], (5431 ^ _176355) ^ [_377303] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _377303)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_377303)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5535 ^ _176355) ^ [_381283, _381285] : [class_Int_Oring__char__0(_381283), hBOOL(hAPP(hAPP(c_member(_381283), _381285), c_Int_Oring__1__class_OInts(_381283))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_381283), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_381283), c_Groups_Oone__class_Oone(_381283)), _381285)), _381285) = c_Groups_Ozero__class_Ozero(_381283)], (4406 ^ _176355) ^ [_340679, _340681, _340683, _340685, _340687, _340689, _340691] : [hBOOL(hAPP(_340679, _340681)), hBOOL(hAPP(hAPP(c_member(tc_prod(_340683, _340683)), hAPP(hAPP(c_Product__Type_OPair(_340683, _340683), _340685), _340687)), hAPP(_340689, _340681))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_340691, _340683), tc_prod(_340691, _340683))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_340691, _340683), tc_prod(_340691, _340683)), hAPP(hAPP(c_Product__Type_OPair(_340691, _340683), _340681), _340685)), hAPP(hAPP(c_Product__Type_OPair(_340691, _340683), _340681), _340687))), c_Recdef_Osame__fst(_340691, _340683, _340679, _340689))))], (3932 ^ _176355) ^ [] : [-(c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))], (1611 ^ _176355) ^ [_233414, _233416] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _233414), _233416) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _233416), _233414))], (6027 ^ _176355) ^ [_402559, _402561, _402563, _402565, _402567] : [hBOOL(hAPP(hAPP(c_member(_402559), _402561), c_Set_Oimage(_402563, _402559, _402565, _402567))), -(hBOOL(hAPP(hAPP(c_member(_402563), hAPP(c_Hilbert__Choice_Oinv__into(_402563, _402559, _402567, _402565), _402561)), _402567)))], (1252 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_P____), c_Arrow__Order__Mirabelle_OProf)))], (1915 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 1913 ^ []), c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))))], (2225 ^ _176355) ^ [_257963, _257965, _257967, _257969] : [class_Orderings_Oord(_257963), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_257963, _257965), _257967)), _257967 = _257969, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_257963, _257965), _257969)))], (2081 ^ _176355) ^ [_252695, _252697, _252699, _252701] : [hBOOL(hAPP(hAPP(c_member(_252695), _252697), _252699)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_252695, tc_HOL_Obool), _252699), _252701)), -(hBOOL(hAPP(hAPP(c_member(_252695), _252697), _252701)))], (5164 ^ _176355) ^ [_367910, _367912] : [hAPP(c_Nat_OSuc, _367910) = hAPP(c_Nat_OSuc, _367912), -(_367910 = _367912)], (5762 ^ _176355) ^ [_390772, _390774, _390776, _390778] : [c_Set_Oimage(_390772, _390774, _390776, c_Orderings_Otop__class_Otop(tc_fun(_390772, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_390774, tc_HOL_Obool)), -(c_Set_Oimage(_390772, _390774, _390776, c_Set_Oimage(_390774, _390772, c_Hilbert__Choice_Oinv__into(_390772, _390774, c_Orderings_Otop__class_Otop(tc_fun(_390772, tc_HOL_Obool)), _390776), _390778)) = _390778)], (5617 ^ _176355) ^ [_384859, _384861, _384863] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_384859, tc_HOL_Obool), tc_fun(_384859, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_384859, tc_HOL_Obool), tc_fun(_384859, tc_HOL_Obool)), _384861), _384863)), c_Wellfounded_Ofinite__psubset(_384859)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_384859, tc_HOL_Obool)), _384861), _384863)), c_Finite__Set_Ofinite(_384859, _384863)], (6369 ^ _176355) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (4504 ^ _176355) ^ [_344159, _344161] : [class_Groups_Omonoid__add(_344159), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_344159), c_Groups_Ozero__class_Ozero(_344159)), _344161) = _344161)], (2267 ^ _176355) ^ [_259335, _259337, _259339] : [class_Orderings_Oorder(_259335), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_259335, _259337), _259339)), 2274 ^ _176355 : [(2275 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_259335, _259339), _259337)), -(_259339 = _259337)], (2281 ^ _176355) ^ [] : [_259339 = _259337, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_259335, _259339), _259337)))]]], (5545 ^ _176355) ^ [_381639, _381641] : [class_Rings_Ocomm__semiring__1(_381639), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_381639), c_Groups_Ozero__class_Ozero(_381639)), _381641) = _381641)], (4662 ^ _176355) ^ [_349468, _349470, _349472] : [class_Groups_Oordered__comm__monoid__add(_349468), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_349468, _349470), c_Groups_Ozero__class_Ozero(_349468))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_349468, _349472), c_Groups_Ozero__class_Ozero(_349468))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_349468, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_349468), _349470), _349472)), c_Groups_Ozero__class_Ozero(_349468))))], (6093 ^ _176355) ^ [_405900, _405902, _405904, _405906, _405908] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_405900, _405902)), _405904), c_FuncSet_OPi(_405900, _405902, _405906, hAPP(c_COMBK(tc_fun(_405902, tc_HOL_Obool), _405900), _405908)))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_405902, tc_HOL_Obool), c_Set_Oimage(_405900, _405902, _405904, _405906)), _405908)))], (6173 ^ _176355) ^ [_408899, _408901] : [-(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _408899, _408901)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _408899), hAPP(c_Nat_OSuc, _408901)))], (6087 ^ _176355) ^ [_405578, _405580, _405582] : [c_Fun_Oinj__on(_405578, _405580, _405582, c_Orderings_Otop__class_Otop(tc_fun(_405578, tc_HOL_Obool))), -(c_Set_Oimage(_405580, _405578, c_Hilbert__Choice_Oinv__into(_405578, _405580, c_Orderings_Otop__class_Otop(tc_fun(_405578, tc_HOL_Obool)), _405582), c_Orderings_Otop__class_Otop(tc_fun(_405580, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_405578, tc_HOL_Obool)))], (2071 ^ _176355) ^ [_252304, _252306, _252308, _252310] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_252304, tc_HOL_Obool), _252306), _252308)), hBOOL(hAPP(hAPP(c_member(_252304), _252310), _252306)), -(hBOOL(hAPP(hAPP(c_member(_252304), _252310), _252308)))], (6045 ^ _176355) ^ [_403480, _403482, _403484, _403486] : [-(hBOOL(hAPP(hAPP(c_member(_403480), hAPP(_403482, _403484)), c_Set_Oimage(_403486, _403480, _403482, c_Orderings_Otop__class_Otop(tc_fun(_403486, tc_HOL_Obool))))))], (6177 ^ _176355) ^ [_409180] : [c_Finite__Set_Ofinite(tc_Nat_Onat, _409180), 6181 ^ _176355 : [(6182 ^ _176355) ^ [_409390] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _409390), _409180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _409390), 6180 ^ [_409180])))]]], (216 ^ _176355) ^ [_183958, _183960] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_183958)), _183960 = _183958, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_183960)], (3602 ^ _176355) ^ [_307714, _307716, _307718, _307720] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_307714, tc_HOL_Obool), _307716), _307718)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_307714, tc_HOL_Obool), _307718), _307720)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_307714, tc_HOL_Obool), _307716), _307720)))], (4374 ^ _176355) ^ [_339345, _339347, _339349, _339351] : [-(c_Finite__Set_Ocard(tc_sum(_339345, _339349), c_Sum__Type_OPlus(_339345, _339349, _339347, _339351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Finite__Set_Ocard(_339345, _339347)), c_Finite__Set_Ocard(_339349, _339351))), c_Finite__Set_Ofinite(_339345, _339347), c_Finite__Set_Ofinite(_339349, _339351)], (6321 ^ _176355) ^ [_414418, _414420] : [class_Orderings_Oorder(_414418), -(class_Orderings_Oorder(tc_fun(_414420, _414418)))], (4798 ^ _176355) ^ [_354152, _354154, _354156] : [class_Groups_Oordered__comm__monoid__add(_354152), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_354152, _354154), c_Groups_Ozero__class_Ozero(_354152))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_354152), _354156), c_Groups_Ozero__class_Ozero(_354152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_354152), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_354152), _354154), _354156)), c_Groups_Ozero__class_Ozero(_354152))))], (4422 ^ _176355) ^ [_341443] : [-(_341443 = 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)), _341443)))], (1398 ^ _176355) ^ [_225308, _225310, _225312] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225308), _225310)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225308), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _225312), _225310))))], (4384 ^ _176355) ^ [_339662, _339664, _339666, _339668] : [4385 ^ _176355 : [(4386 ^ _176355) ^ [] : [-(c_Finite__Set_Ofinite(_339662, _339664))], (4388 ^ _176355) ^ [] : [-(c_Finite__Set_Ofinite(_339666, _339668))]], -(c_Finite__Set_Ocard(tc_sum(_339662, _339666), c_Sum__Type_OPlus(_339662, _339666, _339664, _339668)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1880 ^ _176355) ^ [_243914, _243916, _243918, _243920, _243922] : [class_Groups_Oordered__cancel__ab__semigroup__add(_243914), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_243914, _243916), _243918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_243914), _243920), _243922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_243914), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_243914), _243916), _243920)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_243914), _243918), _243922))))], (2648 ^ _176355) ^ [_272162, _272164, _272166] : [class_Orderings_Olinorder(_272162), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_272162), _272164), _272166))), -(_272164 = _272166), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_272162), _272166), _272164)))], (3690 ^ _176355) ^ [_311482, _311484] : [-(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)), _311482), _311484))], (5112 ^ _176355) ^ [_365869, _365871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _365869)), hAPP(c_Nat_OSuc, _365871))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _365869), _365871)))], (2135 ^ _176355) ^ [_254924, _254926, _254928] : [class_Orderings_Olinorder(_254924), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_254924, _254926), _254928))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_254924, _254928), _254926)))], (1933 ^ _176355) ^ [_245991, _245993, _245995, _245997] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_245991, tc_HOL_Obool), _245993), _245995)), hBOOL(hAPP(hAPP(c_member(_245991), _245997), _245993)), -(hBOOL(hAPP(hAPP(c_member(_245991), _245997), _245995)))], (3793 ^ _176355) ^ [_316184, _316186, _316188, _316190] : [3795 ^ _176355 : [(3796 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_316184), 3794 ^ [_316184, _316186, _316188, _316190]), _316190)))], (3801 ^ _176355) ^ [] : [-(hAPP(_316188, 3794 ^ [_316184, _316186, _316188, _316190]) = hAPP(_316188, 3797 ^ [_316184, _316186, _316188, _316190]))], (3803 ^ _176355) ^ [] : [3794 ^ [_316184, _316186, _316188, _316190] = 3797 ^ [_316184, _316186, _316188, _316190]], (3799 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_316184), 3797 ^ [_316184, _316186, _316188, _316190]), _316190)))]], -(c_Fun_Oinj__on(_316184, _316186, _316188, _316190))], (1947 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), v_F), c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Arrow__Order__Mirabelle_OProf, hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_Arrow__Order__Mirabelle_OLin)))))], (1505 ^ _176355) ^ [_229524, _229526, _229528] : [class_Rings_Olinordered__idom(_229524), -(_229526 = _229528), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_229524), _229526), _229528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_229524), _229528), _229526)))], (3306 ^ _176355) ^ [_295016, _295018, _295020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _295016), _295018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _295016), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _295018), _295020))))], (4310 ^ _176355) ^ [_336717, _336719, _336721, _336723] : [c_Finite__Set_Ofinite(_336717, _336719), c_Finite__Set_Ofinite(_336721, _336723), -(c_Finite__Set_Ofinite(tc_sum(_336717, _336721), c_Sum__Type_OPlus(_336717, _336721, _336719, _336723)))], (6341 ^ _176355) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (3286 ^ _176355) ^ [_294220, _294222, _294224, _294226] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_294220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_294220), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_294220), _294222), _294224)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_294220), _294226), _294224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_294220), _294222), _294226)))], (3333 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), 3329 ^ []), c_Arrow__Order__Mirabelle_OLin)))], (3592 ^ _176355) ^ [_307343, _307345, _307347, _307349] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_307343, tc_HOL_Obool), _307345), _307347)), hBOOL(hAPP(_307345, _307349)), -(hBOOL(hAPP(_307347, _307349)))], (1077 ^ _176355) ^ [_213776] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(v_P____, _213776)))), 1080 ^ _176355 : [(1081 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _213776)), v_n____)))], (1083 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop, hAPP(v_P____, _213776)), v_e____)))]], 1084 ^ _176355 : [(1085 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _213776)), v_n____))], (1087 ^ _176355) ^ [] : [1088 ^ _176355 : [(1089 ^ _176355) ^ [] : [-(hAPP(v_h____, _213776) = v_n____)], (1091 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove, hAPP(v_P____, _213776)), v_c____), v_e____)))]], 1092 ^ _176355 : [(1093 ^ _176355) ^ [] : [hAPP(v_h____, _213776) = v_n____], (1095 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot, hAPP(v_P____, _213776)), v_e____)))]]]]], (5154 ^ _176355) ^ [_367370, _367372] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _367370)), _367372) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _367370), hAPP(c_Nat_OSuc, _367372)))], (2820 ^ _176355) ^ [_278106, _278108, _278110] : [class_Orderings_Olinorder(_278106), 2823 ^ _176355 : [(2824 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_278106), _278108), _278110))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_278106, _278110), _278108)))], (2830 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_278106, _278110), _278108)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_278106), _278108), _278110))]]], (5652 ^ _176355) ^ [_386301, _386303] : [c_Finite__Set_Ofinite(_386301, _386303), -(c_Finite__Set_Ocard(_386301, _386303) = c_Finite__Set_Ofold__image(tc_Nat_Onat, _386301, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _386301), c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _386303))], (3210 ^ _176355) ^ [_291253, _291255, _291257, _291259] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_291253), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_291253, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_291253), _291255), _291257)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_291253), _291255), _291259))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_291253, _291257), _291259)))], (4098 ^ _176355) ^ [_327879, _327881] : [c_Finite__Set_Ofinite(tc_fun(_327879, _327881), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_327879, _327881), tc_HOL_Obool))), -(c_Finite__Set_Ofinite(_327881, c_Orderings_Otop__class_Otop(tc_fun(_327881, tc_HOL_Obool))))], (6069 ^ _176355) ^ [_404676, _404678, _404680] : [c_Set_Oimage(_404676, _404678, _404680, c_Orderings_Otop__class_Otop(tc_fun(_404676, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_404678, tc_HOL_Obool)), -(c_Fun_Oinj__on(_404678, _404676, c_Hilbert__Choice_Oinv__into(_404676, _404678, c_Orderings_Otop__class_Otop(tc_fun(_404676, tc_HOL_Obool)), _404680), c_Orderings_Otop__class_Otop(tc_fun(_404678, tc_HOL_Obool))))], (2968 ^ _176355) ^ [_282896, _282898, _282900] : [class_Orderings_Oorder(_282896), -(_282898 = _282900), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_282896, _282898), _282900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_282896), _282898), _282900)))], (2884 ^ _176355) ^ [_280194, _280196, _280198] : [class_Orderings_Opreorder(_280194), 2887 ^ _176355 : [(2888 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_280194), _280196), _280198)), 2891 ^ _176355 : [(2892 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_280194, _280196), _280198)))], (2894 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_280194, _280198), _280196))]]], (2896 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_280194), _280196), _280198))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_280194, _280196), _280198)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_280194, _280198), _280196)))]]], (3338 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), 3334 ^ []), c_Arrow__Order__Mirabelle_OLin)))], (1246 ^ _176355) ^ [_219660, _219662, _219664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _219660), _219662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _219660), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _219662), _219664))))], (1416 ^ _176355) ^ [_226073, _226075, _226077] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226075), _226077)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _226073), _226075)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _226073), _226077))))], (4498 ^ _176355) ^ [_343948] : [class_Rings_Ozero__neq__one(_343948), c_Groups_Ozero__class_Ozero(_343948) = c_Groups_Oone__class_Oone(_343948)], (2183 ^ _176355) ^ [_256595, _256597, _256599, _256601] : [class_Orderings_Opreorder(_256595), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_256595, _256597), _256599)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_256595, _256599), _256601)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_256595, _256597), _256601)))], (2329 ^ _176355) ^ [_261361, _261363, _261365] : [class_Orderings_Olinorder(_261361), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_261361, _261363), _261365))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_261361, _261365), _261363)))], (4242 ^ _176355) ^ [_334167, _334169, _334171, _334173] : [hBOOL(hAPP(hAPP(c_member(_334167), _334169), c_Set_Oinsert(_334167, _334171, _334173))), -(_334169 = _334171), -(hBOOL(hAPP(hAPP(c_member(_334167), _334169), _334173)))], (5296 ^ _176355) ^ [_372354, _372356] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _372354), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _372356), _372354)))))], (4532 ^ _176355) ^ [_345109, _345111] : [class_Groups_Omonoid__add(_345109), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_345109), _345111), c_Groups_Ozero__class_Ozero(_345109)) = _345111)], (4252 ^ _176355) ^ [_334475, _334477, _334479, _334481] : [4253 ^ _176355 : [(4254 ^ _176355) ^ [] : [_334477 = _334479], (4256 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_334475), _334477), _334481))]], -(hBOOL(hAPP(hAPP(c_member(_334475), _334477), c_Set_Oinsert(_334475, _334479, _334481))))], (4020 ^ _176355) ^ [] : [-(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))], (3809 ^ _176355) ^ [_317086, _317088] : [c_Arrow__Order__Mirabelle_Odictator(_317086, _317088), 3812 ^ _176355 : [(3813 ^ _176355) ^ [_317234] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _317234), c_Arrow__Order__Mirabelle_OProf)), -(hAPP(_317086, _317234) = hAPP(_317234, _317088))]]], (4448 ^ _176355) ^ [_342288] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _342288) = _342288)], (5682 ^ _176355) ^ [_387437, _387439] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387437), _387439)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _387437)), _387439)))], (724 ^ _176355) ^ [_201447, _201449] : [_201449 = _201447, -(tc_Option_Ooption(_201449) = tc_Option_Ooption(_201447))], (6417 ^ _176355) ^ [_417279, _417281, _417283, _417285] : [-(hAPP(hAPP(c_COMBK(_417279, _417281), _417283), _417285) = _417283)], (3730 ^ _176355) ^ [_313422, _313424] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _313422), c_FuncSet_OPi(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Arrow__Order__Mirabelle_OProf, hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_Arrow__Order__Mirabelle_OLin)))), 3736 ^ _176355 : [(3737 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), 3735 ^ [_313422, _313424]), c_Arrow__Order__Mirabelle_OProf)))], (3743 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3738 ^ [_313422, _313424]), 3739 ^ [_313422, _313424])), hAPP(3735 ^ [_313422, _313424], _313424))))], (3745 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3738 ^ [_313422, _313424]), 3739 ^ [_313422, _313424])), hAPP(_313422, 3735 ^ [_313422, _313424])))], (3741 ^ _176355) ^ [] : [3738 ^ [_313422, _313424] = 3739 ^ [_313422, _313424]]], -(c_Arrow__Order__Mirabelle_Odictator(_313422, _313424))], (4604 ^ _176355) ^ [_347576, _347578, _347580] : [class_Groups_Oordered__comm__monoid__add(_347576), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_347576, c_Groups_Ozero__class_Ozero(_347576)), _347578)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_347576, c_Groups_Ozero__class_Ozero(_347576)), _347580)), 4615 ^ _176355 : [(4616 ^ _176355) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_347576), _347578), _347580) = c_Groups_Ozero__class_Ozero(_347576), 4619 ^ _176355 : [(4620 ^ _176355) ^ [] : [-(_347578 = c_Groups_Ozero__class_Ozero(_347576))], (4622 ^ _176355) ^ [] : [-(_347580 = c_Groups_Ozero__class_Ozero(_347576))]]], (4624 ^ _176355) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_347576), _347578), _347580) = c_Groups_Ozero__class_Ozero(_347576)), _347578 = c_Groups_Ozero__class_Ozero(_347576), _347580 = c_Groups_Ozero__class_Ozero(_347576)]]], (6347 ^ _176355) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (6289 ^ _176355) ^ [_413335, _413337, _413339, _413341, _413343] : [class_Orderings_Olinorder(_413335), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_413335, tc_HOL_Obool), c_SetInterval_Oord__class_OatLeastLessThan(_413335, _413337, _413339)), c_SetInterval_Oord__class_OatLeastLessThan(_413335, _413341, _413343))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_413335, _413339), _413337))), 6300 ^ _176355 : [(6301 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_413335, _413341), _413337)))], (6303 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_413335, _413339), _413343)))]]], (246 ^ _176355) ^ [_184843, _184845] : [-(class_Groups_Oordered__ab__semigroup__add(_184843)), _184845 = _184843, class_Groups_Oordered__ab__semigroup__add(_184845)], (5720 ^ _176355) ^ [_389090, _389092, _389094, _389096] : [c_Finite__Set_Ofinite(_389090, c_Set_Oimage(_389092, _389090, _389094, _389096)), c_Fun_Oinj__on(_389092, _389090, _389094, _389096), -(c_Finite__Set_Ofinite(_389092, _389096))], (504 ^ _176355) ^ [_193175, _193177] : [_193177 = _193175, -(c_Nat_Onat_Onat__size(_193177) = c_Nat_Onat_Onat__size(_193175))], (6425 ^ _176355) ^ [_417929, _417931] : [hBOOL(hAPP(hAPP(c_fequal, _417929), _417931)), -(_417929 = _417931)], (5509 ^ _176355) ^ [_380458] : [class_Rings_Oring__1(_380458), -(hBOOL(hAPP(hAPP(c_member(_380458), c_Groups_Oone__class_Oone(_380458)), c_Int_Oring__1__class_OInts(_380458))))], (2392 ^ _176355) ^ [_263651, _263653, _263655] : [class_Orderings_Olinorder(_263651), 2395 ^ _176355 : [(2406 ^ _176355) ^ [] : [2407 ^ _176355 : [(2408 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_263651), _263653), _263655))], (2410 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_263651), _263655), _263653))]], _263653 = _263655], (2396 ^ _176355) ^ [] : [-(_263653 = _263655), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_263651), _263653), _263655))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_263651), _263655), _263653)))]]], (5803 ^ _176355) ^ [_393064, _393066, _393068, _393070, _393072] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_393064, tc_HOL_Obool), _393066), c_Set_Oimage(_393068, _393064, _393070, _393072))), 5807 ^ _176355 : [(5808 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_393068, tc_HOL_Obool), 5806 ^ [_393064, _393066, _393068, _393070, _393072]), _393072)))], (5810 ^ _176355) ^ [] : [-(_393066 = c_Set_Oimage(_393068, _393064, _393070, 5806 ^ [_393064, _393066, _393068, _393070, _393072]))]]], (714 ^ _176355) ^ [_201116, _201118, _201120, _201122] : [-(tc_sum(_201122, _201118) = tc_sum(_201120, _201116)), _201122 = _201120, _201118 = _201116], (4152 ^ _176355) ^ [_330126, _330128, _330130, _330132] : [4153 ^ _176355 : [(4154 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_330126), _330128), _330130))], (4156 ^ _176355) ^ [] : [_330128 = _330132]], -(hBOOL(hAPP(hAPP(c_member(_330126), _330128), c_Set_Oinsert(_330126, _330132, _330130))))], (1282 ^ _176355) ^ [_220954, _220956] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _220954), _220956)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _220956), _220954)), -(_220954 = _220956)], (5381 ^ _176355) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1039 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(v_F, v_P____))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(v_F, c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), v_n____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Omktop), v_P____)), v_e____)), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_fequal), v_h____)), v_n____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Oabove), v_P____)), v_c____)), v_e____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Omkbot), v_P____)), v_e____)))))))], (4240 ^ _176355) ^ [_333988, _333990, _333992] : [-(hBOOL(hAPP(hAPP(c_member(_333988), _333990), c_Set_Oinsert(_333988, _333990, _333992))))], (4138 ^ _176355) ^ [_329574, _329576, _329578, _329580, _329582, _329584, _329586, _329588] : [c_Finite__Set_Ofolding__image__simple__idem(_329574, _329576, _329578, _329580, _329582, _329584), c_Finite__Set_Ofinite(_329576, _329586), hBOOL(hAPP(hAPP(c_member(_329576), _329588), _329586)), -(hAPP(hAPP(_329578, hAPP(_329582, _329588)), hAPP(_329584, _329586)) = hAPP(_329584, _329586))], (426 ^ _176355) ^ [_190133, _190135] : [-(hBOOL(_190133)), _190135 = _190133, hBOOL(_190135)], (3036 ^ _176355) ^ [_285083, _285085, _285087] : [class_Orderings_Oorder(_285083), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_285083, _285085), _285087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_285083), _285085), _285087))), -(_285085 = _285087)], (985 ^ _176355) ^ [_210817, _210819, _210821, _210823] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _210817), _210819)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot, _210821), _210823)))), -(_210819 = _210823), 992 ^ _176355 : [(993 ^ _176355) ^ [] : [-(_210817 = _210823)], (995 ^ _176355) ^ [] : [-(_210817 = _210819)]], 996 ^ _176355 : [(997 ^ _176355) ^ [] : [_210817 = _210823], (999 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _210817), _210819)), _210821))]]], (5787 ^ _176355) ^ [_392081, _392083, _392085, _392087, _392089] : [c_Fun_Oinj__on(_392081, _392083, _392085, _392087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_392081, tc_HOL_Obool)), _392089), _392087)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_392083, tc_HOL_Obool)), c_Set_Oimage(_392081, _392083, _392085, _392089)), c_Set_Oimage(_392081, _392083, _392085, _392087))))], (80 ^ _176355) ^ [_179284, _179286, _179288, _179290, _179292, _179294, _179296, _179298, _179300, _179302, _179304, _179306] : [-(c_Finite__Set_Ofolding__image__simple__idem(_179304, _179300, _179296, _179292, _179288, _179284)), c_Finite__Set_Ofolding__image__simple__idem(_179306, _179302, _179298, _179294, _179290, _179286), _179306 = _179304, _179302 = _179300, _179298 = _179296, _179294 = _179292, _179290 = _179288, _179286 = _179284], (4022 ^ _176355) ^ [_325251, _325253, _325255] : [c_Finite__Set_Ofinite(_325251, _325253), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_325251, tc_HOL_Obool), _325255), _325253)), -(c_Finite__Set_Ofinite(_325251, _325255))], (1230 ^ _176355) ^ [_218905, _218907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _218905), _218907)), _218905))], (5435 ^ _176355) ^ [_377533, _377535, _377537, _377539] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_377533, _377533)), hAPP(hAPP(c_Product__Type_OPair(_377533, _377533), _377535), _377537)), c_Wellfounded_Omeasure(_377533, _377539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_377539, _377535)), hAPP(_377539, _377537))))], (6311 ^ _176355) ^ [_414119, _414121] : [-(class_Finite__Set_Ofinite(tc_fun(_414119, _414121))), class_Finite__Set_Ofinite(_414119), class_Finite__Set_Ofinite(_414121)], (5383 ^ _176355) ^ [_375615] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _375615) = c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _375615)))], (326 ^ _176355) ^ [_187203, _187205] : [-(class_Rings_Ozero__neq__one(_187203)), _187205 = _187203, class_Rings_Ozero__neq__one(_187205)], (5305 ^ _176355) ^ [_372762, _372764] : [5306 ^ _176355 : [(5307 ^ _176355) ^ [_372846] : [_372764 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _372762), _372846))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _372762), _372764)))], (6142 ^ _176355) ^ [] : [-(c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, 6138 ^ [], c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))))], (1258 ^ _176355) ^ [_220038] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _220038), _220038)))], (5369 ^ _176355) ^ [_375165, _375167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _375165), _375167)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _375165)), _375167)))], (236 ^ _176355) ^ [_184548, _184550] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_184548)), _184550 = _184548, class_Groups_Oordered__ab__semigroup__add__imp__le(_184550)], (6421 ^ _176355) ^ [_417617, _417619, _417621, _417623, _417625, _417627] : [-(hAPP(hAPP(hAPP(c_COMBC(_417617, _417619, _417621), _417623), _417625), _417627) = hAPP(hAPP(_417623, _417627), _417625))], (4204 ^ _176355) ^ [_332380, _332382, _332384, _332386] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_332380, tc_HOL_Obool), _332382), _332384)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_332380, tc_HOL_Obool), c_Set_Oinsert(_332380, _332386, _332382)), c_Set_Oinsert(_332380, _332386, _332384))))], (202 ^ _176355) ^ [_183542, _183544, _183546, _183548] : [-(c_Finite__Set_Ofinite(_183546, _183542)), c_Finite__Set_Ofinite(_183548, _183544), _183548 = _183546, _183544 = _183542], (3914 ^ _176355) ^ [_321061, _321063, _321065, _321067, _321069] : [3916 ^ _176355 : [(3917 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_321061), 3915 ^ [_321061, _321063, _321065, _321067, _321069]), _321063)))], (3919 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_321065, tc_HOL_Obool), hAPP(_321067, 3915 ^ [_321061, _321063, _321065, _321067, _321069])), hAPP(_321069, 3915 ^ [_321061, _321063, _321065, _321067, _321069])))]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_321061, _321065), tc_HOL_Obool), c_FuncSet_OPi(_321061, _321065, _321063, _321067)), c_FuncSet_OPi(_321061, _321065, _321063, _321069))))], (2862 ^ _176355) ^ [_279504, _279506, _279508] : [class_Orderings_Oorder(_279504), 2865 ^ _176355 : [(2866 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_279504), _279506), _279508)), 2869 ^ _176355 : [(2870 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_279504, _279506), _279508)))], (2872 ^ _176355) ^ [] : [_279506 = _279508]]], (2874 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_279504), _279506), _279508))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_279504, _279506), _279508)), -(_279506 = _279508)]]], (3692 ^ _176355) ^ [] : [-(c_Arrow__Order__Mirabelle_OProf = c_FuncSet_OPi(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), hAPP(c_COMBK(tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi), c_Arrow__Order__Mirabelle_OLin)))], (5768 ^ _176355) ^ [_391092, _391094, _391096, _391098] : [c_Set_Oimage(_391092, _391094, _391096, c_Orderings_Otop__class_Otop(tc_fun(_391092, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_391094, tc_HOL_Obool)), -(hAPP(_391096, hAPP(c_Hilbert__Choice_Oinv__into(_391092, _391094, c_Orderings_Otop__class_Otop(tc_fun(_391092, tc_HOL_Obool)), _391096), _391098)) = _391098)], (4854 ^ _176355) ^ [_356112, _356114, _356116] : [class_Groups_Oordered__comm__monoid__add(_356112), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_356112, c_Groups_Ozero__class_Ozero(_356112)), _356114)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_356112), c_Groups_Ozero__class_Ozero(_356112)), _356116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_356112), c_Groups_Ozero__class_Ozero(_356112)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_356112), _356114), _356116))))], (4434 ^ _176355) ^ [_341787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _341787), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6208 ^ _176355) ^ [_410413] : [6210 ^ _176355 : [(6211 ^ _176355) ^ [_410582] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 6209 ^ [_410413, _410582]), _410413)))], (6213 ^ _176355) ^ [_410639] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 6209 ^ [_410413, _410639]), _410639))]], -(c_Finite__Set_Ofinite(tc_Nat_Onat, _410413))], (6265 ^ _176355) ^ [_412448, _412450, _412452, _412454, _412456] : [class_Orderings_Olinorder(_412448), c_SetInterval_Oord__class_OatLeastLessThan(_412448, _412450, _412452) = c_SetInterval_Oord__class_OatLeastLessThan(_412448, _412454, _412456), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_412448), _412450), _412452)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_412448), _412454), _412456)), -(_412452 = _412456)], (6365 ^ _176355) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (5000 ^ _176355) ^ [_361861, _361863] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361861), _361863)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _361861)), hAPP(c_Nat_OSuc, _361863))))], (4784 ^ _176355) ^ [_353609, _353611] : [4785 ^ _176355 : [(4786 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _353609))], (4788 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _353611))]], -(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), _353609), _353611))))], (4216 ^ _176355) ^ [_332939, _332941, _332943] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_332939, tc_HOL_Obool), _332941), c_Set_Oinsert(_332939, _332943, _332941))))], (4070 ^ _176355) ^ [_326922] : [c_Finite__Set_Ofinite(tc_Option_Ooption(_326922), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_326922), tc_HOL_Obool))), -(c_Finite__Set_Ofinite(_326922, c_Orderings_Otop__class_Otop(tc_fun(_326922, tc_HOL_Obool))))], (3900 ^ _176355) ^ [_320515, _320517, _320519, _320521, _320523] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_320515, _320517)), _320519), c_FuncSet_OPi(_320515, _320517, _320521, hAPP(c_COMBK(tc_fun(_320517, tc_HOL_Obool), _320515), _320523)))), c_Fun_Oinj__on(_320515, _320517, _320519, _320521), c_Finite__Set_Ofinite(_320517, _320523), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Finite__Set_Ocard(_320515, _320521)), c_Finite__Set_Ocard(_320517, _320523))))], (2684 ^ _176355) ^ [_273502, _273504, _273506, _273508] : [class_Groups_Ocancel__semigroup__add(_273502), 2687 ^ _176355 : [(2688 ^ _176355) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_273502), _273504), _273506) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_273502), _273508), _273506), -(_273504 = _273508)], (2694 ^ _176355) ^ [] : [_273504 = _273508, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_273502), _273504), _273506) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_273502), _273508), _273506))]]], (336 ^ _176355) ^ [_187498, _187500] : [-(class_Orderings_Olinorder(_187498)), _187500 = _187498, class_Orderings_Olinorder(_187500)], (4104 ^ _176355) ^ [_328149, _328151, _328153, _328155] : [c_Finite__Set_Ofinite(_328149, _328151), c_Finite__Set_Ofinite(_328153, _328155), -(c_Finite__Set_Ocard(tc_sum(_328149, _328153), c_Sum__Type_OPlus(_328149, _328153, _328151, _328155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Finite__Set_Ocard(_328149, _328151)), c_Finite__Set_Ocard(_328153, _328155)))], (1429 ^ _176355) ^ [_226611, _226613] : [1430 ^ _176355 : [(1431 ^ _176355) ^ [_226692] : [_226613 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _226611), _226692)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226611), _226613)))], (5248 ^ _176355) ^ [_370866, _370868] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _370866), _370868)), 5249 ^ _176355 : [(5250 ^ _176355) ^ [] : [_370866 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _370868 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5256 ^ _176355) ^ [] : [_370866 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _370868 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (1439 ^ _176355) ^ [_227105, _227107, _227109, _227111] : [_227105 = _227107, hBOOL(hAPP(hAPP(c_member(_227109), _227107), _227111)), -(hBOOL(hAPP(hAPP(c_member(_227109), _227105), _227111)))], (3749 ^ _176355) ^ [_314477, _314479, _314481, _314483, _314485] : [c_Fun_Oinj__on(_314477, _314479, _314481, c_Orderings_Otop__class_Otop(tc_fun(_314477, tc_HOL_Obool))), 3752 ^ _176355 : [(3753 ^ _176355) ^ [] : [hAPP(_314481, _314483) = hAPP(_314481, _314485), -(_314483 = _314485)], (3759 ^ _176355) ^ [] : [_314483 = _314485, -(hAPP(_314481, _314483) = hAPP(_314481, _314485))]]], (4718 ^ _176355) ^ [_351398, _351400] : [class_Groups_Olinordered__ab__group__add(_351398), 4721 ^ _176355 : [(4722 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_351398), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_351398), _351400), _351400)), c_Groups_Ozero__class_Ozero(_351398))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_351398), _351400), c_Groups_Ozero__class_Ozero(_351398))))], (4728 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_351398), _351400), c_Groups_Ozero__class_Ozero(_351398))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_351398), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_351398), _351400), _351400)), c_Groups_Ozero__class_Ozero(_351398))))]]], (1953 ^ _176355) ^ [_246817, _246819, _246821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_246817, tc_HOL_Obool)), _246819), _246821)), 1956 ^ _176355 : [(1957 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_246817, tc_HOL_Obool), _246819), _246821)))], (1959 ^ _176355) ^ [] : [_246819 = _246821]]], (1499 ^ _176355) ^ [_229274, _229276, _229278] : [hBOOL(hAPP(_229278, _229276)), -(hBOOL(hAPP(hAPP(c_member(_229274), _229276), _229278)))], (2504 ^ _176355) ^ [_267242, _267244, _267246] : [class_Orderings_Opreorder(_267242), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_267242), _267244), _267246)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_267242), _267246), _267244))], (6383 ^ _176355) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (5710 ^ _176355) ^ [_388707, _388709, _388711, _388713, _388715] : [c_Finite__Set_Ofinite(_388707, _388709), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_388711, tc_HOL_Obool), _388713), c_Set_Oimage(_388707, _388711, _388715, _388709))), -(c_Finite__Set_Ofinite(_388711, _388713))], (4962 ^ _176355) ^ [_360402] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _360402)], (2436 ^ _176355) ^ [_265043, _265045, _265047] : [class_Orderings_Olinorder(_265043), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_265043), _265045), _265047))), -(_265045 = _265047), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_265043), _265047), _265045)))], (5569 ^ _176355) ^ [_382695, _382697, _382699, _382701] : [class_Rings_Ocomm__semiring__1(_382695), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_382695), _382697), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_382695), _382699), _382701)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_382695), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_382695), _382697), _382699)), _382701))], (2554 ^ _176355) ^ [_268978, _268980, _268982, _268984] : [class_Orderings_Oord(_268978), _268980 = _268982, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_268978), _268982), _268984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_268978), _268980), _268984)))], (2129 ^ _176355) ^ [_254668, _254670] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), _254668), c_Arrow__Order__Mirabelle_OLin)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop, _254668), _254670)), c_Arrow__Order__Mirabelle_OLin)))], (4186 ^ _176355) ^ [_331620, _331622, _331624] : [c_Finite__Set_Ofinite(_331620, c_Set_Oinsert(_331620, _331622, _331624)), -(c_Finite__Set_Ofinite(_331620, _331624))], (6075 ^ _176355) ^ [_404984, _404986, _404988, _404990] : [c_Fun_Oinj__on(_404984, _404986, _404988, c_Orderings_Otop__class_Otop(tc_fun(_404984, tc_HOL_Obool))), -(c_Set_Oimage(_404986, _404984, c_Hilbert__Choice_Oinv__into(_404984, _404986, c_Orderings_Otop__class_Otop(tc_fun(_404984, tc_HOL_Obool)), _404988), c_Set_Oimage(_404984, _404986, _404988, _404990)) = _404990)], (486 ^ _176355) ^ [_192570, _192572, _192574, _192576, _192578, _192580, _192582, _192584] : [-(c_Wellfounded_Olex__prod(_192584, _192580, _192576, _192572) = c_Wellfounded_Olex__prod(_192582, _192578, _192574, _192570)), _192584 = _192582, _192580 = _192578, _192576 = _192574, _192572 = _192570], (1631 ^ _176355) ^ [_234374, _234376, _234378, _234380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _234374), _234376)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _234378), _234376) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _234374), _234380), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _234378), _234380)))], (2047 ^ _176355) ^ [_250381, _250383, _250385] : [class_Orderings_Otop(_250381), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_250383, _250381)), _250385) = c_Orderings_Otop__class_Otop(_250381))], (5658 ^ _176355) ^ [_386495, _386497] : [-(c_Finite__Set_Ofinite(_386495, _386497)), -(c_Finite__Set_Ocard(_386495, _386497) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (680 ^ _176355) ^ [_199882, _199884, _199886, _199888] : [-(c_Finite__Set_Ocard(_199888, _199884) = c_Finite__Set_Ocard(_199886, _199882)), _199888 = _199886, _199884 = _199882], (4014 ^ _176355) ^ [_324976, _324978] : [class_Finite__Set_Ofinite(_324976), -(c_Finite__Set_Ofinite(_324976, _324978))], (4416 ^ _176355) ^ [_341154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _341154), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5080 ^ _176355) ^ [_364779, _364781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _364779), _364781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _364779), hAPP(c_Nat_OSuc, _364781))))], (6327 ^ _176355) ^ [_414630, _414632] : [class_Orderings_Otop(_414630), -(class_Orderings_Otop(tc_fun(_414632, _414630)))], (2376 ^ _176355) ^ [_263050, _263052, _263054] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), _263050), c_Arrow__Order__Mirabelle_OLin)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _263052), _263054)), _263050)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _263054), _263052)), _263050))], (4676 ^ _176355) ^ [_349954, _349956, _349958, _349960] : [class_Rings_Olinordered__semidom(_349954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_349954), c_Groups_Ozero__class_Ozero(_349954)), _349956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_349954), _349958), _349960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_349954), _349958), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_349954), _349956), _349960))))], (1917 ^ _176355) ^ [_245351] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _245351), 1913 ^ [])), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_b____), v_a____)), hAPP(v_F, hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), _245351))), v_Lab____)), v_Lba____)))))], (3984 ^ _176355) ^ [_323967, _323969, _323971] : [c_Finite__Set_Ofinite(_323967, _323969), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_323967, tc_HOL_Obool), _323971), _323969)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Finite__Set_Ocard(_323967, _323971)), c_Finite__Set_Ocard(_323967, _323969))))], (3236 ^ _176355) ^ [_292258, _292260, _292262, _292264] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_292258), 3239 ^ _176355 : [(3240 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_292258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_292258), _292260), _292262)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_292258), _292260), _292264))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_292258), _292262), _292264)))], (3246 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_292258), _292262), _292264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_292258), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_292258), _292260), _292262)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_292258), _292260), _292264))))]]], (4492 ^ _176355) ^ [_343751] : [class_Rings_Ozero__neq__one(_343751), c_Groups_Oone__class_Oone(_343751) = c_Groups_Ozero__class_Ozero(_343751)], (3318 ^ _176355) ^ [_295526, _295528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _295526), _295528)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _295526), _295528)))], (6379 ^ _176355) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (1234 ^ _176355) ^ [_219172, _219174, _219176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _219172), _219174)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _219172), _219176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _219174), _219176)))], (544 ^ _176355) ^ [_194627, _194629] : [_194629 = _194627, -(c_Int_Oring__1__class_OInts(_194629) = c_Int_Oring__1__class_OInts(_194627))], (5298 ^ _176355) ^ [_372506, _372508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _372506), _372508)), -(_372508 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _372506), 5301 ^ [_372506, _372508])))], (346 ^ _176355) ^ [_187793, _187795] : [-(class_Groups_Omonoid__add(_187793)), _187795 = _187793, class_Groups_Omonoid__add(_187795)], (5184 ^ _176355) ^ [_368639, _368641] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _368639), hAPP(c_Nat_OSuc, _368641))), -(_368639 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5192 ^ _176355 : [(5193 ^ _176355) ^ [] : [-(_368639 = hAPP(c_Nat_OSuc, 5191 ^ [_368639, _368641]))], (5195 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 5191 ^ [_368639, _368641]), _368641)))]]], (5627 ^ _176355) ^ [_385256, _385258] : [-(hBOOL(hAPP(_385256, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_385256, _385258)), 5635 ^ _176355 : [(5638 ^ _176355) ^ [_385716] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _385716), 5634 ^ [_385256, _385258])), hBOOL(hAPP(_385256, _385716))], (5644 ^ _176355) ^ [] : [-(hBOOL(hAPP(_385256, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 5634 ^ [_385256, _385258]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (5636 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 5634 ^ [_385256, _385258]), _385258)))]]], (4978 ^ _176355) ^ [_361068, _361070] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361068), hAPP(c_Nat_OSuc, _361070))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361068), _361070))), -(_361068 = hAPP(c_Nat_OSuc, _361070))], (3336 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_b____), v_a____)), 3334 ^ [])))], (4198 ^ _176355) ^ [_332092, _332094, _332096, _332098, _332100, _332102, _332104] : [c_Finite__Set_Ofolding__image__simple__idem(_332092, _332094, _332096, _332098, _332100, _332102), -(hAPP(hAPP(_332096, _332104), _332104) = _332104)], (1878 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(v_P____, hAPP(c_Hilbert__Choice_Oinv__into(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), v_h____), v_n____)))))], (4452 ^ _176355) ^ [_342511, _342513] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _342511), _342513) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 4455 ^ _176355 : [(4456 ^ _176355) ^ [] : [-(_342511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4458 ^ _176355) ^ [] : [-(_342513 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2239 ^ _176355) ^ [_258425, _258427, _258429, _258431] : [class_Orderings_Oorder(_258425), _258427 = _258429, hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_258425, _258431), _258429)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_258425, _258431), _258427)))], (5170 ^ _176355) ^ [_368084, _368086] : [_368084 = _368086, -(hAPP(c_Nat_OSuc, _368084) = hAPP(c_Nat_OSuc, _368086))], (3092 ^ _176355) ^ [_286898, _286900, _286902, _286904] : [class_Orderings_Oorder(_286898), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_286898), _286900), _286902)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_286898, _286904), _286900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_286898), _286904), _286902)))], (5994 ^ _176355) ^ [_401074, _401076, _401078, _401080, _401082] : [hBOOL(hAPP(hAPP(c_member(_401074), _401076), c_Set_Oimage(_401078, _401074, _401080, _401082))), 5998 ^ _176355 : [(5999 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_401078), 5997 ^ [_401074, _401076, _401078, _401080, _401082]), _401082)))], (6001 ^ _176355) ^ [] : [-(_401076 = hAPP(_401080, 5997 ^ [_401074, _401076, _401078, _401080, _401082]))]]], (2101 ^ _176355) ^ [_253492, _253494, _253496] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_253492, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_253492, tc_fun(_253492, tc_HOL_Obool), tc_HOL_Obool), c_member(_253492)), _253494)), hAPP(hAPP(c_COMBC(_253492, tc_fun(_253492, tc_HOL_Obool), tc_HOL_Obool), c_member(_253492)), _253496))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_253492, tc_HOL_Obool), _253494), _253496)))], (3150 ^ _176355) ^ [_288934, _288936, _288938, _288940] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_288934), 3153 ^ _176355 : [(3154 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_288934, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_288934), _288936), _288938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_288934), _288936), _288940))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_288934, _288938), _288940)))], (3160 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_288934, _288938), _288940)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_288934, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_288934), _288936), _288938)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_288934), _288936), _288940))))]]], (6361 ^ _176355) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (4960 ^ _176355) ^ [_360322] : [hAPP(c_Nat_OSuc, _360322) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1099 ^ _176355) ^ [_214543] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), _214543))), v_Lab____)), v_Lba____)), c_Arrow__Order__Mirabelle_OProf)))], (6175 ^ _176355) ^ [_409026, _409028, _409030] : [-(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)), _409026), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _409028, _409030)) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _409028), _409026), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _409030), _409026)))], (6413 ^ _176355) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (893 ^ _176355) ^ [_207803] : [896 ^ _176355 : [(897 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _207803)), v_n____)))], (899 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_e____)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop, hAPP(v_P____, _207803)), v_e____)))]], 900 ^ _176355 : [(901 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _207803)), v_n____))], (903 ^ _176355) ^ [] : [904 ^ _176355 : [(905 ^ _176355) ^ [] : [-(hAPP(v_h____, _207803) = v_n____)], (907 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_e____)), hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove, hAPP(v_P____, _207803)), v_c____), v_e____)))]], 908 ^ _176355 : [(909 ^ _176355) ^ [] : [hAPP(v_h____, _207803) = v_n____], (911 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_e____)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot, hAPP(v_P____, _207803)), v_e____)))]]]], 912 ^ _176355 : [(913 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _207803)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), v_n____), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), v_Lab____)))], (919 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _207803)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), v_n____), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), v_Lba____)))]]], (3469 ^ _176355) ^ [_301486] : [c_Arrow__Order__Mirabelle_OIIA(_301486), 3472 ^ _176355 : [(3473 ^ _176355) ^ [_301727] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _301727), c_Arrow__Order__Mirabelle_OProf)), 3476 ^ _176355 : [(3477 ^ _176355) ^ [_301970] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _301970), c_Arrow__Order__Mirabelle_OProf)), 3480 ^ _176355 : [(3481 ^ _176355) ^ [_302217, _302219] : [3485 ^ _176355 : [(3486 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _302219), _302217)), hAPP(_301727, 3482 ^ [_301486, _301727, _301970, _302217, _302219]))))], (3488 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _302219), _302217)), hAPP(_301970, 3482 ^ [_301486, _301727, _301970, _302217, _302219])))]], 3489 ^ _176355 : [(3490 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _302219), _302217)), hAPP(_301970, 3482 ^ [_301486, _301727, _301970, _302217, _302219]))))], (3492 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _302219), _302217)), hAPP(_301727, 3482 ^ [_301486, _301727, _301970, _302217, _302219])))]], 3493 ^ _176355 : [(3494 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _302219), _302217)), hAPP(_301486, _301727))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _302219), _302217)), hAPP(_301486, _301970))))], (3500 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _302219), _302217)), hAPP(_301486, _301970))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _302219), _302217)), hAPP(_301486, _301727))))]]]]]]]]], (5427 ^ _176355) ^ [_377132] : [-(hAPP(c_Nat_OSuc, _377132) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _377132), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (2996 ^ _176355) ^ [_283778, _283780, _283782] : [class_Orderings_Olinorder(_283778), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_283778, _283780), _283782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_283778), _283782), _283780))], (4348 ^ _176355) ^ [_338238, _338240, _338242, _338244] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_338238, tc_HOL_Obool), c_Set_Oinsert(_338238, _338240, _338242)), _338244)), 4351 ^ _176355 : [(4352 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_338238), _338240), _338244)))], (4354 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_338238, tc_HOL_Obool), _338242), _338244)))]]], (6343 ^ _176355) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (5575 ^ _176355) ^ [_383007, _383009, _383011, _383013] : [class_Rings_Ocomm__semiring__1(_383007), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383007), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383007), _383009), _383011)), _383013) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383007), _383009), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383007), _383011), _383013)))], (556 ^ _176355) ^ [_195203, _195205, _195207, _195209, _195211, _195213, _195215, _195217, _195219, _195221, _195223, _195225] : [-(c_Finite__Set_Ofold__image(_195225, _195221, _195217, _195213, _195209, _195205) = c_Finite__Set_Ofold__image(_195223, _195219, _195215, _195211, _195207, _195203)), _195225 = _195223, _195221 = _195219, _195217 = _195215, _195213 = _195211, _195209 = _195207, _195205 = _195203], (1943 ^ _176355) ^ [_246339, _246341] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_246339, tc_HOL_Obool)), _246341)))], (6171 ^ _176355) ^ [_408801, _408803] : [-(c_Finite__Set_Ofinite(tc_Nat_Onat, c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _408801, _408803)))], (814 ^ _176355) ^ [_204874, _204876, _204878, _204880, _204882, _204884, _204886, _204888] : [-(c_COMBB(_204888, _204884, _204880, _204876) = c_COMBB(_204886, _204882, _204878, _204874)), _204888 = _204886, _204884 = _204882, _204880 = _204878, _204876 = _204874], (5050 ^ _176355) ^ [_363758, _363760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _363758), hAPP(c_Nat_OSuc, _363760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _363758), _363760))), -(_363758 = _363760)], (396 ^ _176355) ^ [_189268, _189270] : [-(class_Orderings_Otop(_189268)), _189270 = _189268, class_Orderings_Otop(_189270)], (1657 ^ _176355) ^ [_235426, _235428, _235430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _235426), _235428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _235426), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _235430), _235428))))], (1925 ^ _176355) ^ [_245662, _245664, _245666] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _245662), _245664)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _245662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _245666), _245664))))], (3960 ^ _176355) ^ [_323128, _323130, _323132] : [c_Finite__Set_Ofinite(_323128, _323130), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_323128, tc_HOL_Obool), _323132), _323130)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Finite__Set_Ocard(_323128, _323132)), c_Finite__Set_Ocard(_323128, _323130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_323128, tc_HOL_Obool)), _323132), _323130)))], (832 ^ _176355) ^ [_205507, _205509, _205511, _205513] : [-(tc_fun(_205513, _205509) = tc_fun(_205511, _205507)), _205513 = _205511, _205509 = _205507], (2524 ^ _176355) ^ [_267928, _267930, _267932] : [class_Orderings_Oorder(_267928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_267928), _267930), _267932)), _267932 = _267930], (5221 ^ _176355) ^ [_369965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _369965)), -(_369965 = hAPP(c_Nat_OSuc, 5224 ^ [_369965]))], (2113 ^ _176355) ^ [_254076, _254078, _254080] : [-(_254076 = _254078), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), _254080), c_Arrow__Order__Mirabelle_OLin)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove, _254080), _254076), _254078)), c_Arrow__Order__Mirabelle_OLin)))], (842 ^ _176355) ^ [_205838, _205840] : [_205840 = _205838, -(c_Orderings_Oord__class_Oless(_205840) = c_Orderings_Oord__class_Oless(_205838))], (736 ^ _176355) ^ [_201911, _201913, _201915, _201917] : [-(c_COMBK(_201917, _201913) = c_COMBK(_201915, _201911)), _201917 = _201915, _201913 = _201911], (790 ^ _176355) ^ [_203943, _203945, _203947, _203949] : [-(tc_prod(_203949, _203945) = tc_prod(_203947, _203943)), _203949 = _203947, _203945 = _203943], (5465 ^ _176355) ^ [_378971, _378973] : [class_Rings_Olinordered__idom(_378971), hBOOL(hAPP(hAPP(c_member(_378971), _378973), c_Int_Oring__1__class_OInts(_378971))), 5472 ^ _176355 : [(5473 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_378971), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_378971), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_378971), c_Groups_Oone__class_Oone(_378971)), _378973)), _378973)), c_Groups_Ozero__class_Ozero(_378971))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_378971), _378973), c_Groups_Ozero__class_Ozero(_378971))))], (5479 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_378971), _378973), c_Groups_Ozero__class_Ozero(_378971))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_378971), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_378971), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_378971), c_Groups_Oone__class_Oone(_378971)), _378973)), _378973)), c_Groups_Ozero__class_Ozero(_378971))))]]], (5609 ^ _176355) ^ [_384528, _384530, _384532] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_384528, tc_HOL_Obool), tc_fun(_384528, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_384528, tc_HOL_Obool), tc_fun(_384528, tc_HOL_Obool)), _384530), _384532)), c_Wellfounded_Ofinite__psubset(_384528))), 5612 ^ _176355 : [(5613 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_384528, tc_HOL_Obool)), _384530), _384532)))], (5615 ^ _176355) ^ [] : [-(c_Finite__Set_Ofinite(_384528, _384532))]]], (4840 ^ _176355) ^ [_355626, _355628, _355630, _355632] : [class_Groups_Oordered__comm__monoid__add(_355626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_355626), c_Groups_Ozero__class_Ozero(_355626)), _355628)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_355626, _355630), _355632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_355626), _355630), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_355626), _355628), _355632))))], (5060 ^ _176355) ^ [_364100, _364102, _364104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _364100), _364102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _364102), _364104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _364100)), _364104)))], (5086 ^ _176355) ^ [_365015, _365017] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _365015), _365017))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _365015), hAPP(c_Nat_OSuc, _365017))), -(_365017 = _365015)], (10 ^ _176355) ^ [_176810, _176812, _176814] : [-(_176814 = _176810), _176814 = _176812, _176812 = _176810], (800 ^ _176355) ^ [_204330, _204332, _204334, _204336, _204338, _204340] : [-(c_COMBC(_204340, _204336, _204332) = c_COMBC(_204338, _204334, _204330)), _204340 = _204338, _204336 = _204334, _204332 = _204330], (1352 ^ _176355) ^ [_223418, _223420] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _223418), _223420))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _223418), _223420)), -(_223418 = _223420)], (877 ^ _176355) ^ [] : [-(c_Arrow__Order__Mirabelle_OIIA(v_F))], (3934 ^ _176355) ^ [_322239, _322241, _322243, _322245, _322247, _322249] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_322239, _322241)), _322243), c_FuncSet_OPi(_322239, _322241, _322245, hAPP(c_COMBK(tc_fun(_322241, tc_HOL_Obool), _322239), _322247)))), c_Fun_Oinj__on(_322239, _322241, _322243, _322245), hBOOL(hAPP(hAPP(c_member(tc_fun(_322241, _322239)), _322249), c_FuncSet_OPi(_322241, _322239, _322247, hAPP(c_COMBK(tc_fun(_322239, tc_HOL_Obool), _322241), _322245)))), c_Fun_Oinj__on(_322241, _322239, _322249, _322247), c_Finite__Set_Ofinite(_322239, _322245), c_Finite__Set_Ofinite(_322241, _322247), -(c_Finite__Set_Ocard(_322239, _322245) = c_Finite__Set_Ocard(_322241, _322247))], (662 ^ _176355) ^ [_199249, _199251, _199253, _199255, _199257, _199259, _199261, _199263] : [-(c_Set_Oimage(_199263, _199259, _199255, _199251) = c_Set_Oimage(_199261, _199257, _199253, _199249)), _199263 = _199261, _199259 = _199257, _199255 = _199253, _199251 = _199249], (967 ^ _176355) ^ [_210231, _210233, _210235, _210237] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _210231), _210233)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot, _210235), _210237))), 970 ^ _176355 : [(979 ^ _176355) ^ [] : [-(_210231 = _210237), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _210231), _210233)), _210235)))], (973 ^ _176355) ^ [] : [_210231 = _210237, _210231 = _210233], (971 ^ _176355) ^ [] : [_210233 = _210237]]], (6283 ^ _176355) ^ [_413021, _413023] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool), _413021), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _413023, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _413023), c_Finite__Set_Ocard(tc_Nat_Onat, _413021))))), -(_413021 = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _413023, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _413023), c_Finite__Set_Ocard(tc_Nat_Onat, _413021))))], (1894 ^ _176355) ^ [_244454, _244456, _244458, _244460, _244462] : [class_Groups_Oordered__cancel__ab__semigroup__add(_244454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_244454), _244456), _244458)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_244454, _244460), _244462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_244454), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_244454), _244456), _244460)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_244454), _244458), _244462))))], (416 ^ _176355) ^ [_189858, _189860] : [-(class_Finite__Set_Ofinite(_189858)), _189860 = _189858, class_Finite__Set_Ofinite(_189860)], (6144 ^ _176355) ^ [_407801, _407803, _407805, _407807] : [c_Finite__Set_Ofinite(_407801, _407803), c_Finite__Set_Ofinite(_407805, _407807), 6151 ^ _176355 : [(6162 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Finite__Set_Ocard(_407801, _407803)), c_Finite__Set_Ocard(_407805, _407807))), 6166 ^ _176355 : [(6167 ^ _176355) ^ [] : [-(c_Fun_Oinj__on(_407801, _407805, 6165 ^ [_407801, _407803, _407805, _407807], _407803))], (6169 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_407805, tc_HOL_Obool), c_Set_Oimage(_407801, _407805, 6165 ^ [_407801, _407803, _407805, _407807], _407803)), _407807)))]]], (6152 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Finite__Set_Ocard(_407801, _407803)), c_Finite__Set_Ocard(_407805, _407807)))), 6153 ^ _176355 : [(6154 ^ _176355) ^ [_408138] : [c_Fun_Oinj__on(_407801, _407805, _408138, _407803), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_407805, tc_HOL_Obool), c_Set_Oimage(_407801, _407805, _408138, _407803)), _407807))]]]]], (3828 ^ _176355) ^ [_317886, _317888, _317890, _317892, _317894, _317896] : [c_Fun_Oinj__on(_317886, _317888, _317890, _317892), -(_317894 = _317896), hBOOL(hAPP(hAPP(c_member(_317886), _317894), _317892)), hBOOL(hAPP(hAPP(c_member(_317886), _317896), _317892)), hAPP(_317890, _317894) = hAPP(_317890, _317896)], (6381 ^ _176355) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (6039 ^ _176355) ^ [_403199, _403201, _403203, _403205, _403207] : [_403199 = hAPP(_403201, _403203), -(hBOOL(hAPP(hAPP(c_member(_403205), _403199), c_Set_Oimage(_403207, _403205, _403201, c_Orderings_Otop__class_Otop(tc_fun(_403207, tc_HOL_Obool))))))], (2356 ^ _176355) ^ [_262386, _262388, _262390] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), _262386), c_Arrow__Order__Mirabelle_OLin)), -(_262388 = _262390), 2363 ^ _176355 : [(2364 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _262388), _262390)), _262386))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _262390), _262388)), _262386)))], (2370 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _262390), _262388)), _262386)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _262388), _262390)), _262386))]]], (3220 ^ _176355) ^ [_291650, _291652, _291654, _291656] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_291650), 3223 ^ _176355 : [(3224 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_291650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_291650), _291652), _291654)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_291650), _291656), _291654))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_291650), _291652), _291656)))], (3230 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_291650), _291652), _291656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_291650), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_291650), _291652), _291654)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_291650), _291656), _291654))))]]], (1961 ^ _176355) ^ [_247099, _247101, _247103] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_247099, tc_HOL_Obool)), _247101), _247103))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_247099, tc_HOL_Obool), _247101), _247103)), -(_247101 = _247103)], (4574 ^ _176355) ^ [_346566, _346568] : [class_Groups_Olinordered__ab__group__add(_346566), 4577 ^ _176355 : [(4578 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_346566, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_346566), _346568), _346568)), c_Groups_Ozero__class_Ozero(_346566))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_346566, _346568), c_Groups_Ozero__class_Ozero(_346566))))], (4584 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_346566, _346568), c_Groups_Ozero__class_Ozero(_346566))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_346566, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_346566), _346568), _346568)), c_Groups_Ozero__class_Ozero(_346566))))]]], (5978 ^ _176355) ^ [_400306, _400308, _400310, _400312, _400314, _400316] : [hBOOL(hAPP(hAPP(c_member(_400306), _400308), _400310)), _400312 = hAPP(_400314, _400308), -(hBOOL(hAPP(hAPP(c_member(_400316), _400312), c_Set_Oimage(_400306, _400316, _400314, _400310))))], (2145 ^ _176355) ^ [_255296, _255298, _255300, _255302, _255304] : [class_Orderings_Oord(_255296), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_255298, _255296), _255300), _255302)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_255296, hAPP(_255300, _255304)), hAPP(_255302, _255304))))], (4418 ^ _176355) ^ [_341237] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _341237)))], (881 ^ _176355) ^ [] : [v_a____ = v_b____], (1601 ^ _176355) ^ [_232919, _232921, _232923] : [_232921 = _232923, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _232919), _232921) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _232919), _232923))], (3724 ^ _176355) ^ [_313138, _313140, _313142, _313144] : [c_Fun_Oinj__on(_313138, _313140, _313142, c_Orderings_Otop__class_Otop(tc_fun(_313138, tc_HOL_Obool))), -(c_Fun_Oinj__on(_313138, tc_fun(_313144, _313140), hAPP(c_COMBB(_313140, tc_fun(_313144, _313140), _313138, c_COMBK(_313140, _313144)), _313142), c_Orderings_Otop__class_Otop(tc_fun(_313138, tc_HOL_Obool))))], (3331 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), 3329 ^ [])))], (2307 ^ _176355) ^ [_260679, _260681, _260683] : [class_Orderings_Oorder(_260679), 2310 ^ _176355 : [(2311 ^ _176355) ^ [] : [_260681 = _260683, 2314 ^ _176355 : [(2315 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_260679, _260681), _260683)))], (2317 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_260679, _260683), _260681)))]]], (2319 ^ _176355) ^ [] : [-(_260681 = _260683), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_260679, _260681), _260683)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_260679, _260683), _260681))]]], (1625 ^ _176355) ^ [_234098, _234100, _234102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _234098), _234100)), _234102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _234098), _234102)))], (1581 ^ _176355) ^ [_232095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _232095), _232095))], (3324 ^ _176355) ^ [_295770, _295772, _295774] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _295770), _295772)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _295770), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _295772), _295774))))], (961 ^ _176355) ^ [_209914] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _209914), v_n____)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_b____), v_a____)), hAPP(v_F, hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), _209914))), v_Lab____)), v_Lba____)))))], (5339 ^ _176355) ^ [_373990, _373992] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _373990), _373992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _373990), hAPP(c_Nat_OSuc, _373992))))], (2938 ^ _176355) ^ [_281935, _281937, _281939] : [class_Orderings_Olinorder(_281935), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_281935, _281937), _281939))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_281935), _281939), _281937)))], (864 ^ _176355) ^ [_206613, _206615] : [_206615 = _206613, -(c_Groups_Oone__class_Oone(_206615) = c_Groups_Oone__class_Oone(_206613))], (883 ^ _176355) ^ [] : [v_c____ = v_d____], (5176 ^ _176355) ^ [_368308, _368310] : [hAPP(c_Nat_OSuc, _368308) = hAPP(c_Nat_OSuc, _368310), -(_368308 = _368310)], (3361 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), hAPP(v_F, hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 3351 ^ []), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_Lab____)), v_Lba____)))))], (5215 ^ _176355) ^ [_369734] : [_369734 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _369734), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (784 ^ _176355) ^ [_203697, _203699] : [_203699 = _203697, -(c_If(_203699) = c_If(_203697))], (2720 ^ _176355) ^ [_274822, _274824, _274826, _274828] : [class_Groups_Ocancel__semigroup__add(_274822), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_274822), _274824), _274826) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_274822), _274828), _274826), -(_274824 = _274828)], (2668 ^ _176355) ^ [_272936, _272938, _272940, _272942] : [class_Groups_Ocancel__semigroup__add(_272936), 2671 ^ _176355 : [(2672 ^ _176355) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_272936), _272938), _272940) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_272936), _272938), _272942), -(_272940 = _272942)], (2678 ^ _176355) ^ [] : [_272940 = _272942, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_272936), _272938), _272940) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_272936), _272938), _272942))]]], (614 ^ _176355) ^ [_197435, _197437, _197439, _197441, _197443, _197445, _197447, _197449] : [-(c_Hilbert__Choice_Oinv__into(_197449, _197445, _197441, _197437) = c_Hilbert__Choice_Oinv__into(_197447, _197443, _197439, _197435)), _197449 = _197447, _197445 = _197443, _197441 = _197439, _197437 = _197435], (582 ^ _176355) ^ [_196230, _196232, _196234, _196236, _196238, _196240, _196242, _196244] : [-(c_Nat_Onat_Onat__case(_196244, _196240, _196236, _196232) = c_Nat_Onat_Onat__case(_196242, _196238, _196234, _196230)), _196244 = _196242, _196240 = _196238, _196236 = _196234, _196232 = _196230], (4882 ^ _176355) ^ [_357044] : [class_Rings_Olinordered__semidom(_357044), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_357044), c_Groups_Ozero__class_Ozero(_357044)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_357044), c_Groups_Oone__class_Oone(_357044)), c_Groups_Oone__class_Oone(_357044)))))], (4088 ^ _176355) ^ [_327538, _327540] : [c_Finite__Set_Ofinite(_327538, c_Orderings_Otop__class_Otop(tc_fun(_327538, tc_HOL_Obool))), c_Finite__Set_Ocard(_327538, _327540) = c_Finite__Set_Ocard(_327538, c_Orderings_Otop__class_Otop(tc_fun(_327538, tc_HOL_Obool))), -(_327540 = c_Orderings_Otop__class_Otop(tc_fun(_327538, tc_HOL_Obool)))], (3765 ^ _176355) ^ [_315059, _315061, _315063, _315065, _315067] : [c_Fun_Oinj__on(_315059, _315061, _315063, c_Orderings_Otop__class_Otop(tc_fun(_315059, tc_HOL_Obool))), hAPP(_315063, _315065) = hAPP(_315063, _315067), -(_315065 = _315067)], (6247 ^ _176355) ^ [_411833, _411835, _411837, _411839, _411841] : [class_Orderings_Olinorder(_411833), c_SetInterval_Oord__class_OatLeastLessThan(_411833, _411835, _411837) = c_SetInterval_Oord__class_OatLeastLessThan(_411833, _411839, _411841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_411833), _411835), _411837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_411833), _411839), _411841)), -(_411835 = _411839)], (4076 ^ _176355) ^ [_327106] : [c_Finite__Set_Ofinite(_327106, c_Orderings_Otop__class_Otop(tc_fun(_327106, tc_HOL_Obool))), -(c_Finite__Set_Ofinite(tc_Option_Ooption(_327106), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_327106), tc_HOL_Obool))))], (2596 ^ _176355) ^ [_270388, _270390, _270392, _270394] : [class_Orderings_Oorder(_270388), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_270388), _270390), _270392)), _270390 = _270394, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_270388), _270394), _270392)))], (870 ^ _176355) ^ [_207076, _207078] : [hAPP(_207076, 871 ^ [_207076, _207078]) = hAPP(_207078, 871 ^ [_207076, _207078]), -(_207076 = _207078)], (5507 ^ _176355) ^ [] : [-(c_Nat_Osize__class_Osize(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5156 ^ _176355) ^ [_367482, _367484] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _367482)), _367484) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _367482), _367484)))], (5264 ^ _176355) ^ [_371371, _371373] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _371371), _371373) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5269 ^ _176355 : [(5270 ^ _176355) ^ [] : [-(_371371 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5272 ^ _176355) ^ [] : [-(_371373 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 5273 ^ _176355 : [(5274 ^ _176355) ^ [] : [-(_371371 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5276 ^ _176355) ^ [] : [-(_371373 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (5698 ^ _176355) ^ [_388146, _388148, _388150, _388152] : [c_Finite__Set_Ofinite(_388146, _388148), -(c_Finite__Set_Ofinite(_388150, c_Set_Oimage(_388146, _388150, _388152, _388148)))], (2494 ^ _176355) ^ [_266892, _266894, _266896] : [class_Orderings_Opreorder(_266892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_266892), _266894), _266896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_266892), _266896), _266894))], (3700 ^ _176355) ^ [_311962, _311964] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_311962, _311962)), c_COMBI(_311962)), c_FuncSet_OPi(_311962, _311962, _311964, hAPP(c_COMBK(tc_fun(_311962, tc_HOL_Obool), _311962), _311964)))))], (4042 ^ _176355) ^ [_325915, _325917] : [c_Finite__Set_Ofinite(_325915, c_Orderings_Otop__class_Otop(tc_fun(_325915, tc_HOL_Obool))), c_Finite__Set_Ofinite(_325917, c_Orderings_Otop__class_Otop(tc_fun(_325917, tc_HOL_Obool))), -(c_Finite__Set_Ofinite(tc_prod(_325915, _325917), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_325915, _325917), tc_HOL_Obool))))], (1198 ^ _176355) ^ [_216762, _216764] : [class_Rings_Olinordered__semidom(_216762), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_216762), _216764), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_216762), _216764), c_Groups_Oone__class_Oone(_216762)))))], (6140 ^ _176355) ^ [] : [-(c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, 6138 ^ [], c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))], (5197 ^ _176355) ^ [_369076, _369078] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _369076), hAPP(c_Nat_OSuc, _369078)))), 5198 ^ _176355 : [(5199 ^ _176355) ^ [] : [_369076 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5201 ^ _176355) ^ [_369255] : [_369076 = hAPP(c_Nat_OSuc, _369255), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _369255), _369078))]]], (5395 ^ _176355) ^ [_376111, _376113, _376115] : [c_Finite__Set_Ofinite(_376111, _376113), 5398 ^ _176355 : [(5399 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_376111), _376115), _376113)), -(c_Finite__Set_Ocard(_376111, c_Set_Oinsert(_376111, _376115, _376113)) = c_Finite__Set_Ocard(_376111, _376113))], (5405 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_376111), _376115), _376113))), -(c_Finite__Set_Ocard(_376111, c_Set_Oinsert(_376111, _376115, _376113)) = hAPP(c_Nat_OSuc, c_Finite__Set_Ocard(_376111, _376113)))]]], (6063 ^ _176355) ^ [_404394, _404396, _404398, _404400, _404402] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_404394, tc_HOL_Obool), _404396), c_Set_Oimage(_404398, _404394, _404400, _404402))), -(c_Fun_Oinj__on(_404394, _404398, c_Hilbert__Choice_Oinv__into(_404398, _404394, _404402, _404400), _404396))], (1553 ^ _176355) ^ [_231189, _231191] : [-(_231189 = _231191), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _231189), _231191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _231191), _231189)))], (2514 ^ _176355) ^ [_267592, _267594, _267596] : [class_Orderings_Oorder(_267592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_267592), _267594), _267596)), _267594 = _267596], (3666 ^ _176355) ^ [_310582, _310584, _310586, _310588, _310590] : [c_Fun_Oinj__on(_310582, _310584, _310586, c_Orderings_Otop__class_Otop(tc_fun(_310582, tc_HOL_Obool))), hAPP(_310586, _310588) = _310590, -(hAPP(c_Hilbert__Choice_Oinv__into(_310582, _310584, c_Orderings_Otop__class_Otop(tc_fun(_310582, tc_HOL_Obool)), _310586), _310590) = _310588)], (4928 ^ _176355) ^ [_358960, _358962, _358964, _358966, _358968, _358970, _358972, _358974] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_358960, _358962), tc_prod(_358960, _358962))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_358960, _358962), tc_prod(_358960, _358962)), hAPP(hAPP(c_Product__Type_OPair(_358960, _358962), _358964), _358966)), hAPP(hAPP(c_Product__Type_OPair(_358960, _358962), _358968), _358970))), c_Wellfounded_Olex__prod(_358960, _358962, _358972, _358974)))), 4929 ^ _176355 : [(4930 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_358960, _358960)), hAPP(hAPP(c_Product__Type_OPair(_358960, _358960), _358964), _358968)), _358972))], (4932 ^ _176355) ^ [] : [_358964 = _358968, hBOOL(hAPP(hAPP(c_member(tc_prod(_358962, _358962)), hAPP(hAPP(c_Product__Type_OPair(_358962, _358962), _358966), _358970)), _358974))]]], (6355 ^ _176355) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (1196 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), v_n____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Omktop), v_P____)), v_e____)), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_fequal), v_h____)), v_n____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Oabove), v_P____)), v_c____)), v_e____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Omkbot), v_P____)), v_e____)))), c_Arrow__Order__Mirabelle_OProf)))], (4052 ^ _176355) ^ [_326285, _326287] : [c_Finite__Set_Ofinite(tc_sum(_326285, _326287), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_326285, _326287), tc_HOL_Obool))), 4055 ^ _176355 : [(4056 ^ _176355) ^ [] : [-(c_Finite__Set_Ofinite(_326285, c_Orderings_Otop__class_Otop(tc_fun(_326285, tc_HOL_Obool))))], (4058 ^ _176355) ^ [] : [-(c_Finite__Set_Ofinite(_326287, c_Orderings_Otop__class_Otop(tc_fun(_326287, tc_HOL_Obool))))]]], (1051 ^ _176355) ^ [_213002] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(v_P____, _213002))), 1054 ^ _176355 : [(1055 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _213002)), v_n____)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop, hAPP(v_P____, _213002)), v_e____))))], (1061 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, _213002)), v_n____))), 1064 ^ _176355 : [(1065 ^ _176355) ^ [] : [hAPP(v_h____, _213002) = v_n____, -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove, hAPP(v_P____, _213002)), v_c____), v_e____))))], (1071 ^ _176355) ^ [] : [-(hAPP(v_h____, _213002) = v_n____), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot, hAPP(v_P____, _213002)), v_e____))))]]]]], (450 ^ _176355) ^ [_191192, _191194, _191196, _191198, _191200, _191202, _191204, _191206] : [-(c_Sum__Type_OPlus(_191206, _191202, _191198, _191194) = c_Sum__Type_OPlus(_191204, _191200, _191196, _191192)), _191206 = _191204, _191202 = _191200, _191198 = _191196, _191194 = _191192], (4970 ^ _176355) ^ [_360722] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _360722)], (5278 ^ _176355) ^ [_371785, _371787] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _371785), _371787) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 5279 ^ _176355 : [(5280 ^ _176355) ^ [] : [_371785 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _371787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5286 ^ _176355) ^ [] : [_371785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _371787 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4032 ^ _176355) ^ [_325590, _325592, _325594] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_325590, tc_HOL_Obool), _325592), _325594)), c_Finite__Set_Ofinite(_325590, _325594), -(c_Finite__Set_Ofinite(_325590, _325592))], (5463 ^ _176355) ^ [_378849] : [-(c_Nat_Osize__class_Osize(tc_Nat_Onat, hAPP(c_Nat_OSuc, _378849)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_Nat_Onat, _378849)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2730 ^ _176355) ^ [_275171, _275173] : [class_Groups_Oone(_275171), 2733 ^ _176355 : [(2734 ^ _176355) ^ [] : [c_Groups_Oone__class_Oone(_275171) = _275173, -(_275173 = c_Groups_Oone__class_Oone(_275171))], (2740 ^ _176355) ^ [] : [_275173 = c_Groups_Oone__class_Oone(_275171), -(c_Groups_Oone__class_Oone(_275171) = _275173)]]], (5822 ^ _176355) ^ [_393991, _393993, _393995, _393997, _393999] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_393991, tc_HOL_Obool), _393993), _393995)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_393997, tc_HOL_Obool), c_Set_Oimage(_393991, _393997, _393999, _393993)), c_Set_Oimage(_393991, _393997, _393999, _393995))))], (2065 ^ _176355) ^ [_251560, _251562, _251564, _251566] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), _251564), _251566)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_251560, tc_fun(_251562, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_251560, tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_fun(_251562, tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_251562, tc_fun(tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_fun(_251562, tc_HOL_Obool)), _251560, c_COMBC(_251562, tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_251562, tc_prod(_251560, _251562)), tc_fun(_251562, tc_fun(tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_HOL_Obool)), _251560, c_COMBB(tc_prod(_251560, _251562), tc_fun(tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_HOL_Obool), _251562, c_member(tc_prod(_251560, _251562)))), c_Product__Type_OPair(_251560, _251562)))), _251564)), hAPP(hAPP(c_COMBC(_251560, tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_fun(_251562, tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_251562, tc_fun(tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_fun(_251562, tc_HOL_Obool)), _251560, c_COMBC(_251562, tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_251562, tc_prod(_251560, _251562)), tc_fun(_251562, tc_fun(tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_HOL_Obool)), _251560, c_COMBB(tc_prod(_251560, _251562), tc_fun(tc_fun(tc_prod(_251560, _251562), tc_HOL_Obool), tc_HOL_Obool), _251562, c_member(tc_prod(_251560, _251562)))), c_Product__Type_OPair(_251560, _251562)))), _251566))))], (5124 ^ _176355) ^ [_366336, _366338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _366336), hAPP(c_Nat_OSuc, _366338))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _366336), _366338))), -(_366336 = _366338)], (5411 ^ _176355) ^ [_376667, _376669] : [class_Groups_Olinordered__ab__group__add(_376667), 5414 ^ _176355 : [(5415 ^ _176355) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_376667), _376669), _376669) = c_Groups_Ozero__class_Ozero(_376667), -(_376669 = c_Groups_Ozero__class_Ozero(_376667))], (5421 ^ _176355) ^ [] : [_376669 = c_Groups_Ozero__class_Ozero(_376667), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_376667), _376669), _376669) = c_Groups_Ozero__class_Ozero(_376667))]]], (1993 ^ _176355) ^ [_248260, _248262, _248264] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_248260, tc_HOL_Obool), _248262), _248264)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_248260, tc_HOL_Obool)), _248262), _248264))), -(_248262 = _248264)], (3704 ^ _176355) ^ [_312290, _312292, _312294, _312296, _312298, _312300] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_312290, _312292)), _312294), c_FuncSet_OPi(_312290, _312292, _312296, _312298))), hBOOL(hAPP(hAPP(c_member(_312290), _312300), _312296)), -(hBOOL(hAPP(hAPP(c_member(_312292), hAPP(_312294, _312300)), hAPP(_312298, _312300))))], (316 ^ _176355) ^ [_186908, _186910] : [-(class_Rings_Ocomm__semiring__1(_186908)), _186910 = _186908, class_Rings_Ocomm__semiring__1(_186910)], (1003 ^ _176355) ^ [_211513, _211515, _211517, _211519] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _211513), _211515)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop, _211517), _211519))), 1006 ^ _176355 : [(1015 ^ _176355) ^ [] : [-(_211515 = _211519), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _211513), _211515)), _211517)))], (1009 ^ _176355) ^ [] : [_211515 = _211519, _211513 = _211515], (1007 ^ _176355) ^ [] : [_211513 = _211519]]], (2017 ^ _176355) ^ [_249182, _249184, _249186, _249188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_249182, tc_HOL_Obool)), _249184), _249186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_249182, tc_HOL_Obool)), _249186), _249188)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_249182, tc_HOL_Obool)), _249184), _249188)))], (46 ^ _176355) ^ [_178110, _178112] : [-(c_Arrow__Order__Mirabelle_Ounanimity(_178110)), _178112 = _178110, c_Arrow__Order__Mirabelle_Ounanimity(_178112)], (5730 ^ _176355) ^ [_389465, _389467, _389469, _389471, _389473] : [c_Fun_Oinj__on(_389465, _389467, _389469, c_Orderings_Otop__class_Otop(tc_fun(_389465, tc_HOL_Obool))), 5733 ^ _176355 : [(5734 ^ _176355) ^ [] : [c_Set_Oimage(_389465, _389467, _389469, _389471) = c_Set_Oimage(_389465, _389467, _389469, _389473), -(_389471 = _389473)], (5740 ^ _176355) ^ [] : [_389471 = _389473, -(c_Set_Oimage(_389465, _389467, _389469, _389471) = c_Set_Oimage(_389465, _389467, _389469, _389473))]]], (1931 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), v_n____), c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))))], (1224 ^ _176355) ^ [_218249, _218251, _218253, _218255] : [_218253 = _218255, -(hAPP(hAPP(c_COMBC(_218249, tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_fun(_218251, tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_218251, tc_fun(tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_fun(_218251, tc_HOL_Obool)), _218249, c_COMBC(_218251, tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_218251, tc_prod(_218249, _218251)), tc_fun(_218251, tc_fun(tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_HOL_Obool)), _218249, c_COMBB(tc_prod(_218249, _218251), tc_fun(tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_HOL_Obool), _218251, c_member(tc_prod(_218249, _218251)))), c_Product__Type_OPair(_218249, _218251)))), _218253) = hAPP(hAPP(c_COMBC(_218249, tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_fun(_218251, tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_218251, tc_fun(tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_fun(_218251, tc_HOL_Obool)), _218249, c_COMBC(_218251, tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_218251, tc_prod(_218249, _218251)), tc_fun(_218251, tc_fun(tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_HOL_Obool)), _218249, c_COMBB(tc_prod(_218249, _218251), tc_fun(tc_fun(tc_prod(_218249, _218251), tc_HOL_Obool), tc_HOL_Obool), _218251, c_member(tc_prod(_218249, _218251)))), c_Product__Type_OPair(_218249, _218251)))), _218255))], (3775 ^ _176355) ^ [_315471, _315473, _315475, _315477] : [c_Fun_Oinj__on(_315471, _315473, _315475, _315477), 3778 ^ _176355 : [(3779 ^ _176355) ^ [_315657] : [hBOOL(hAPP(hAPP(c_member(_315471), _315657), _315477)), 3782 ^ _176355 : [(3783 ^ _176355) ^ [_315847] : [hBOOL(hAPP(hAPP(c_member(_315471), _315847), _315477)), hAPP(_315475, _315657) = hAPP(_315475, _315847), -(_315657 = _315847)]]]]], (1481 ^ _176355) ^ [_228619, _228621, _228623] : [hBOOL(hAPP(hAPP(c_member(_228619), _228621), hAPP(c_fequal, _228623))), -(_228621 = _228623)], (56 ^ _176355) ^ [_178405, _178407] : [-(c_Arrow__Order__Mirabelle_OIIA(_178405)), _178407 = _178405, c_Arrow__Order__Mirabelle_OIIA(_178407)], (256 ^ _176355) ^ [_185138, _185140] : [-(class_Groups_Oordered__comm__monoid__add(_185138)), _185140 = _185138, class_Groups_Oordered__comm__monoid__add(_185140)], (2155 ^ _176355) ^ [_255689, _255691, _255693, _255695] : [class_Orderings_Oorder(_255689), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_255689, _255691), _255693)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_255689, _255695), _255691)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_255689, _255695), _255693)))], (2253 ^ _176355) ^ [_258887, _258889, _258891, _258893] : [class_Orderings_Oord(_258887), _258889 = _258891, hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_258887, _258891), _258893)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_258887, _258889), _258893)))], (3994 ^ _176355) ^ [_324328, _324330, _324332] : [c_Finite__Set_Ofinite(_324328, _324330), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_324328, tc_HOL_Obool), _324332), _324330)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Finite__Set_Ocard(_324328, _324330)), c_Finite__Set_Ocard(_324328, _324332))), -(_324332 = _324330)], (2544 ^ _176355) ^ [_268614, _268616, _268618] : [class_Orderings_Oorder(_268614), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_268614), _268616), _268618)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_268614), _268618), _268616))], (5948 ^ _176355) ^ [_398979, _398981, _398983, _398985] : [c_Fun_Oinj__on(_398979, _398981, _398983, c_Orderings_Otop__class_Otop(tc_fun(_398979, tc_HOL_Obool))), 5951 ^ _176355 : [(5952 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_398981), _398985), c_Set_Oimage(_398979, _398981, _398983, c_Orderings_Otop__class_Otop(tc_fun(_398979, tc_HOL_Obool))))), 5956 ^ _176355 : [(5957 ^ _176355) ^ [] : [-(_398985 = hAPP(_398983, 5955 ^ [_398979, _398981, _398983, _398985]))], (5959 ^ _176355) ^ [_399471] : [_398985 = hAPP(_398983, _399471), -(_399471 = 5955 ^ [_398979, _398981, _398983, _398985])]]], (5965 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_398981), _398985), c_Set_Oimage(_398979, _398981, _398983, c_Orderings_Otop__class_Otop(tc_fun(_398979, tc_HOL_Obool)))))), 5966 ^ _176355 : [(5967 ^ _176355) ^ [_399746] : [_398985 = hAPP(_398983, _399746), 5971 ^ _176355 : [(5972 ^ _176355) ^ [] : [-(_398985 = hAPP(_398983, 5970 ^ [_398979, _398981, _398983, _398985, _399746]))], (5974 ^ _176355) ^ [] : [5970 ^ [_398979, _398981, _398983, _398985, _399746] = _399746]]]]]]], (4762 ^ _176355) ^ [_352869] : [class_Rings_Olinordered__semidom(_352869), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_352869), c_Groups_Ozero__class_Ozero(_352869)), c_Groups_Oone__class_Oone(_352869))))], (4332 ^ _176355) ^ [_337612, _337614, _337616, _337618] : [-(hBOOL(hAPP(hAPP(c_member(_337612), _337614), _337616))), 4335 ^ _176355 : [(4336 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_337612, tc_HOL_Obool), _337616), c_Set_Oinsert(_337612, _337614, _337618))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_337612, tc_HOL_Obool), _337616), _337618)))], (4342 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_337612, tc_HOL_Obool), _337616), _337618)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_337612, tc_HOL_Obool), _337616), c_Set_Oinsert(_337612, _337614, _337618))))]]], (5148 ^ _176355) ^ [_367146, _367148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _367148), hAPP(c_Nat_OSuc, _367146))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _367146), _367148))], (1240 ^ _176355) ^ [_219384, _219386, _219388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _219386), _219388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _219384), _219386)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _219384), _219388))))], (1362 ^ _176355) ^ [_223756, _223758, _223760] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _223756), _223758)), _223760)), 1365 ^ _176355 : [(1366 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _223756), _223760)))], (1368 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _223758), _223760)))]]], (2624 ^ _176355) ^ [_271342, _271344, _271346, _271348] : [class_Orderings_Oorder(_271342), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_271342), _271344), _271346)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_271342), _271348), _271344)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_271342), _271348), _271346)))], (3134 ^ _176355) ^ [_288338, _288340, _288342, _288344] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_288338), 3137 ^ _176355 : [(3138 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_288338, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_288338), _288340), _288342)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_288338), _288344), _288342))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_288338, _288340), _288344)))], (3144 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_288338, _288340), _288344)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_288338, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_288338), _288340), _288342)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_288338), _288344), _288342))))]]], (1951 ^ _176355) ^ [_246652, _246654] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_246652, tc_HOL_Obool), _246654), c_Orderings_Otop__class_Otop(tc_fun(_246652, tc_HOL_Obool)))))], (2836 ^ _176355) ^ [_278632, _278634, _278636] : [class_Orderings_Olinorder(_278632), 2839 ^ _176355 : [(2840 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_278632, _278634), _278636))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_278632), _278636), _278634)))], (2846 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_278632), _278636), _278634)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_278632, _278634), _278636))]]], (1583 ^ _176355) ^ [_232250, _232252, _232254] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _232250), _232252) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _232254), _232252), -(_232250 = _232254)], (1392 ^ _176355) ^ [_225034, _225036, _225038] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225034), _225036)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _225034), _225038)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _225036), _225038))))], (858 ^ _176355) ^ [_206415, _206417] : [_206417 = _206415, -(c_Groups_Oplus__class_Oplus(_206417) = c_Groups_Oplus__class_Oplus(_206415))], (3580 ^ _176355) ^ [_306837, _306839, _306841] : [_306837 = _306839, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_306841, tc_HOL_Obool), _306837), _306839)))], (1045 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(v_F, c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), v_n____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Omktop), v_P____)), v_e____)), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_fequal), v_h____)), v_n____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Oabove), v_P____)), v_c____)), v_e____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Omkbot), v_P____)), v_e____)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_d____)), hAPP(v_F, v_P____))))], (4648 ^ _176355) ^ [_348990, _348992, _348994, _348996] : [class_Groups_Oordered__comm__monoid__add(_348990), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_348990, c_Groups_Ozero__class_Ozero(_348990)), _348992)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_348990, _348994), _348996)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_348990, _348994), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_348990), _348996), _348992))))], (4082 ^ _176355) ^ [_327326] : [class_Finite__Set_Ofinite(_327326), -(c_Finite__Set_Ofinite(_327326, c_Orderings_Otop__class_Otop(tc_fun(_327326, tc_HOL_Obool))))], (6047 ^ _176355) ^ [_403655, _403657, _403659, _403661, _403663] : [hBOOL(hAPP(hAPP(c_member(_403655), _403657), _403659)), -(c_Set_Oinsert(_403661, hAPP(_403663, _403657), c_Set_Oimage(_403655, _403661, _403663, _403659)) = c_Set_Oimage(_403655, _403661, _403663, _403659))], (3560 ^ _176355) ^ [_306109, _306111, _306113] : [-(_306109 = _306111), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_306113, tc_HOL_Obool), _306109), _306111)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_306113, tc_HOL_Obool), _306111), _306109))], (5840 ^ _176355) ^ [_394978, _394980, _394982, _394984] : [c_Finite__Set_Ofinite(_394978, _394980), c_Finite__Set_Ocard(_394982, c_Set_Oimage(_394978, _394982, _394984, _394980)) = c_Finite__Set_Ocard(_394978, _394980), -(c_Fun_Oinj__on(_394978, _394982, _394984, _394980))], (5030 ^ _176355) ^ [_362956, _362958] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _362958)), _362956)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362956), _362958))], (4950 ^ _176355) ^ [_359941, _359943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _359941), _359943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _359941)), hAPP(c_Nat_OSuc, _359943))))], (3898 ^ _176355) ^ [_320352, _320354] : [-(hBOOL(hAPP(hAPP(c_member(_320352), _320354), c_Orderings_Otop__class_Otop(tc_fun(_320352, tc_HOL_Obool)))))], (5797 ^ _176355) ^ [_392501, _392503, _392505, _392507, _392509] : [-(c_Set_Oimage(_392501, _392503, hAPP(c_COMBB(_392505, _392503, _392501, _392507), _392509), c_Orderings_Otop__class_Otop(tc_fun(_392501, tc_HOL_Obool))) = c_Set_Oimage(_392505, _392503, _392507, c_Set_Oimage(_392501, _392505, _392509, c_Orderings_Otop__class_Otop(tc_fun(_392501, tc_HOL_Obool)))))], (2906 ^ _176355) ^ [_280899, _280901, _280903] : [class_Orderings_Oorder(_280899), 2909 ^ _176355 : [(2920 ^ _176355) ^ [] : [2921 ^ _176355 : [(2922 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_280899), _280901), _280903))], (2924 ^ _176355) ^ [] : [_280901 = _280903]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_280899, _280901), _280903)))], (2910 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_280899, _280901), _280903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_280899), _280901), _280903))), -(_280901 = _280903)]]], (6423 ^ _176355) ^ [_417794, _417796, _417798, _417800, _417802, _417804] : [-(hAPP(c_COMBS(_417794, _417796, _417798, _417800, _417802), _417804) = hAPP(hAPP(_417800, _417804), hAPP(_417802, _417804)))], (3694 ^ _176355) ^ [_311691, _311693, _311695, _311697, _311699] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_311691, tc_HOL_Obool), _311693), _311695)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_311691, _311697), tc_HOL_Obool), c_FuncSet_OPi(_311691, _311697, _311695, _311699)), c_FuncSet_OPi(_311691, _311697, _311693, _311699))))], (5581 ^ _176355) ^ [_383319, _383321, _383323, _383325] : [class_Rings_Ocomm__semiring__1(_383319), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383319), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383319), _383321), _383323)), _383325) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383319), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383319), _383321), _383325)), _383323))], (4826 ^ _176355) ^ [_355126, _355128, _355130, _355132] : [class_Groups_Oordered__comm__monoid__add(_355126), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_355126, c_Groups_Ozero__class_Ozero(_355126)), _355128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_355126), _355130), _355132)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_355126), _355130), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_355126), _355128), _355132))))], (4690 ^ _176355) ^ [_350444, _350446, _350448] : [class_Groups_Oordered__comm__monoid__add(_350444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_350444), _350446), c_Groups_Ozero__class_Ozero(_350444))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_350444), _350448), c_Groups_Ozero__class_Ozero(_350444))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_350444), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_350444), _350446), _350448)), c_Groups_Ozero__class_Ozero(_350444))))], (4280 ^ _176355) ^ [_335516, _335518, _335520, _335522] : [hBOOL(hAPP(hAPP(c_member(_335516), _335518), _335520)), -(hBOOL(hAPP(hAPP(c_member(_335516), _335518), c_Set_Oinsert(_335516, _335522, _335520))))], (5038 ^ _176355) ^ [_363280, _363282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _363280)), hAPP(c_Nat_OSuc, _363282))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _363280), _363282)))], (1595 ^ _176355) ^ [_232727, _232729, _232731] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _232727), _232729) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _232727), _232731), -(_232729 = _232731)], (4320 ^ _176355) ^ [_337080, _337082, _337084, _337086] : [c_Finite__Set_Ofinite(tc_sum(_337080, _337082), c_Sum__Type_OPlus(_337080, _337082, _337084, _337086)), -(c_Finite__Set_Ofinite(_337080, _337084))], (6385 ^ _176355) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (3660 ^ _176355) ^ [_310272, _310274, _310276, _310278] : [c_Fun_Oinj__on(_310272, _310274, _310276, c_Orderings_Otop__class_Otop(tc_fun(_310272, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_310272, _310274, c_Orderings_Otop__class_Otop(tc_fun(_310272, tc_HOL_Obool)), _310276), hAPP(_310276, _310278)) = _310278)], (632 ^ _176355) ^ [_198124, _198126, _198128, _198130, _198132, _198134, _198136, _198138] : [-(c_FuncSet_OPi(_198138, _198134, _198130, _198126) = c_FuncSet_OPi(_198136, _198132, _198128, _198124)), _198138 = _198136, _198134 = _198132, _198130 = _198128, _198126 = _198124], (2386 ^ _176355) ^ [_263414, _263416] : [class_Orderings_Opreorder(_263414), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_263414), _263416), _263416))], (266 ^ _176355) ^ [_185433, _185435] : [-(class_Groups_Ocancel__ab__semigroup__add(_185433)), _185435 = _185433, class_Groups_Ocancel__ab__semigroup__add(_185435)], (1449 ^ _176355) ^ [_227480, _227482, _227484, _227486] : [_227480 = _227482, 1452 ^ _176355 : [(1453 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_227484), _227480), _227486)), -(hBOOL(hAPP(hAPP(c_member(_227484), _227482), _227486)))], (1459 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_227484), _227482), _227486)), -(hBOOL(hAPP(hAPP(c_member(_227484), _227480), _227486)))]]], (5664 ^ _176355) ^ [_386786, _386788, _386790, _386792, _386794, _386796, _386798] : [c_Finite__Set_Ofolding__image__simple(_386786, _386788, _386790, _386792, _386794, _386796), c_Finite__Set_Ofinite(_386788, _386798), -(hAPP(_386796, _386798) = c_Finite__Set_Ofold__image(_386786, _386788, _386790, _386794, _386792, _386798))], (1218 ^ _176355) ^ [_217627, _217629, _217631, _217633] : [hAPP(hAPP(c_COMBC(_217627, tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_fun(_217629, tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_217629, tc_fun(tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_fun(_217629, tc_HOL_Obool)), _217627, c_COMBC(_217629, tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_217629, tc_prod(_217627, _217629)), tc_fun(_217629, tc_fun(tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_HOL_Obool)), _217627, c_COMBB(tc_prod(_217627, _217629), tc_fun(tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_HOL_Obool), _217629, c_member(tc_prod(_217627, _217629)))), c_Product__Type_OPair(_217627, _217629)))), _217631) = hAPP(hAPP(c_COMBC(_217627, tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_fun(_217629, tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_217629, tc_fun(tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_fun(_217629, tc_HOL_Obool)), _217627, c_COMBC(_217629, tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_217629, tc_prod(_217627, _217629)), tc_fun(_217629, tc_fun(tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_HOL_Obool)), _217627, c_COMBB(tc_prod(_217627, _217629), tc_fun(tc_fun(tc_prod(_217627, _217629), tc_HOL_Obool), tc_HOL_Obool), _217629, c_member(tc_prod(_217627, _217629)))), c_Product__Type_OPair(_217627, _217629)))), _217633), -(_217631 = _217633)], (2700 ^ _176355) ^ [_274068, _274070, _274072, _274074] : [class_Groups_Ocancel__semigroup__add(_274068), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_274068), _274070), _274072) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_274068), _274070), _274074), -(_274072 = _274074)], (4192 ^ _176355) ^ [_331796, _331798, _331800] : [c_Finite__Set_Ofinite(_331796, _331800), -(c_Finite__Set_Ofinite(_331796, c_Set_Oinsert(_331796, _331798, _331800)))], (1923 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), hAPP(v_F, hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 1913 ^ []), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_Lab____)), v_Lba____)))))], (4756 ^ _176355) ^ [_352663] : [class_Rings_Olinordered__semidom(_352663), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_352663, c_Groups_Ozero__class_Ozero(_352663)), c_Groups_Oone__class_Oone(_352663))))], (5866 ^ _176355) ^ [_395910, _395912, _395914, _395916] : [c_Finite__Set_Ofinite(_395910, _395912), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Finite__Set_Ocard(_395914, c_Set_Oimage(_395910, _395914, _395916, _395912))), c_Finite__Set_Ocard(_395910, _395912))))], (3200 ^ _176355) ^ [_290856, _290858, _290860, _290862] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_290856), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_290856, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_290856), _290858), _290860)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_290856), _290862), _290860))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_290856, _290858), _290862)))], (5333 ^ _176355) ^ [_373754, _373756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _373754), _373756)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _373754)), _373756)))], (2662 ^ _176355) ^ [_272624, _272626, _272628, _272630] : [class_Groups_Oab__semigroup__add(_272624), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_272624), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_272624), _272626), _272628)), _272630) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_272624), _272626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_272624), _272628), _272630)))], (5162 ^ _176355) ^ [_367771] : [hAPP(c_Nat_OSuc, _367771) = _367771], (690 ^ _176355) ^ [_200269, _200271, _200273, _200275, _200277, _200279] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_200279, _200275, _200271) = c_SetInterval_Oord__class_OatLeastLessThan(_200277, _200273, _200269)), _200279 = _200277, _200275 = _200273, _200271 = _200269], (2027 ^ _176355) ^ [_249589, _249591, _249593, _249595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_249589, tc_HOL_Obool)), _249591), _249593)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_249589, tc_HOL_Obool), _249593), _249595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_249589, tc_HOL_Obool)), _249591), _249595)))], (226 ^ _176355) ^ [_184253, _184255] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_184253)), _184255 = _184253, class_Groups_Oordered__cancel__ab__semigroup__add(_184255)], (5688 ^ _176355) ^ [_387735, _387737, _387739, _387741, _387743, _387745] : [_387735 = hAPP(_387737, _387739), hBOOL(hAPP(hAPP(c_member(_387741), _387739), _387743)), -(hBOOL(hAPP(hAPP(c_member(_387745), _387735), c_Set_Oimage(_387741, _387745, _387737, _387743))))], (356 ^ _176355) ^ [_188088, _188090] : [-(class_Groups_Ozero(_188088)), _188090 = _188088, class_Groups_Ozero(_188090)], (4286 ^ _176355) ^ [_335788, _335790, _335792] : [hBOOL(hAPP(hAPP(c_member(_335788), _335790), _335792)), -(c_Set_Oinsert(_335788, _335790, _335792) = _335792)], (4966 ^ _176355) ^ [_360562] : [hAPP(c_Nat_OSuc, _360562) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4220 ^ _176355) ^ [_333197, _333199, _333201, _333203] : [-(c_Set_Oinsert(_333197, _333199, c_Set_Oinsert(_333197, _333201, _333203)) = c_Set_Oinsert(_333197, _333201, c_Set_Oinsert(_333197, _333199, _333203)))], (5593 ^ _176355) ^ [_383981, _383983, _383985] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_383981), 5596 ^ _176355 : [(5597 ^ _176355) ^ [] : [_383983 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383981), _383983), _383985), -(_383985 = c_Groups_Ozero__class_Ozero(_383981))], (5603 ^ _176355) ^ [] : [_383985 = c_Groups_Ozero__class_Ozero(_383981), -(_383983 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383981), _383983), _383985))]]], (5294 ^ _176355) ^ [_372246, _372248] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _372246), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _372246), _372248)))))], (2414 ^ _176355) ^ [_264347, _264349, _264351] : [class_Orderings_Olinorder(_264347), 2417 ^ _176355 : [(2428 ^ _176355) ^ [] : [2429 ^ _176355 : [(2430 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_264347), _264351), _264349))], (2432 ^ _176355) ^ [] : [_264349 = _264351]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_264347), _264349), _264351))], (2418 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_264347), _264349), _264351))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_264347), _264351), _264349))), -(_264349 = _264351)]]], (5182 ^ _176355) ^ [_368501] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _368501))], (3630 ^ _176355) ^ [_308917, _308919, _308921, _308923, _308925, _308927] : [hBOOL(hAPP(hAPP(_308917, _308919), _308921)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_308923, tc_fun(_308925, tc_HOL_Obool)), _308917), _308927)), -(hBOOL(hAPP(hAPP(_308927, _308919), _308921)))], (1292 ^ _176355) ^ [_221301, _221303, _221305, _221307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_221301, tc_HOL_Obool)), _221303), _221305)), hBOOL(hAPP(hAPP(c_member(_221301), _221307), _221303)), -(hBOOL(hAPP(hAPP(c_member(_221301), _221307), _221305)))], (2568 ^ _176355) ^ [_269448, _269450, _269452, _269454] : [class_Orderings_Oorder(_269448), _269450 = _269452, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_269448), _269454), _269452)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_269448), _269454), _269450)))], (296 ^ _176355) ^ [_186318, _186320] : [-(class_Groups_Oab__semigroup__add(_186318)), _186320 = _186318, class_Groups_Oab__semigroup__add(_186320)], (4956 ^ _176355) ^ [_360154] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _360154), hAPP(c_Nat_OSuc, _360154))))], (6375 ^ _176355) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (6099 ^ _176355) ^ [_406258, _406260, _406262, _406264, _406266, _406268] : [c_Fun_Oinj__on(_406258, _406260, _406262, _406264), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_406260, tc_HOL_Obool), c_Set_Oimage(_406258, _406260, _406262, _406264)), _406266)), c_Fun_Oinj__on(_406260, _406258, _406268, _406266), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_406258, tc_HOL_Obool), c_Set_Oimage(_406260, _406258, _406268, _406266)), _406264)), c_Finite__Set_Ofinite(_406258, _406264), c_Finite__Set_Ofinite(_406260, _406266), -(c_Finite__Set_Ocard(_406258, _406264) = c_Finite__Set_Ocard(_406260, _406266))], (6188 ^ _176355) ^ [_409589] : [6190 ^ _176355 : [(6191 ^ _176355) ^ [_409758] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 6189 ^ [_409589, _409758]), _409589)))], (6193 ^ _176355) ^ [_409815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 6189 ^ [_409589, _409815]), _409815))]], -(c_Finite__Set_Ofinite(tc_Nat_Onat, _409589))], (6003 ^ _176355) ^ [_401483, _401485, _401487, _401489, _401491] : [-(hBOOL(hAPP(hAPP(c_member(_401483), _401485), c_Set_Oimage(_401487, _401483, _401489, _401491)))), 6004 ^ _176355 : [(6005 ^ _176355) ^ [_401603] : [hBOOL(hAPP(hAPP(c_member(_401487), _401603), _401491)), _401485 = hAPP(_401489, _401603)]]], (3540 ^ _176355) ^ [_305346, _305348, _305350] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_305346, tc_HOL_Obool), _305348), _305350)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_305346, tc_HOL_Obool), _305350), _305348)), -(_305348 = _305350)], (5834 ^ _176355) ^ [_394666, _394668, _394670, _394672, _394674] : [c_Finite__Set_Ofinite(_394666, c_Set_Oimage(_394668, _394666, _394670, c_Orderings_Otop__class_Otop(tc_fun(_394668, tc_HOL_Obool)))), -(c_Finite__Set_Ofinite(_394672, c_Set_Oimage(_394668, _394672, hAPP(c_COMBB(_394666, _394672, _394668, _394674), _394670), c_Orderings_Otop__class_Otop(tc_fun(_394668, tc_HOL_Obool)))))], (656 ^ _176355) ^ [_198947, _198949] : [_198949 = _198947, -(c_Orderings_Otop__class_Otop(_198949) = c_Orderings_Otop__class_Otop(_198947))], (4590 ^ _176355) ^ [_347104, _347106, _347108] : [class_Groups_Oordered__comm__monoid__add(_347104), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_347104, c_Groups_Ozero__class_Ozero(_347104)), _347106)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_347104, c_Groups_Ozero__class_Ozero(_347104)), _347108)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_347104, c_Groups_Ozero__class_Ozero(_347104)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_347104), _347106), _347108))))], (650 ^ _176355) ^ [_198729, _198731] : [_198731 = _198729, -(c_Groups_Ozero__class_Ozero(_198731) = c_Groups_Ozero__class_Ozero(_198729))], (6197 ^ _176355) ^ [_410004] : [c_Finite__Set_Ofinite(tc_Nat_Onat, _410004), 6201 ^ _176355 : [(6202 ^ _176355) ^ [_410214] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _410214), _410004)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _410214), 6200 ^ [_410004])))]]], (5375 ^ _176355) ^ [_375353, _375355] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _375353)), _375355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _375353), _375355)))], (5801 ^ _176355) ^ [_392853, _392855, _392857, _392859, _392861, _392863] : [-(c_Set_Oimage(_392853, _392855, _392857, c_Set_Oimage(_392859, _392853, _392861, _392863)) = c_Set_Oimage(_392859, _392855, hAPP(c_COMBB(_392853, _392855, _392859, _392857), _392861), _392863))], (4634 ^ _176355) ^ [_348498, _348500, _348502, _348504] : [class_Groups_Oordered__comm__monoid__add(_348498), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_348498, c_Groups_Ozero__class_Ozero(_348498)), _348500)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_348498, _348502), _348504)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_348498, _348502), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_348498), _348500), _348504))))], (6403 ^ _176355) ^ [_416815, _416817] : [-(class_Finite__Set_Ofinite(tc_prod(_416815, _416817))), class_Finite__Set_Ofinite(_416815), class_Finite__Set_Ofinite(_416817)], (3846 ^ _176355) ^ [_318539, _318541, _318543, _318545, _318547, _318549] : [c_Fun_Oinj__on(_318539, _318541, _318543, _318545), hBOOL(hAPP(hAPP(c_member(_318539), _318547), _318545)), hBOOL(hAPP(hAPP(c_member(_318539), _318549), _318545)), 3857 ^ _176355 : [(3858 ^ _176355) ^ [] : [hAPP(_318543, _318547) = hAPP(_318543, _318549), -(_318547 = _318549)], (3864 ^ _176355) ^ [] : [_318547 = _318549, -(hAPP(_318543, _318547) = hAPP(_318543, _318549))]]], (436 ^ _176355) ^ [_190648, _190650, _190652, _190654, _190656, _190658] : [-(c_Arrow__Order__Mirabelle_Obelow(_190658, _190654, _190650) = c_Arrow__Order__Mirabelle_Obelow(_190656, _190652, _190648)), _190658 = _190656, _190654 = _190652, _190650 = _190648], (1376 ^ _176355) ^ [_224371, _224373, _224375] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _224371), _224373)), _224375)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _224373), _224375)))], (4768 ^ _176355) ^ [_353079] : [class_Rings_Olinordered__semidom(_353079), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_353079), c_Groups_Oone__class_Oone(_353079)), c_Groups_Ozero__class_Ozero(_353079)))], (5385 ^ _176355) ^ [_375745, _375747, _375749] : [c_Finite__Set_Ofinite(_375745, _375747), -(hBOOL(hAPP(hAPP(c_member(_375745), _375749), _375747))), -(c_Finite__Set_Ocard(_375745, c_Set_Oinsert(_375745, _375749, _375747)) = hAPP(c_Nat_OSuc, c_Finite__Set_Ocard(_375745, _375747)))], (5457 ^ _176355) ^ [_378582, _378584, _378586, _378588, _378590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_378582, _378584)), hAPP(_378582, _378586))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_378588, _378588)), hAPP(hAPP(c_Product__Type_OPair(_378588, _378588), _378584), _378586)), c_Wellfounded_Omlex__prod(_378588, _378582, _378590))))], (1310 ^ _176355) ^ [_221972, _221974] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _221972), _221974)), -(_221972 = _221974), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _221972), _221974)))], (6339 ^ _176355) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (1266 ^ _176355) ^ [_220381, _220383] : [_220381 = _220383, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _220381), _220383)))], (2982 ^ _176355) ^ [_283337, _283339, _283341] : [class_Orderings_Oorder(_283337), -(_283339 = _283341), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_283337, _283341), _283339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_283337), _283341), _283339)))], (5676 ^ _176355) ^ [_387245, _387247] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _387245)), _387247)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _387245), _387247)))], (4476 ^ _176355) ^ [_343295, _343297] : [class_Groups_Ozero(_343295), 4479 ^ _176355 : [(4480 ^ _176355) ^ [] : [c_Groups_Ozero__class_Ozero(_343295) = _343297, -(_343297 = c_Groups_Ozero__class_Ozero(_343295))], (4486 ^ _176355) ^ [] : [_343297 = c_Groups_Ozero__class_Ozero(_343295), -(c_Groups_Ozero__class_Ozero(_343295) = _343297)]]], (4894 ^ _176355) ^ [_357494] : [c_Finite__Set_Ofinite(_357494, c_Orderings_Otop__class_Otop(tc_fun(_357494, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Finite__Set_Ocard(_357494, c_Orderings_Otop__class_Otop(tc_fun(_357494, tc_HOL_Obool))))))], (120 ^ _176355) ^ [_180639, _180641] : [-(class_Rings_Olinordered__idom(_180639)), _180641 = _180639, class_Rings_Olinordered__idom(_180641)], (2948 ^ _176355) ^ [_282283, _282285, _282287] : [class_Orderings_Olinorder(_282283), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_282283), _282285), _282287))), 2955 ^ _176355 : [(2956 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_282283, _282285), _282287)), -(_282285 = _282287)], (2962 ^ _176355) ^ [] : [_282285 = _282287, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_282283, _282285), _282287)))]]], (6363 ^ _176355) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (746 ^ _176355) ^ [_202354, _202356, _202358, _202360, _202362, _202364, _202366, _202368, _202370, _202372] : [-(c_COMBS(_202372, _202368, _202364, _202360, _202356) = c_COMBS(_202370, _202366, _202362, _202358, _202354)), _202372 = _202370, _202368 = _202366, _202364 = _202362, _202360 = _202358, _202356 = _202354], (6353 ^ _176355) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (4300 ^ _176355) ^ [_336352, _336354, _336356, _336358] : [-(c_Finite__Set_Ofinite(tc_sum(_336352, _336354), c_Sum__Type_OPlus(_336352, _336354, _336356, _336358))), c_Finite__Set_Ofinite(_336352, _336356), c_Finite__Set_Ofinite(_336354, _336358)], (6333 ^ _176355) ^ [_414842, _414844] : [class_Orderings_Oord(_414842), -(class_Orderings_Oord(tc_fun(_414844, _414842)))], (3612 ^ _176355) ^ [_308137, _308139, _308141, _308143, _308145, _308147] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_308137, tc_fun(_308139, tc_HOL_Obool)), _308141), _308143)), hBOOL(hAPP(hAPP(_308141, _308145), _308147)), -(hBOOL(hAPP(hAPP(_308143, _308145), _308147)))], (4964 ^ _176355) ^ [_360482] : [hAPP(c_Nat_OSuc, _360482) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3176 ^ _176355) ^ [_289927, _289929, _289931, _289933] : [class_Groups_Oordered__ab__semigroup__add(_289927), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_289927, _289929), _289931)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_289927, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_289927), _289933), _289929)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_289927), _289933), _289931))))], (4292 ^ _176355) ^ [_336083, _336085, _336087, _336089] : [c_Finite__Set_Ofinite(tc_sum(_336083, _336085), c_Sum__Type_OPlus(_336083, _336085, _336087, _336089)), 4295 ^ _176355 : [(4296 ^ _176355) ^ [] : [-(c_Finite__Set_Ofinite(_336083, _336087))], (4298 ^ _176355) ^ [] : [-(c_Finite__Set_Ofinite(_336085, _336089))]]], (376 ^ _176355) ^ [_188678, _188680] : [-(class_Orderings_Opreorder(_188678)), _188680 = _188678, class_Orderings_Opreorder(_188680)], (4326 ^ _176355) ^ [_337346, _337348, _337350, _337352] : [c_Finite__Set_Ofinite(tc_sum(_337346, _337348), c_Sum__Type_OPlus(_337346, _337348, _337350, _337352)), -(c_Finite__Set_Ofinite(_337348, _337352))], (4160 ^ _176355) ^ [_330492, _330494, _330496, _330498] : [hBOOL(hAPP(hAPP(c_member(_330492), _330494), c_Set_Oinsert(_330492, _330496, _330498))), -(_330494 = _330496), -(hBOOL(hAPP(hAPP(c_member(_330492), _330494), _330498)))], (2287 ^ _176355) ^ [_259969, _259971, _259973, _259975, _259977] : [class_Orderings_Oord(_259969), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_259971, _259969), _259973), _259975)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_259969, hAPP(_259973, _259977)), hAPP(_259975, _259977))))], (5016 ^ _176355) ^ [_362418, _362420] : [5017 ^ _176355 : [(5018 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362418), _362420))], (5020 ^ _176355) ^ [] : [_362418 = hAPP(c_Nat_OSuc, _362420)]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362418), hAPP(c_Nat_OSuc, _362420))))], (6033 ^ _176355) ^ [_402883, _402885, _402887, _402889, _402891] : [hBOOL(hAPP(hAPP(c_member(_402883), _402885), c_Set_Oimage(_402887, _402883, _402889, _402891))), -(hAPP(_402889, hAPP(c_Hilbert__Choice_Oinv__into(_402887, _402883, _402891, _402889), _402885)) = _402885)], (3676 ^ _176355) ^ [_311013, _311015, _311017, _311019, _311021, _311023] : [c_Fun_Oinj__on(_311013, _311015, _311017, _311019), hBOOL(hAPP(hAPP(c_member(_311013), _311021), _311019)), hAPP(_311017, _311021) = _311023, -(hAPP(c_Hilbert__Choice_Oinv__into(_311013, _311015, _311019, _311017), _311023) = _311021)], (4176 ^ _176355) ^ [_331172, _331174, _331176, _331178, _331180, _331182, _331184, _331186] : [c_Finite__Set_Ofolding__image__simple__idem(_331172, _331174, _331176, _331178, _331180, _331182), c_Finite__Set_Ofinite(_331174, _331184), -(hAPP(_331182, c_Set_Oinsert(_331174, _331186, _331184)) = hAPP(hAPP(_331176, hAPP(_331180, _331186)), hAPP(_331182, _331184)))], (4516 ^ _176355) ^ [_344615, _344617] : [class_Groups_Olinordered__ab__group__add(_344615), 4519 ^ _176355 : [(4520 ^ _176355) ^ [] : [c_Groups_Ozero__class_Ozero(_344615) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_344615), _344617), _344617), -(_344617 = c_Groups_Ozero__class_Ozero(_344615))], (4526 ^ _176355) ^ [] : [_344617 = c_Groups_Ozero__class_Ozero(_344615), -(c_Groups_Ozero__class_Ozero(_344615) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_344615), _344617), _344617))]]], (2211 ^ _176355) ^ [_257501, _257503, _257505, _257507] : [class_Orderings_Oorder(_257501), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_257501, _257503), _257505)), _257503 = _257507, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_257501, _257507), _257505)))], (2037 ^ _176355) ^ [_249992, _249994, _249996, _249998] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_249992, tc_HOL_Obool), _249994), _249996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_249992, tc_HOL_Obool)), _249996), _249998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_249992, tc_HOL_Obool)), _249994), _249998)))], (3166 ^ _176355) ^ [_289530, _289532, _289534, _289536] : [class_Groups_Oordered__ab__semigroup__add(_289530), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_289530, _289532), _289534)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_289530, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_289530), _289532), _289536)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_289530), _289534), _289536))))], (5752 ^ _176355) ^ [_390349, _390351, _390353, _390355, _390357, _390359] : [c_Set_Oimage(_390349, _390351, _390353, _390355) = _390357, hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_390351, tc_HOL_Obool), _390359), _390357)), -(c_Set_Oimage(_390349, _390351, _390353, c_Set_Oimage(_390351, _390349, c_Hilbert__Choice_Oinv__into(_390349, _390351, _390355, _390353), _390359)) = _390359)], (3923 ^ _176355) ^ [_321624, _321626, _321628, _321630, _321632] : [3925 ^ _176355 : [(3926 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_321624), 3924 ^ [_321624, _321626, _321628, _321630, _321632]), _321626)))], (3928 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_321628), hAPP(_321630, 3924 ^ [_321624, _321626, _321628, _321630, _321632])), hAPP(_321632, 3924 ^ [_321624, _321626, _321628, _321630, _321632])))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_321624, _321628)), _321630), c_FuncSet_OPi(_321624, _321628, _321626, _321632))))], (1945 ^ _176355) ^ [_246440, _246442] : [-(hBOOL(hAPP(hAPP(c_member(_246440), _246442), c_Orderings_Otop__class_Otop(tc_fun(_246440, tc_HOL_Obool)))))], (5850 ^ _176355) ^ [_395351, _395353, _395355, _395357] : [c_Finite__Set_Ofinite(_395351, _395353), 5853 ^ _176355 : [(5854 ^ _176355) ^ [] : [c_Fun_Oinj__on(_395351, _395355, _395357, _395353), -(c_Finite__Set_Ocard(_395355, c_Set_Oimage(_395351, _395355, _395357, _395353)) = c_Finite__Set_Ocard(_395351, _395353))], (5860 ^ _176355) ^ [] : [c_Finite__Set_Ocard(_395355, c_Set_Oimage(_395351, _395355, _395357, _395353)) = c_Finite__Set_Ocard(_395351, _395353), -(c_Fun_Oinj__on(_395351, _395355, _395357, _395353))]]], (1563 ^ _176355) ^ [_231543, _231545] : [-(_231543 = _231545), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _231543), _231545))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _231545), _231543)))], (1437 ^ _176355) ^ [_226957, _226959] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226957), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _226959), _226957))))], (5812 ^ _176355) ^ [_393484, _393486, _393488, _393490, _393492] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_393484, tc_HOL_Obool), _393486), c_Set_Oimage(_393488, _393484, _393490, _393492)))), 5813 ^ _176355 : [(5814 ^ _176355) ^ [_393608] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_393488, tc_HOL_Obool), _393608), _393492)), _393486 = c_Set_Oimage(_393488, _393484, _393490, _393608)]]], (6373 ^ _176355) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (730 ^ _176355) ^ [_201665, _201667] : [_201667 = _201665, -(c_COMBI(_201667) = c_COMBI(_201665))], (704 ^ _176355) ^ [_200757, _200759, _200761, _200763] : [-(c_Orderings_Oord__class_Oless__eq(_200763, _200759) = c_Orderings_Oord__class_Oless__eq(_200761, _200757)), _200763 = _200761, _200759 = _200757], (5160 ^ _176355) ^ [_367691] : [_367691 = hAPP(c_Nat_OSuc, _367691)], (3262 ^ _176355) ^ [_293271, _293273, _293275, _293277] : [class_Groups_Oordered__cancel__ab__semigroup__add(_293271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_293271), _293273), _293275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_293271), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_293271), _293277), _293273)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_293271), _293277), _293275))))], (6305 ^ _176355) ^ [_413907, _413909] : [class_Orderings_Opreorder(_413907), -(class_Orderings_Opreorder(tc_fun(_413909, _413907)))], (4260 ^ _176355) ^ [_334841, _334843, _334845, _334847] : [-(hBOOL(hAPP(hAPP(c_member(_334841), _334843), _334845))), -(hBOOL(hAPP(hAPP(c_member(_334841), _334843), _334847))), 4267 ^ _176355 : [(4268 ^ _176355) ^ [] : [c_Set_Oinsert(_334841, _334843, _334845) = c_Set_Oinsert(_334841, _334843, _334847), -(_334845 = _334847)], (4274 ^ _176355) ^ [] : [_334845 = _334847, -(c_Set_Oinsert(_334841, _334843, _334845) = c_Set_Oinsert(_334841, _334843, _334847))]]], (180 ^ _176355) ^ [_182808, _182810, _182812, _182814, _182816, _182818, _182820, _182822] : [-(c_Fun_Oinj__on(_182820, _182816, _182812, _182808)), c_Fun_Oinj__on(_182822, _182818, _182814, _182810), _182822 = _182820, _182818 = _182816, _182814 = _182812, _182810 = _182808], (1101 ^ _176355) ^ [] : [-(v_c____ = v_e____), -(v_a____ = v_b____), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), v_n____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Omktop), v_P____)), v_e____)), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_fequal), v_h____)), v_n____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Oabove), v_P____)), v_c____)), v_e____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Omkbot), v_P____)), v_e____)))), c_Arrow__Order__Mirabelle_OProf)), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), v_n____), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_Lab____)), v_Lba____)), c_Arrow__Order__Mirabelle_OProf)), 1183 ^ _176355 : [(1184 ^ _176355) ^ [] : 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^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_e____)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot, hAPP(v_P____, 1118 ^ [])), v_e____)))]]]]]], 1121 ^ _176355 : [(1128 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, 1118 ^ [])), v_n____))), 1131 ^ _176355 : [(1132 ^ _176355) ^ [] : [hAPP(v_h____, 1118 ^ []) = v_n____, -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_e____)), hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove, hAPP(v_P____, 1118 ^ [])), v_c____), v_e____))))], (1138 ^ _176355) ^ [] : [-(hAPP(v_h____, 1118 ^ []) = v_n____), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, 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[hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), v_Lab____))]], 1149 ^ _176355 : [(1150 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(v_h____, 1118 ^ [])), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), v_n____), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (1152 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), v_Lba____))]]]]], (3702 ^ _176355) ^ [_312096, _312098, _312100] : [-(c_FuncSet_OPi(_312096, _312098, _312100, hAPP(c_COMBK(tc_fun(_312098, tc_HOL_Obool), _312096), c_Orderings_Otop__class_Otop(tc_fun(_312098, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_312096, _312098), tc_HOL_Obool)))], (3456 ^ _176355) ^ [_300689] : [3458 ^ _176355 : [(3465 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3460 ^ [_300689]), 3461 ^ [_300689])), hAPP(_300689, 3457 ^ [_300689])))], (3463 ^ _176355) ^ [_301207] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3460 ^ [_300689]), 3461 ^ [_300689])), hAPP(3457 ^ [_300689], _301207))))], (3459 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), 3457 ^ [_300689]), c_Arrow__Order__Mirabelle_OProf)))]], -(c_Arrow__Order__Mirabelle_Ounanimity(_300689))], (5317 ^ 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-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _220615), _220619)))], (3650 ^ _176355) ^ [_309823, _309825, _309827, _309829, _309831, _309833] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_309823, _309825)), _309827), c_FuncSet_OPi(_309823, _309825, _309829, hAPP(c_COMBK(tc_fun(_309825, tc_HOL_Obool), _309823), _309831)))), hBOOL(hAPP(hAPP(c_member(_309823), _309833), _309829)), -(hBOOL(hAPP(hAPP(c_member(_309825), hAPP(_309827, _309833)), _309831)))], (6439 ^ _176355) ^ [] : [6440 ^ _176355 : [(6441 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_c____), v_e____)), hAPP(v_F, c_COMBS(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), 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hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_fequal), v_h____)), v_n____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Oabove), v_P____)), v_c____)), v_e____)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_Arrow__Order__Mirabelle_Oalt, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), tc_Arrow__Order__Mirabelle_Oindi, c_Arrow__Order__Mirabelle_Omkbot), v_P____)), v_e____))))))]]], (4218 ^ _176355) ^ [_333061, _333063, _333065] : [-(c_Set_Oinsert(_333061, _333063, c_Set_Oinsert(_333061, _333063, _333065)) = c_Set_Oinsert(_333061, _333063, _333065))], (5345 ^ _176355) ^ [_374255, _374257] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _374255)), _374257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _374255), _374257)))], (2091 ^ _176355) ^ [_253086, _253088, _253090, _253092] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_253086, tc_HOL_Obool), _253088), _253090)), hBOOL(hAPP(hAPP(c_member(_253086), _253092), _253088)), -(hBOOL(hAPP(hAPP(c_member(_253086), _253092), _253090)))], (1465 ^ _176355) ^ [_228042, _228044, _228046, _228048] : [_228042 = _228044, 1468 ^ _176355 : [(1469 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_228046), _228048), _228042)), -(hBOOL(hAPP(hAPP(c_member(_228046), _228048), _228044)))], (1475 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_228046), _228048), _228044)), -(hBOOL(hAPP(hAPP(c_member(_228046), _228048), _228042)))]]], (848 ^ _176355) ^ [_206084, _206086, _206088, _206090] : [-(hAPP(_206090, _206086) = hAPP(_206088, _206084)), _206090 = _206088, _206086 = _206084], (5363 ^ _176355) ^ [_374898, _374900] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _374898), _374900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _374898), hAPP(c_Nat_OSuc, _374900))))], (5674 ^ _176355) ^ [] : [-(c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, v_h____, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))) = c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))))], (366 ^ _176355) ^ [_188383, _188385] : [-(class_Groups_Oone(_188383)), _188385 = _188383, class_Groups_Oone(_188385)], (4510 ^ _176355) ^ [_344387, _344389] : [class_Groups_Ocomm__monoid__add(_344387), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_344387), c_Groups_Ozero__class_Ozero(_344387)), _344389) = _344389)], (4734 ^ _176355) ^ [_351934, _351936] : [class_Groups_Olinordered__ab__group__add(_351934), 4737 ^ _176355 : [(4738 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_351934), c_Groups_Ozero__class_Ozero(_351934)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_351934), _351936), _351936))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_351934), c_Groups_Ozero__class_Ozero(_351934)), _351936)))], (4744 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_351934), c_Groups_Ozero__class_Ozero(_351934)), _351936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_351934), c_Groups_Ozero__class_Ozero(_351934)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_351934), _351936), _351936))))]]], (386 ^ _176355) ^ [_188973, _188975] : [-(class_Orderings_Oorder(_188973)), _188975 = _188973, class_Orderings_Oorder(_188975)], (3312 ^ _176355) ^ [_295278, _295280, _295282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _295278), _295280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _295278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _295282), _295280))))], (3355 ^ _176355) ^ [_297090] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _297090), 3351 ^ [])), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_b____), v_a____)), hAPP(v_F, hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), _297090))), v_Lab____)), v_Lba____)))))], (2638 ^ _176355) ^ [_271812, _271814, _271816] : [class_Orderings_Opreorder(_271812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_271812), _271814), _271816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_271812), _271816), _271814))], (879 ^ _176355) ^ [] : [-(c_Arrow__Order__Mirabelle_Ounanimity(v_F))], (2450 ^ _176355) ^ [_265487, _265489, _265491] : [class_Orderings_Olinorder(_265487), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_265487), _265489), _265491))), 2457 ^ _176355 : [(2458 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_265487), _265491), _265489))), -(_265491 = _265489)], (2464 ^ _176355) ^ [] : [_265491 = _265489, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_265487), _265491), _265489))]]], (1786 ^ _176355) ^ [_240408, _240410, _240412, _240414, _240416, _240418] : [-(_240408 = _240410), -(_240412 = _240414), -(_240408 = _240414), -(_240410 = _240412), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _240416), c_Arrow__Order__Mirabelle_OProf)), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _240418), c_Arrow__Order__Mirabelle_OProf)), 1814 ^ _176355 : [(1815 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _240408), _240410)), hAPP(_240416, 1811 ^ [_240408, _240410, _240412, _240414, _240416, _240418]))))], (1817 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _240412), _240414)), hAPP(_240418, 1811 ^ [_240408, _240410, _240412, _240414, _240416, _240418])))]], 1818 ^ _176355 : [(1819 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _240412), _240414)), hAPP(_240418, 1811 ^ [_240408, _240410, _240412, _240414, _240416, _240418]))))], (1821 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _240408), _240410)), hAPP(_240416, 1811 ^ [_240408, _240410, _240412, _240414, _240416, _240418])))]], hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _240408), _240410)), hAPP(v_F, _240416))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _240412), _240414)), hAPP(v_F, _240418))))], (891 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_b____), v_a____)), v_Lab____))], (4558 ^ _176355) ^ [_346042, _346044] : [class_Groups_Olinordered__ab__group__add(_346042), 4561 ^ _176355 : [(4562 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_346042, c_Groups_Ozero__class_Ozero(_346042)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_346042), _346044), _346044))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_346042, c_Groups_Ozero__class_Ozero(_346042)), _346044)))], (4568 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_346042, c_Groups_Ozero__class_Ozero(_346042)), _346044)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_346042, c_Groups_Ozero__class_Ozero(_346042)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_346042), _346044), _346044))))]]], (1336 ^ _176355) ^ [_222825, _222827] : [1337 ^ _176355 : [(1338 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _222825), _222827))], (1340 ^ _176355) ^ [] : [_222825 = _222827]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _222825), _222827)))], (6367 ^ _176355) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (3888 ^ _176355) ^ [_320014, _320016, _320018, _320020, _320022] : [c_Fun_Oinj__on(_320014, _320016, _320018, _320020), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_320014, tc_HOL_Obool), _320022), _320020)), -(c_Fun_Oinj__on(_320014, _320016, _320018, _320022))], (1344 ^ _176355) ^ [_223160, _223162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _223160), _223162)), 1347 ^ _176355 : [(1348 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _223160), _223162)))], (1350 ^ _176355) ^ [] : [_223160 = _223162]]], (2 ^ _176355) ^ [_176499] : [-(_176499 = _176499)], (130 ^ _176355) ^ [_180934, _180936] : [-(class_Rings_Oring__1(_180934)), _180936 = _180934, class_Rings_Oring__1(_180936)], (276 ^ _176355) ^ [_185728, _185730] : [-(class_Groups_Ocancel__semigroup__add(_185728)), _185730 = _185728, class_Groups_Ocancel__semigroup__add(_185730)], (1204 ^ _176355) ^ [_217032, _217034, _217036, _217038] : [_217032 = _217034, 1209 ^ _176355 : [(1210 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_217036), _217038), _217032)))], (1212 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_217036), _217038), _217034)))]], 1213 ^ _176355 : [(1214 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_217036), _217038), _217032))], (1216 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(_217036), _217038), _217034))]]], (3622 ^ _176355) ^ [_308532, _308534, _308536] : [_308532 = _308534, 3625 ^ _176355 : [(3626 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_308536, tc_HOL_Obool), _308532), _308534)))], (3628 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_308536, tc_HOL_Obool), _308534), _308532)))]]], (5746 ^ _176355) ^ [_390045, _390047, _390049, _390051] : [c_Fun_Oinj__on(_390045, _390047, _390049, _390051), -(c_Finite__Set_Ocard(_390047, c_Set_Oimage(_390045, _390047, _390049, _390051)) = c_Finite__Set_Ocard(_390045, _390051))], (3431 ^ _176355) ^ [_299621, _299623, _299625] : [-(_299621 = _299623), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), _299625), c_Arrow__Order__Mirabelle_OLin)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), c_Arrow__Order__Mirabelle_Obelow(_299625, _299621, _299623)), c_Arrow__Order__Mirabelle_OLin)))], (1949 ^ _176355) ^ [] : [-(c_Fun_Oinj__on(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, v_h____, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))], (5587 ^ _176355) ^ [_383645, _383647, _383649, _383651, _383653] : [class_Rings_Ocomm__semiring__1(_383645), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383645), _383647), _383649)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383645), _383651), _383653)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383645), _383647), _383651)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_383645), _383649), _383653)))], (2059 ^ _176355) ^ [_250894, _250896, _250898, _250900] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_250894, tc_fun(_250896, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_250894, tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_fun(_250896, tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_250896, tc_fun(tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_fun(_250896, tc_HOL_Obool)), _250894, c_COMBC(_250896, tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_250896, tc_prod(_250894, _250896)), tc_fun(_250896, tc_fun(tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_HOL_Obool)), _250894, c_COMBB(tc_prod(_250894, _250896), tc_fun(tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_HOL_Obool), _250896, c_member(tc_prod(_250894, _250896)))), c_Product__Type_OPair(_250894, _250896)))), _250898)), hAPP(hAPP(c_COMBC(_250894, tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_fun(_250896, tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_250896, tc_fun(tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_fun(_250896, tc_HOL_Obool)), _250894, c_COMBC(_250896, tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(_250896, tc_prod(_250894, _250896)), tc_fun(_250896, tc_fun(tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_HOL_Obool)), _250894, c_COMBB(tc_prod(_250894, _250896), tc_fun(tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), tc_HOL_Obool), _250896, c_member(tc_prod(_250894, _250896)))), c_Product__Type_OPair(_250894, _250896)))), _250900))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_250894, _250896), tc_HOL_Obool), _250898), _250900)))], (4988 ^ _176355) ^ [_361402, _361404] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361402), _361404)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361402), hAPP(c_Nat_OSuc, _361404))))], (468 ^ _176355) ^ [_191881, _191883, _191885, _191887, _191889, _191891, _191893, _191895] : [-(c_Recdef_Osame__fst(_191895, _191891, _191887, _191883) = c_Recdef_Osame__fst(_191893, _191889, _191885, _191881)), _191895 = _191893, _191891 = _191889, _191887 = _191885, _191883 = _191881], (510 ^ _176355) ^ [_193421, _193423, _193425, _193427] : [-(c_Wellfounded_Omeasure(_193427, _193423) = c_Wellfounded_Omeasure(_193425, _193421)), _193427 = _193425, _193423 = _193421], (3506 ^ _176355) ^ [_303276] : [-(c_Arrow__Order__Mirabelle_OIIA(_303276)), 3508 ^ _176355 : [(3512 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), 3510 ^ [_303276]), c_Arrow__Order__Mirabelle_OProf)))], (3509 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), 3507 ^ [_303276]), c_Arrow__Order__Mirabelle_OProf)))], (3516 ^ _176355) ^ [_304285] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3513 ^ [_303276]), 3514 ^ [_303276])), hAPP(3507 ^ [_303276], _304285))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3513 ^ [_303276]), 3514 ^ [_303276])), hAPP(3510 ^ [_303276], _304285))))], (3528 ^ _176355) ^ [] : [3529 ^ _176355 : [(3530 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3513 ^ [_303276]), 3514 ^ [_303276])), hAPP(_303276, 3507 ^ [_303276]))))], (3532 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3513 ^ [_303276]), 3514 ^ [_303276])), hAPP(_303276, 3510 ^ [_303276])))]], 3533 ^ _176355 : [(3534 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3513 ^ [_303276]), 3514 ^ [_303276])), hAPP(_303276, 3510 ^ [_303276]))))], (3536 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3513 ^ [_303276]), 3514 ^ [_303276])), hAPP(_303276, 3507 ^ [_303276])))]]], (3522 ^ _176355) ^ [_304565] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3513 ^ [_303276]), 3514 ^ [_303276])), hAPP(3510 ^ [_303276], _304565))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), 3513 ^ [_303276]), 3514 ^ [_303276])), hAPP(3507 ^ [_303276], _304565))))]]], (3640 ^ _176355) ^ [_309354, _309356, _309358, _309360, _309362, _309364] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_309354, _309356)), _309358), c_FuncSet_OPi(_309354, _309356, _309360, _309362))), -(hBOOL(hAPP(hAPP(c_member(_309356), hAPP(_309358, _309364)), hAPP(_309362, _309364)))), hBOOL(hAPP(hAPP(c_member(_309354), _309364), _309360))], (5096 ^ _176355) ^ [_365343, _365345] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _365343), _365345))), 5099 ^ _176355 : [(5100 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _365343), hAPP(c_Nat_OSuc, _365345))), -(_365343 = _365345)], (5106 ^ _176355) ^ [] : [_365343 = _365345, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _365343), hAPP(c_Nat_OSuc, _365345))))]]], (1519 ^ _176355) ^ [_229972, _229974, _229976] : [1520 ^ _176355 : [(1521 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _229972), _229974)))], (1523 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(_229976, _229974), _229972))]], 1526 ^ _176355 : [(1527 ^ _176355) ^ [] : [-(_229972 = _229974)], (1529 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(_229976, _229974), _229972))]], 1532 ^ _176355 : [(1533 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _229974), _229972)))], (1535 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(_229976, _229974), _229972))]], -(hBOOL(hAPP(hAPP(_229976, _229974), _229972)))], (3870 ^ _176355) ^ [_319379, _319381, _319383, _319385, _319387, _319389] : [c_Fun_Oinj__on(_319379, _319381, _319383, _319385), hAPP(_319383, _319387) = hAPP(_319383, _319389), hBOOL(hAPP(hAPP(c_member(_319379), _319387), _319385)), hBOOL(hAPP(hAPP(c_member(_319379), _319389), _319385)), -(_319387 = _319389)], (3296 ^ _176355) ^ [_294625, _294627, _294629, _294631] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_294625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_294625), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_294625), _294627), _294629)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_294625), _294627), _294631))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_294625), _294629), _294631)))], (5118 ^ _176355) ^ [_366063, _366065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _366063), _366065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _366063)), hAPP(c_Nat_OSuc, _366065))))], (887 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_b____), v_a____)), v_Lba____)))], (520 ^ _176355) ^ [_193808, _193810, _193812, _193814, _193816, _193818] : [-(c_Wellfounded_Omlex__prod(_193818, _193814, _193810) = c_Wellfounded_Omlex__prod(_193816, _193812, _193808)), _193818 = _193816, _193814 = _193812, _193810 = _193808], (4792 ^ _176355) ^ [_353919, _353921] : [-(c_Finite__Set_Ofinite(_353919, _353921)), -(c_Finite__Set_Ocard(_353919, _353921) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4420 ^ _176355) ^ [_341316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _341316), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6377 ^ _176355) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (2123 ^ _176355) ^ [_254426, _254428] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), _254426), c_Arrow__Order__Mirabelle_OLin)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omkbot, _254426), _254428)), c_Arrow__Order__Mirabelle_OLin)))], (1410 ^ _176355) ^ [_225861, _225863, _225865] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _225861), _225863)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _225861), _225865))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _225863), _225865)))], (534 ^ _176355) ^ [_194296, _194298, _194300, _194302] : [-(c_Nat_Osize__class_Osize(_194302, _194298) = c_Nat_Osize__class_Osize(_194300, _194296)), _194302 = _194300, _194298 = _194296], (306 ^ _176355) ^ [_186613, _186615] : [-(class_Groups_Ocomm__monoid__add(_186613)), _186615 = _186613, class_Groups_Ocomm__monoid__add(_186615)], (4750 ^ _176355) ^ [_352456] : [class_Rings_Olinordered__semidom(_352456), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_352456, c_Groups_Oone__class_Oone(_352456)), c_Groups_Ozero__class_Ozero(_352456)))], (3064 ^ _176355) ^ [_285963, _285965, _285967] : [class_Orderings_Oorder(_285963), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_285963, _285965), _285967)), -(_285967 = _285965), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_285963), _285965), _285967)))], (5485 ^ _176355) ^ [_379615] : [-(c_Nat_Osize__class_Osize(tc_Nat_Onat, _379615) = _379615)], (2610 ^ _176355) ^ [_270858, _270860, _270862, _270864] : [class_Orderings_Opreorder(_270858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_270858), _270860), _270862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_270858), _270862), _270864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_270858), _270860), _270864)))], (5704 ^ _176355) ^ [_388406, _388408, _388410, _388412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Finite__Set_Ocard(_388406, c_Set_Oimage(_388408, _388406, _388410, _388412))), c_Finite__Set_Ocard(_388408, _388412))), c_Fun_Oinj__on(_388408, _388406, _388410, _388412)], (6437 ^ _176355) ^ [] : [hBOOL(c_fFalse)], (5832 ^ _176355) ^ [_394508, _394510, _394512] : [-(c_Nat_Onat_Onat__case(_394508, _394510, _394512, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _394510)], (1422 ^ _176355) ^ [_226364, _226366] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _226364), _226366)), -(_226366 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _226364), 1425 ^ [_226364, _226366]))], (4972 ^ _176355) ^ [_360832, _360834] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _360832)), _360834)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _360832), _360834)))], (5551 ^ _176355) ^ [_381867, _381869] : [class_Rings_Ocomm__semiring__1(_381867), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_381867), _381869), c_Groups_Ozero__class_Ozero(_381867)) = _381869)], (5774 ^ _176355) ^ [_391419, _391421, _391423] : [c_Set_Oimage(_391419, _391421, _391423, c_Orderings_Otop__class_Otop(tc_fun(_391419, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_391421, tc_HOL_Obool)), 5777 ^ _176355 : [(5778 ^ _176355) ^ [_391585] : [-(hAPP(_391423, hAPP(c_Hilbert__Choice_Oinv__into(_391419, _391421, c_Orderings_Otop__class_Otop(tc_fun(_391419, tc_HOL_Obool)), _391423), _391585)) = _391585)]]], (2746 ^ _176355) ^ [_275627] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), _275627), c_Arrow__Order__Mirabelle_OLin)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi), _275627)), c_Arrow__Order__Mirabelle_OProf)))], (110 ^ _176355) ^ [_180344, _180346] : [-(class_Groups_Olinordered__ab__group__add(_180344)), _180346 = _180344, class_Groups_Olinordered__ab__group__add(_180346)], (1370 ^ _176355) ^ [_224109, _224111, _224113] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _224109), _224111)), _224113)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _224109), _224113)))], (5209 ^ _176355) ^ [_369568] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _369568), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_369568 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (406 ^ _176355) ^ [_189563, _189565] : [-(class_Orderings_Oord(_189563)), _189565 = _189563, class_Orderings_Oord(_189565)], (3353 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 3351 ^ []), c_Finite__Set_Ocard(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))))], (768 ^ _176355) ^ [_203120, _203122] : [_203122 = _203120, -(c_member(_203122) = c_member(_203120))], (4008 ^ _176355) ^ [_324768, _324770] : [class_Finite__Set_Ofinite(_324768), -(c_Finite__Set_Ofinite(_324768, _324770))], (6397 ^ _176355) ^ [_416611] : [class_Finite__Set_Ofinite(_416611), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_416611)))], (1609 ^ _176355) ^ [_233294, _233296, _233298] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _233294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _233296), _233298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _233296), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _233294), _233298)))], (6419 ^ _176355) ^ [_417442, _417444, _417446, _417448, _417450, _417452] : [-(hAPP(hAPP(c_COMBB(_417442, _417444, _417446, _417448), _417450), _417452) = hAPP(_417448, hAPP(_417450, _417452)))], (1551 ^ _176355) ^ [_231077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _231077), _231077))], (4450 ^ _176355) ^ [_342369] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _342369), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _342369)], (1256 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_Lab____), c_Arrow__Order__Mirabelle_OLin)))], (4232 ^ _176355) ^ [_333671, _333673, _333675, _333677] : [4233 ^ _176355 : [(4234 ^ _176355) ^ [] : [_333673 = _333677], (4236 ^ _176355) ^ [] : [hBOOL(hAPP(_333675, _333677))]], -(hBOOL(hAPP(c_Set_Oinsert(_333671, _333673, _333675), _333677)))], (6371 ^ _176355) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (4774 ^ _176355) ^ [_353333, _353335] : [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), _353333), _353335))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _353333))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _353335)))], (5357 ^ _176355) ^ [_374710, _374712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _374710), hAPP(c_Nat_OSuc, _374712))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _374710), _374712)))], (6351 ^ _176355) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (600 ^ _176355) ^ [_196891, _196893, _196895, _196897, _196899, _196901] : [-(c_Set_Oinsert(_196901, _196897, _196893) = c_Set_Oinsert(_196899, _196895, _196891)), _196901 = _196899, _196897 = _196895, _196893 = _196891], (20 ^ _176355) ^ [_177235, _177237, _177239, _177241, _177243, _177245, _177247, _177249, _177251, _177253] : [-(c_FunDef_Oin__rel(_177251, _177247, _177243, _177239, _177235)), c_FunDef_Oin__rel(_177253, _177249, _177245, _177241, _177237), _177253 = _177251, _177249 = _177247, _177245 = _177243, _177241 = _177239, _177237 = _177235], (5646 ^ _176355) ^ [_386039, _386041] : [c_Finite__Set_Ofinite(_386039, _386041), -(c_Finite__Set_Ocard(_386039, _386041) = c_Finite__Set_Ofold__image(tc_Nat_Onat, _386039, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _386039), c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _386041))], (1573 ^ _176355) ^ [_231818, _231820] : [1574 ^ _176355 : [(1575 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _231818), _231820))], (1577 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _231820), _231818))]], _231818 = _231820], (3186 ^ _176355) ^ [_290338, _290340, _290342, _290344, _290346] : [class_Groups_Oordered__ab__semigroup__add(_290338), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_290338, _290340), _290342)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_290338, _290344), _290346)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_290338, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_290338), _290340), _290344)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_290338), _290342), _290346))))], (1607 ^ _176355) ^ [_233160, _233162, _233164] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _233160), _233162)), _233164) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _233160), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _233162), _233164)))], (3272 ^ _176355) ^ [_293690, _293692, _293694, _293696, _293698] : [class_Groups_Oordered__cancel__ab__semigroup__add(_293690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_293690), _293692), _293694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_293690), _293696), _293698)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_293690), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_293690), _293692), _293696)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_293690), _293694), _293698))))], (774 ^ _176355) ^ [_203366, _203368, _203370, _203372] : [-(c_Product__Type_OPair(_203372, _203368) = c_Product__Type_OPair(_203370, _203366)), _203372 = _203370, _203368 = _203366], (4812 ^ _176355) ^ [_354632, _354634, _354636] : [class_Groups_Oordered__comm__monoid__add(_354632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_354632), _354634), c_Groups_Ozero__class_Ozero(_354632))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_354632, _354636), c_Groups_Ozero__class_Ozero(_354632))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_354632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_354632), _354634), _354636)), c_Groups_Ozero__class_Ozero(_354632))))], (3586 ^ _176355) ^ [_307083, _307085, _307087] : [_307083 = _307085, -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_307087, tc_HOL_Obool), _307085), _307083)))], (3078 ^ _176355) ^ [_286418, _286420, _286422, _286424] : [class_Orderings_Opreorder(_286418), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_286418), _286420), _286422)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_286418, _286422), _286424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_286418), _286420), _286424)))], (3006 ^ _176355) ^ [_284124, _284126, _284128] : [class_Orderings_Opreorder(_284124), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_284124), _284126), _284128)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_284124, _284126), _284128)))], (4900 ^ _176355) ^ [_357728, _357730] : [class_Rings_Olinordered__idom(_357728), 4903 ^ _176355 : [(4904 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_357728), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_357728), _357730), _357730)), c_Groups_Ozero__class_Ozero(_357728))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_357728), _357730), c_Groups_Ozero__class_Ozero(_357728))))], (4910 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_357728), _357730), c_Groups_Ozero__class_Ozero(_357728))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_357728), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_357728), _357730), _357730)), c_Groups_Ozero__class_Ozero(_357728))))]]], (4994 ^ _176355) ^ [_361667, _361669] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _361667)), hAPP(c_Nat_OSuc, _361669))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _361667), _361669)))], (4538 ^ _176355) ^ [_345337, _345339] : [class_Groups_Ocomm__monoid__add(_345337), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_345337), _345339), c_Groups_Ozero__class_Ozero(_345337)) = _345339)], (6013 ^ _176355) ^ [_401993, _401995, _401997, _401999, _402001, _402003] : [hAPP(c_Hilbert__Choice_Oinv__into(_401993, _401995, _401997, _401999), _402001) = hAPP(c_Hilbert__Choice_Oinv__into(_401993, _401995, _401997, _401999), _402003), hBOOL(hAPP(hAPP(c_member(_401995), _402001), c_Set_Oimage(_401993, _401995, _401999, _401997))), hBOOL(hAPP(hAPP(c_member(_401995), _402003), c_Set_Oimage(_401993, _401995, _401999, _401997))), -(_402001 = _402003)], (2484 ^ _176355) ^ [_266556, _266558, _266560] : [class_Orderings_Oorder(_266556), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_266556), _266558), _266560)), _266558 = _266560], (5799 ^ _176355) ^ [_392676, _392678, _392680, _392682, _392684] : [-(c_Set_Oimage(_392676, _392678, _392680, c_Set_Oinsert(_392676, _392682, _392684)) = c_Set_Oinsert(_392678, hAPP(_392680, _392682), c_Set_Oimage(_392676, _392678, _392680, _392684)))], (5888 ^ _176355) ^ [_396806, _396808] : [c_Finite__Set_Ofinite(_396806, c_Orderings_Otop__class_Otop(tc_fun(_396806, tc_HOL_Obool))), c_Set_Oimage(_396806, _396806, _396808, c_Orderings_Otop__class_Otop(tc_fun(_396806, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_396806, tc_HOL_Obool)), -(c_Fun_Oinj__on(_396806, _396806, _396808, c_Orderings_Otop__class_Otop(tc_fun(_396806, tc_HOL_Obool))))], (4170 ^ _176355) ^ [_330864, _330866, _330868] : [c_Finite__Set_Ofinite(_330864, _330866), -(c_Finite__Set_Ofinite(_330864, c_Set_Oinsert(_330864, _330868, _330866)))], (3441 ^ _176355) ^ [_299976] : [c_Arrow__Order__Mirabelle_Ounanimity(_299976), 3444 ^ _176355 : [(3445 ^ _176355) ^ [_300161] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _300161), c_Arrow__Order__Mirabelle_OProf)), 3448 ^ _176355 : [(3449 ^ _176355) ^ [_300362, _300364] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _300364), _300362)), hAPP(_300161, 3450 ^ [_299976, _300161, _300362, _300364]))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _300364), _300362)), hAPP(_299976, _300161))))]]]]], (5828 ^ _176355) ^ [_394256, _394258] : [-(c_Set_Oimage(_394256, _394256, c_COMBI(_394256), _394258) = _394258)], (6357 ^ _176355) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (4210 ^ _176355) ^ [_332678, _332680, _332682, _332684] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_332678, tc_HOL_Obool), _332680), _332682)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_332678, tc_HOL_Obool), _332680), c_Set_Oinsert(_332678, _332684, _332682))))], (1382 ^ _176355) ^ [_224647, _224649, _224651, _224653] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _224647), _224649)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _224651), _224653)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _224647), _224651)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _224649), _224653))))], (4940 ^ _176355) ^ [_359591, _359593] : [c_Finite__Set_Ofinite(tc_fun(_359591, _359593), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_359591, _359593), tc_HOL_Obool))), -(c_Finite__Set_Ocard(_359593, c_Orderings_Otop__class_Otop(tc_fun(_359593, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(c_Finite__Set_Ofinite(_359591, c_Orderings_Otop__class_Otop(tc_fun(_359591, tc_HOL_Obool))))], (5044 ^ _176355) ^ [_363522, _363524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _363522)), _363524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _363522), _363524)))], (1829 ^ _176355) ^ [_242035, _242037, _242039, _242041, _242043, _242045] : [-(_242035 = _242037), -(_242039 = _242041), -(_242035 = _242041), -(_242037 = _242039), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _242043), c_Arrow__Order__Mirabelle_OProf)), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _242045), c_Arrow__Order__Mirabelle_OProf)), 1857 ^ _176355 : [(1858 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _242035), _242037)), hAPP(_242043, 1854 ^ [_242035, _242037, _242039, _242041, _242043, _242045]))))], (1860 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _242039), _242041)), hAPP(_242045, 1854 ^ [_242035, _242037, _242039, _242041, _242043, _242045])))]], 1861 ^ _176355 : [(1862 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _242039), _242041)), hAPP(_242045, 1854 ^ [_242035, _242037, _242039, _242041, _242043, _242045]))))], (1864 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _242035), _242037)), hAPP(_242043, 1854 ^ [_242035, _242037, _242039, _242041, _242043, _242045])))]], 1865 ^ _176355 : [(1866 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _242035), _242037)), hAPP(v_F, _242043))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _242039), _242041)), hAPP(v_F, _242045))))], (1872 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _242039), _242041)), hAPP(v_F, _242045))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _242035), _242037)), hAPP(v_F, _242043))))]]], (1232 ^ _176355) ^ [_219009, _219011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _219009), _219011)), _219011))], (4868 ^ _176355) ^ [_356592, _356594, _356596] : [class_Groups_Oordered__comm__monoid__add(_356592), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_356592), c_Groups_Ozero__class_Ozero(_356592)), _356594)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_356592, c_Groups_Ozero__class_Ozero(_356592)), _356596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_356592), c_Groups_Ozero__class_Ozero(_356592)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_356592), _356594), _356596))))], (5918 ^ _176355) ^ [_397879, _397881, _397883] : [c_Finite__Set_Ofinite(_397879, _397881), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_397879, tc_HOL_Obool), c_Set_Oimage(_397879, _397879, _397883, _397881)), _397881)), c_Fun_Oinj__on(_397879, _397879, _397883, _397881), -(c_Set_Oimage(_397879, _397879, _397883, _397881) = _397881)], (3819 ^ _176355) ^ [_317433, _317435] : [3821 ^ _176355 : [(3822 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), 3820 ^ [_317433, _317435]), c_Arrow__Order__Mirabelle_OProf)))], (3824 ^ _176355) ^ [] : [hAPP(_317433, 3820 ^ [_317433, _317435]) = hAPP(3820 ^ [_317433, _317435], _317435)]], -(c_Arrow__Order__Mirabelle_Odictator(_317433, _317435))], (5441 ^ _176355) ^ [_377773, _377775, _377777, _377779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_377779, _377775)), hAPP(_377779, _377777))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_377773, _377773)), hAPP(hAPP(c_Product__Type_OPair(_377773, _377773), _377775), _377777)), c_Wellfounded_Omeasure(_377773, _377779))))], (885 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), v_Lab____)))], (1320 ^ _176355) ^ [_222294, _222296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _222294), _222296)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _222294), _222296)))], (4060 ^ _176355) ^ [_326564, _326566] : [-(c_Finite__Set_Ofinite(tc_sum(_326564, _326566), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_326564, _326566), tc_HOL_Obool)))), c_Finite__Set_Ofinite(_326564, c_Orderings_Otop__class_Otop(tc_fun(_326564, tc_HOL_Obool))), c_Finite__Set_Ofinite(_326566, c_Orderings_Otop__class_Otop(tc_fun(_326566, tc_HOL_Obool)))], (1539 ^ _176355) ^ [_230665, _230667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _230665), _230667)), _230665 = _230667], (140 ^ _176355) ^ [_181229, _181231] : [-(class_Int_Oring__char__0(_181229)), _181231 = _181229, class_Int_Oring__char__0(_181231)], (5447 ^ _176355) ^ [_378105, _378107, _378109, _378111, _378113] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(_378105, _378107)), hAPP(_378105, _378109))), hBOOL(hAPP(hAPP(c_member(tc_prod(_378111, _378111)), hAPP(hAPP(c_Product__Type_OPair(_378111, _378111), _378107), _378109)), _378113)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_378111, _378111)), hAPP(hAPP(c_Product__Type_OPair(_378111, _378111), _378107), _378109)), c_Wellfounded_Omlex__prod(_378111, _378105, _378113))))], (3807 ^ _176355) ^ [_316944, _316946] : [-(c_Fun_Oinj__on(_316944, _316944, c_COMBI(_316944), _316946))], (5493 ^ _176355) ^ [_379949, _379951, _379953] : [class_Rings_Oring__1(_379949), hBOOL(hAPP(hAPP(c_member(_379949), _379951), c_Int_Oring__1__class_OInts(_379949))), hBOOL(hAPP(hAPP(c_member(_379949), _379953), c_Int_Oring__1__class_OInts(_379949))), -(hBOOL(hAPP(hAPP(c_member(_379949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_379949), _379951), _379953)), c_Int_Oring__1__class_OInts(_379949))))], (5006 ^ _176355) ^ [_362134, _362136] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362134), hAPP(c_Nat_OSuc, _362136))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _362134), _362136))), -(_362134 = hAPP(c_Nat_OSuc, _362136))], (3120 ^ _176355) ^ [_287858, _287860, _287862, _287864] : [class_Orderings_Oorder(_287858), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_287858, _287860), _287862)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_287858), _287864), _287860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_287858), _287864), _287862)))], (959 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), hAPP(v_F, hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool), tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), tc_Arrow__Order__Mirabelle_Oindi, c_If(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, tc_HOL_Obool), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Oord__class_Oless(tc_Nat_Onat)), v_h____)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), v_n____), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), v_Lab____)), v_Lba____)))))], (286 ^ _176355) ^ [_186023, _186025] : [-(class_Rings_Olinordered__semidom(_186023)), _186025 = _186023, class_Rings_Olinordered__semidom(_186025)], (6125 ^ _176355) ^ [_407131, _407133, _407135, _407137, _407139] : [c_Fun_Oinj__on(_407131, _407133, _407135, _407137), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_407133, tc_HOL_Obool), c_Set_Oimage(_407131, _407133, _407135, _407137)), _407139)), c_Finite__Set_Ofinite(_407133, _407139), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Finite__Set_Ocard(_407131, _407137)), c_Finite__Set_Ocard(_407133, _407139))))], (3570 ^ _176355) ^ [_306480, _306482, _306484, _306486] : [hBOOL(hAPP(_306480, _306482)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_306484, tc_HOL_Obool), _306480), _306486)), -(hBOOL(hAPP(_306486, _306482)))], (4222 ^ _176355) ^ [_333383, _333385, _333387, _333389] : [hBOOL(hAPP(c_Set_Oinsert(_333383, _333385, _333387), _333389)), -(_333385 = _333389), -(hBOOL(hAPP(_333387, _333389)))], (4546 ^ _176355) ^ [_345660] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _345660), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_345660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3050 ^ _176355) ^ [_285522, _285524, _285526] : [class_Orderings_Oorder(_285522), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_285522, _285524), _285526)), -(_285524 = _285526), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_285522), _285524), _285526)))], (4968 ^ _176355) ^ [_360642] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _360642)], (1302 ^ _176355) ^ [_221668, _221670] : [1303 ^ _176355 : [(1304 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _221668), _221670))], (1306 ^ _176355) ^ [] : [_221668 = _221670]], -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _221668), _221670)))], (6415 ^ _176355) ^ [_417152, _417154] : [-(hAPP(c_COMBI(_417152), _417154) = _417154)], (4704 ^ _176355) ^ [_350928, _350930, _350932] : [class_Groups_Oordered__comm__monoid__add(_350928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_350928), c_Groups_Ozero__class_Ozero(_350928)), _350930)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_350928), c_Groups_Ozero__class_Ozero(_350928)), _350932)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_350928), c_Groups_Ozero__class_Ozero(_350928)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_350928), _350930), _350932))))], (4392 ^ _176355) ^ [_340074, _340076, _340078, _340080, _340082, _340084, _340086, _340088] : [c_Finite__Set_Ofolding__image__simple(_340074, _340076, _340078, _340080, _340082, _340084), c_Finite__Set_Ofinite(_340076, _340086), -(hBOOL(hAPP(hAPP(c_member(_340076), _340088), _340086))), -(hAPP(_340084, c_Set_Oinsert(_340076, _340088, _340086)) = hAPP(hAPP(_340078, hAPP(_340082, _340088)), hAPP(_340084, _340086)))], (2011 ^ _176355) ^ [_248902, _248904, _248906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_248902, tc_HOL_Obool)), _248904), _248906)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_248902, tc_HOL_Obool), _248904), _248906)))], (5234 ^ _176355) ^ [_370452, _370454] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _370452), _370454), 5239 ^ _176355 : [(5240 ^ _176355) ^ [] : [-(_370452 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5242 ^ _176355) ^ [] : [-(_370454 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 5243 ^ _176355 : [(5244 ^ _176355) ^ [] : [-(_370452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5246 ^ _176355) ^ [] : [-(_370454 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (2582 ^ _176355) ^ [_269918, _269920, _269922, _269924] : [class_Orderings_Oord(_269918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_269918), _269920), _269922)), _269922 = _269924, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_269918), _269920), _269924)))], (150 ^ _176355) ^ [_181664, _181666, _181668, _181670, _181672, _181674, _181676, _181678, _181680, _181682, _181684, _181686] : [-(c_Finite__Set_Ofolding__image__simple(_181684, _181680, _181676, _181672, _181668, _181664)), c_Finite__Set_Ofolding__image__simple(_181686, _181682, _181678, _181674, _181670, _181666), _181686 = _181684, _181682 = _181680, _181678 = _181676, _181674 = _181672, _181670 = _181668, _181666 = _181664], (1487 ^ _176355) ^ [_228807, _228809, _228811] : [_228809 = _228811, -(hBOOL(hAPP(hAPP(c_member(_228807), _228809), hAPP(c_fequal, _228811))))], (3252 ^ _176355) ^ [_292866, _292868, _292870, _292872] : [class_Groups_Oordered__cancel__ab__semigroup__add(_292866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_292866), _292868), _292870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_292866), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_292866), _292868), _292872)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_292866), _292870), _292872))))], (5311 ^ _176355) ^ [_373024, _373026] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, _373024)), _373026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _373024), _373026)))], (1908 ^ _176355) ^ [_244952, _244954] : [class_Orderings_Opreorder(_244952), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_244952, _244954), _244954)))], (6349 ^ _176355) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (1700 ^ _176355) ^ [_237122, _237124, _237126, _237128, _237130, _237132] : [-(_237122 = _237124), -(_237126 = _237128), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _237130), c_Arrow__Order__Mirabelle_OProf)), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool))), _237132), c_Arrow__Order__Mirabelle_OProf)), 1720 ^ _176355 : [(1721 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _237122), _237124)), hAPP(_237130, 1717 ^ [_237122, _237124, _237126, _237128, _237130, _237132]))))], (1723 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _237126), _237128)), hAPP(_237132, 1717 ^ [_237122, _237124, _237126, _237128, _237130, _237132])))]], 1724 ^ _176355 : [(1725 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _237126), _237128)), hAPP(_237132, 1717 ^ [_237122, _237124, _237126, _237128, _237130, _237132]))))], (1727 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _237122), _237124)), hAPP(_237130, 1717 ^ [_237122, _237124, _237126, _237128, _237130, _237132])))]], 1728 ^ _176355 : [(1729 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _237122), _237124)), hAPP(v_F, _237130))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _237126), _237128)), hAPP(v_F, _237132))))], (1735 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _237126), _237128)), hAPP(v_F, _237132))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _237122), _237124)), hAPP(v_F, _237130))))]]], (1971 ^ _176355) ^ [_247477, _247479, _247481, _247483] : [class_Orderings_Oord(_247477), 1974 ^ _176355 : [(1975 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_247479, _247477)), _247481), _247483)), 1978 ^ _176355 : [(1979 ^ _176355) ^ [] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_247479, _247477), _247481), _247483)))], (1981 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_247479, _247477), _247483), _247481))]]], (1983 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_247479, _247477)), _247481), _247483))), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_247479, _247477), _247481), _247483)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_247479, _247477), _247483), _247481)))]]], (1545 ^ _176355) ^ [_230886, _230888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _230886), _230888)), _230888 = _230886], (4470 ^ _176355) ^ [_343073, _343075] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _343073), _343075) = _343073, -(_343075 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5142 ^ _176355) ^ [_366955, _366957] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _366955), _366957))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _366957), hAPP(c_Nat_OSuc, _366955))))], (6217 ^ _176355) ^ [_410855, _410857, _410859, _410861, _410863] : [class_Orderings_Olinorder(_410855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_410855), _410857), _410859)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_410855), _410861), _410863)), 6228 ^ _176355 : [(6229 ^ _176355) ^ [] : [c_SetInterval_Oord__class_OatLeastLessThan(_410855, _410857, _410859) = c_SetInterval_Oord__class_OatLeastLessThan(_410855, _410861, _410863), 6232 ^ _176355 : [(6233 ^ _176355) ^ [] : [-(_410857 = _410861)], (6235 ^ _176355) ^ [] : [-(_410859 = _410863)]]], (6237 ^ _176355) ^ [] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_410855, _410857, _410859) = c_SetInterval_Oord__class_OatLeastLessThan(_410855, _410861, _410863)), _410857 = _410861, _410859 = _410863]]], (4888 ^ _176355) ^ [_357288, _357290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Finite__Set_Ocard(_357288, _357290))), -(c_Finite__Set_Ofinite(_357288, _357290))], (2197 ^ _176355) ^ [_257053, _257055, _257057] : [class_Orderings_Oorder(_257053), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_257053, _257055), _257057)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_257053, _257057), _257055)), -(_257055 = _257057)], (5563 ^ _176355) ^ [_382383, _382385, _382387, _382389] : [class_Rings_Ocomm__semiring__1(_382383), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_382383), _382385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_382383), _382387), _382389)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_382383), _382387), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_382383), _382385), _382389)))], (2710 ^ _176355) ^ [_274445, _274447, _274449, _274451] : [class_Groups_Ocancel__ab__semigroup__add(_274445), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_274445), _274447), _274449) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_274445), _274447), _274451), -(_274449 = _274451)], (1260 ^ _176355) ^ [_220150, _220152] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _220150), _220152))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _220152), _220150)))], (2339 ^ _176355) ^ [_261717, _261719, _261721, _261723] : [class_Orderings_Oord(_261717), 2342 ^ _176355 : [(2343 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_261719, _261717), _261721), _261723)), 2346 ^ _176355 : [(2347 ^ _176355) ^ [_261988] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_261717, hAPP(_261721, _261988)), hAPP(_261723, _261988))))]]], (2349 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_261717, hAPP(_261721, 2350 ^ [_261717, _261719, _261721, _261723])), hAPP(_261723, 2350 ^ [_261717, _261719, _261721, _261723]))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_261719, _261717), _261721), _261723)))]]], (3363 ^ _176355) ^ [_297429, _297431, _297433, _297435, _297437] : [-(_297429 = _297431), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), _297433), c_Arrow__Order__Mirabelle_OLin)), 3370 ^ _176355 : [(3403 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _297435), _297437)), c_Arrow__Order__Mirabelle_Obelow(_297433, _297429, _297431)))), -(_297435 = _297437), 3410 ^ _176355 : [(3411 ^ _176355) ^ [] : [-(_297437 = _297429)], (3413 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _297435), _297431)), _297433))]], 3414 ^ _176355 : [(3415 ^ _176355) ^ [] : [_297437 = _297429], (3417 ^ _176355) ^ [] : [3418 ^ _176355 : [(3423 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _297431), _297437)), _297433))], (3421 ^ _176355) ^ [] : [_297437 = _297431], (3419 ^ _176355) ^ [] : [-(_297435 = _297429)]], 3424 ^ _176355 : [(3425 ^ _176355) ^ [] : [_297435 = _297429], (3427 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _297435), _297437)), _297433))]]]]], (3371 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _297435), _297437)), c_Arrow__Order__Mirabelle_Obelow(_297433, _297429, _297431))), 3374 ^ _176355 : [(3383 ^ _176355) ^ [] : [-(_297437 = _297429), 3386 ^ _176355 : [(3397 ^ _176355) ^ [] : [-(_297435 = _297429), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _297435), _297437)), _297433)))], (3387 ^ _176355) ^ [] : [_297435 = _297429, -(_297437 = _297431), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _297431), _297437)), _297433)))]]], (3377 ^ _176355) ^ [] : [_297437 = _297429, -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _297435), _297431)), _297433)))], (3375 ^ _176355) ^ [] : [_297435 = _297437]]]]], (1589 ^ _176355) ^ [_232442, _232444, _232446] : [_232442 = _232446, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _232442), _232444) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _232446), _232444))], (5433 ^ _176355) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1619 ^ _176355) ^ [_233806, _233808, _233810] : [_233808 = _233810, -(hAPP(hAPP(c_COMBC(_233806, tc_fun(_233806, tc_HOL_Obool), tc_HOL_Obool), c_member(_233806)), _233808) = hAPP(hAPP(c_COMBC(_233806, tc_fun(_233806, tc_HOL_Obool), tc_HOL_Obool), c_member(_233806)), _233810))], (4436 ^ _176355) ^ [_341899, _341901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _341899), _341901)), _341901 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5487 ^ _176355) ^ [_379711] : [class_Rings_Oring__1(_379711), -(hBOOL(hAPP(hAPP(c_member(_379711), c_Groups_Ozero__class_Ozero(_379711)), c_Int_Oring__1__class_OInts(_379711))))], (3340 ^ _176355) ^ [_296409, _296411, _296413, _296415, _296417] : [c_FunDef_Oin__rel(_296409, _296411, _296413, _296415, _296417), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_296409, _296411)), hAPP(hAPP(c_Product__Type_OPair(_296409, _296411), _296415), _296417)), _296413)))], (1254 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), v_Lba____), c_Arrow__Order__Mirabelle_OLin)))], (4114 ^ _176355) ^ [_328528, _328530, _328532] : [c_Finite__Set_Ofinite(_328528, _328530), -(hBOOL(hAPP(hAPP(c_member(_328528), _328532), _328530))), -(c_Finite__Set_Ocard(_328528, c_Set_Oinsert(_328528, _328532, _328530)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), c_Finite__Set_Ocard(_328528, _328530)))], (4958 ^ _176355) ^ [_360240] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _360240))))], (5988 ^ _176355) ^ [_400731, _400733, _400735, _400737, _400739] : [hBOOL(hAPP(hAPP(c_member(_400731), _400733), _400735)), -(hBOOL(hAPP(hAPP(c_member(_400737), hAPP(_400739, _400733)), c_Set_Oimage(_400731, _400737, _400739, _400735))))], (6359 ^ _176355) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (1021 ^ _176355) ^ [_212099, _212101, _212103, _212105] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _212099), _212101)), hAPP(hAPP(c_Arrow__Order__Mirabelle_Omktop, _212103), _212105)))), -(_212099 = _212105), 1028 ^ _176355 : [(1029 ^ _176355) ^ [] : [-(_212101 = _212105)], (1031 ^ _176355) ^ [] : [-(_212099 = _212101)]], 1032 ^ _176355 : [(1033 ^ _176355) ^ [] : [_212101 = _212105], (1035 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _212099), _212101)), _212103))]]], (5908 ^ _176355) ^ [_397526, _397528, _397530] : [c_Finite__Set_Ofinite(_397526, _397528), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_397526, tc_HOL_Obool), _397528), c_Set_Oimage(_397526, _397526, _397530, _397528))), -(c_Fun_Oinj__on(_397526, _397526, _397530, _397528))], (2752 ^ _176355) ^ [_275899, _275901, _275903, _275905, _275907] : [-(_275899 = _275901), hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), tc_HOL_Obool)), _275903), c_Arrow__Order__Mirabelle_OLin)), 2759 ^ _176355 : [(2792 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _275905), _275907)), hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove, _275903), _275899), _275901)))), -(_275905 = _275907), 2799 ^ _176355 : [(2800 ^ _176355) ^ [] : [-(_275905 = _275901)], (2802 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _275899), _275907)), _275903))]], 2803 ^ _176355 : [(2804 ^ _176355) ^ [] : [_275905 = _275901], (2806 ^ _176355) ^ [] : [2807 ^ _176355 : [(2812 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _275905), _275899)), _275903))], (2810 ^ _176355) ^ [] : [_275905 = _275899], (2808 ^ _176355) ^ [] : [-(_275907 = _275901)]], 2813 ^ _176355 : [(2814 ^ _176355) ^ [] : [_275907 = _275901], (2816 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _275905), _275907)), _275903))]]]]], (2760 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _275905), _275907)), hAPP(hAPP(hAPP(c_Arrow__Order__Mirabelle_Oabove, _275903), _275899), _275901))), 2763 ^ _176355 : [(2772 ^ _176355) ^ [] : [-(_275905 = _275901), 2775 ^ _176355 : [(2786 ^ _176355) ^ [] : [-(_275907 = _275901), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _275905), _275907)), _275903)))], (2776 ^ _176355) ^ [] : [_275907 = _275901, -(_275905 = _275899), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _275905), _275899)), _275903)))]]], (2766 ^ _176355) ^ [] : [_275905 = _275901, -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), _275899), _275907)), _275903)))], (2764 ^ _176355) ^ [] : [_275905 = _275907]]]]], (4916 ^ _176355) ^ [_358377, _358379, _358381, _358383, _358385, _358387, _358389, _358391] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_358377, _358379), tc_prod(_358377, _358379))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_358377, _358379), tc_prod(_358377, _358379)), hAPP(hAPP(c_Product__Type_OPair(_358377, _358379), _358381), _358383)), hAPP(hAPP(c_Product__Type_OPair(_358377, _358379), _358385), _358387))), c_Wellfounded_Olex__prod(_358377, _358379, _358389, _358391))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_358377, _358377)), hAPP(hAPP(c_Product__Type_OPair(_358377, _358377), _358381), _358385)), _358389))), 4923 ^ _176355 : [(4924 ^ _176355) ^ [] : [-(_358381 = _358385)], (4926 ^ _176355) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_358379, _358379)), hAPP(hAPP(c_Product__Type_OPair(_358379, _358379), _358383), _358387)), _358391)))]]], (66 ^ _176355) ^ [_178728, _178730, _178732, _178734] : [-(c_Arrow__Order__Mirabelle_Odictator(_178732, _178728)), c_Arrow__Order__Mirabelle_Odictator(_178734, _178730), _178734 = _178732, _178730 = _178728], (1493 ^ _176355) ^ [_229088, _229090, _229092] : [hBOOL(hAPP(hAPP(c_member(_229088), _229090), _229092)), -(hBOOL(hAPP(_229092, _229090)))], (5429 ^ _176355) ^ [_377219] : [-(hAPP(c_Nat_OSuc, _377219) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _377219))], (5872 ^ _176355) ^ [_396206, _396208, _396210, _396212, _396214] : [c_Fun_Oinj__on(_396206, _396208, _396210, c_Orderings_Otop__class_Otop(tc_fun(_396206, tc_HOL_Obool))), 5875 ^ _176355 : [(5876 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_396208, tc_HOL_Obool), c_Set_Oimage(_396206, _396208, _396210, _396212)), c_Set_Oimage(_396206, _396208, _396210, _396214))), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_396206, tc_HOL_Obool), _396212), _396214)))], (5882 ^ _176355) ^ [] : [hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_396206, tc_HOL_Obool), _396212), _396214)), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_396208, tc_HOL_Obool), c_Set_Oimage(_396206, _396208, _396210, _396212)), c_Set_Oimage(_396206, _396208, _396210, _396214))))]]], (2169 ^ _176355) ^ [_256147, _256149, _256151] : [class_Orderings_Oorder(_256147), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_256147, _256149), _256151)), hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(_256147, _256151), _256149)), -(_256151 = _256149)], (4544 ^ _176355) ^ [_345536] : [-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _345536)))], (4366 ^ _176355) ^ [_338934, _338936, _338938] : [c_Finite__Set_Ofinite(_338934, _338936), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Finite__Set_Ocard(_338934, _338936)), c_Finite__Set_Ocard(_338934, c_Set_Oinsert(_338934, _338938, _338936)))))], (889 ^ _176355) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt)), hAPP(hAPP(c_Product__Type_OPair(tc_Arrow__Order__Mirabelle_Oalt, tc_Arrow__Order__Mirabelle_Oalt), v_a____), v_b____)), v_Lba____))], (4428 ^ _176355) ^ [_341606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _341606)), _341606 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5830 ^ _176355) ^ [_394385, _394387, _394389, _394391] : [-(c_Nat_Onat_Onat__case(_394385, _394387, _394389, hAPP(c_Nat_OSuc, _394391)) = hAPP(_394389, _394391))], (4552 ^ _176355) ^ [_345826] : [_345826 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _345826), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (1641 ^ _176355) ^ [_234765, _234767, _234769, _234771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _234765), _234767)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _234769), _234771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _234765), _234769)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _234767), _234771))))], (2534 ^ _176355) ^ [_268264, _268266, _268268] : [class_Orderings_Opreorder(_268264), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_268264), _268266), _268268)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_268264), _268268), _268266))], (5515 ^ _176355) ^ [_380682, _380684] : [class_Int_Oring__char__0(_380682), hBOOL(hAPP(hAPP(c_member(_380682), _380684), c_Int_Oring__1__class_OInts(_380682))), 5522 ^ _176355 : [(5523 ^ _176355) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_380682), _380684), _380684) = c_Groups_Ozero__class_Ozero(_380682), -(_380684 = c_Groups_Ozero__class_Ozero(_380682))], (5529 ^ _176355) ^ [] : [_380684 = c_Groups_Ozero__class_Ozero(_380682), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_380682), _380684), _380684) = c_Groups_Ozero__class_Ozero(_380682))]]]], input).
% 257.99/248.87  ncf('1',plain,[hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, 6200 ^ [c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))])), 6200 ^ [c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))]))],start(5036 ^ 0,bind([[_363165], [6200 ^ [c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))]]]))).
% 257.99/248.87  ncf('1.1',plain,[-(hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(c_Nat_OSuc, 6200 ^ [c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))])), 6200 ^ [c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))]))), 6202 : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Nat_OSuc, 6200 ^ [c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))])), c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))), 6202 : c_Finite__Set_Ofinite(tc_Nat_Onat, c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))],extension(6197 ^ 1,bind([[_410004, _410214], [c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))), hAPP(c_Nat_OSuc, 6200 ^ [c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))])]]))).
% 257.99/248.87  ncf('1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Nat_OSuc, 6200 ^ [c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))])), c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))))],extension(6045 ^ 4,bind([[_403480, _403482, _403484, _403486], [tc_Nat_Onat, c_Nat_OSuc, 6200 ^ [c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))], tc_Arrow__Order__Mirabelle_Oindi]]))).
% 257.99/248.87  ncf('1.1.2',plain,[-(c_Finite__Set_Ofinite(tc_Nat_Onat, c_Set_Oimage(tc_Arrow__Order__Mirabelle_Oindi, tc_Nat_Onat, c_Nat_OSuc, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))), c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)))],extension(5698 ^ 2,bind([[_388146, _388148, _388150, _388152], [tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool)), tc_Nat_Onat, c_Nat_OSuc]]))).
% 257.99/248.87  ncf('1.1.2.1',plain,[-(c_Finite__Set_Ofinite(tc_Arrow__Order__Mirabelle_Oindi, c_Orderings_Otop__class_Otop(tc_fun(tc_Arrow__Order__Mirabelle_Oindi, tc_HOL_Obool))))],extension(3932 ^ 3)).
% 257.99/248.87  %-----------------------------------------------------
% 257.99/248.87  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------